Die Casting

Published on March 2017 | Categories: Documents | Downloads: 111 | Comments: 0 | Views: 1709
of 185
Download PDF   Embed   Report

Comments

Content



   

  
!"#
&$ %('*),+.-0/21435+7608:9;%*<=%
>?K>YX@?Z7A:[]\ BDT ^DC7_`EGFSHJa&ILb?KNb?MPc OR> c7QPdfO e7c >g>
U
S
W
T
X
V
V
h4…Xt"iyGj km€rlj k†nok.n?j ngp;vmj jkrkPq‡gj suy~ˆ7tDvv‚kf5tutuwNwm5xon‰v"wo€,tDˆ7y`pŠz{tJvoˆox}v"w|7y~w?tuj tk†ŠwLy‹jŒn7losDx‚xoftP€,"tDtDv‚yŽml"ˆƒoj s„j€‘tDvs„kfngtm’noj tŠy kPnD“”Šij k{lDnongpr’Dy~n"j wotuw
„…Xi"t"tryG€rsŠngj k†’„k.•oj ngy–jv—‡?i‚j kJm‡gvy~n"ˆo.v‚j suftmtuw—ˆ7†v"nšw—’ŠiyWn7j kmsutŠ’k5tDk›yŽ„€i"j trk5k.wLj n?n7v˜sDxov€,nD.tDj v‚sutr{k5ˆngy~t—xoy~’suy~tt„kfsŠt"n7yWwo"t,t„wN„ion?yWv‰ngxˆ7‡?q Li‰s„hXngœŠ’žj t„kuno™ yŸnD„i"t"y
“–„noi"yŽtU€,’ˆy– jfv‚tD5yWtuk¡w:ˆowLv"n7wžs"xo’D€my–jv‚t"rv‚¡„i"sutUˆyŽy~y–t„j t„k„k—xoq †ˆ(ku¢£s„ngˆ7’Šv"•w:jvw?‡¤j k†Š’Ly‹tDjŒloyŽ€rx‚fj k5t—kj„ngi"vt0v’Dn"y‹.jŒv‚j s„ft0tuw*j wowLt"n7v‚sD.xoj su€,ˆoq¥tDv‚5n(u¢›„’Diy~j n"k;n?j wov"tutw ¢
jiv"ngsD€,q x"t—w?jŒ’"vˆ‡}‡LtŠi"™ t¦y~tŠ“‹tDy~tDv"s„t„k‰†n¦§¨i"tDy~t˜Ši"t¡k5ngxoy~sut}s„n7wot˜s„ˆ7v(lt—“–ngxov"w(ˆov"w0„i"t—n"©¡sj ˆ7q
„j…Xk›i"t"t«w?yG€rjs„k ng„j k†y–v"k.jw?loj ngjx‚v—fj ngt„j wNvk›k‡gxo“–y~v"noˆ7woy?v‚tD"5y]tDtu„yŽw—l"i"ˆ5tmn—5j€žs„tDngyŽ€¨s„’Šng•;k›’Šˆ7nD•v"“Rjvw˜ˆ}‡Xw?¢7’Lj’tDk yW„yŽn"€ry–jlojj k5wox‚ktufj twmngv˜€¨„i"vn7ˆ‚n"w?.j „jªgsui"tutt{w—j t"wo"v‚tDtD.v‚yWjk..y~t¨jj n?suˆ7y~vt„k4q"kŠ5xonDn;q“`.„jŠvii‡,j jk«kmwonglDtDv"noy–tj ng"™ tup¡wmxo§Rv"nowoyŽtDp y
qh4…Xˆot"i"vyGt*‡g€rx"ˆojˆk†x‚‡Lk.„jtngi¢¥v¬noxoyrjv"kR§Rwo‡gtDngy~y]ˆoxo„v‚q w®i"ftmtuˆow¬ˆ7’o5lD’n‰nDy~tu"s„st¬ngj ˆ‚’Šs„f•¬n?t(v"ˆow?ˆ®v"j w;.jvn?w?n"vj .k k«j„ªgy–“­sujn7loˆ‚y£x‚.f€¨j n?t{n7v*Šw?y~nDˆ7j ªg“Nvtuk„w¡€,q ˆn7"jtDw?ngyWj vªXk.jkPs„n?ˆn"v“Ÿkuj ng™ Šivjkuk›¢4l„noy~ˆon?vpk„jŒq ˆ‚v‚.5n¬j n?vˆokuv¢,nD„ˆ7i"v"t"w y
’y–jv‚5tuw;"tDyWk.j n?vku™£h4i"ˆovopm•„ngx7™

[]Z T

  


_]e @g@?@ _

fO RY S K T


  





wLngi"v"ˆ‚t¨0“–noi"y ˆ‚•„"ngt(x¬•„5ngn7xowoy˜ˆ„• €,:tD€¬’oq lˆ‡7tDyWj ˆk„iy‹j jk„’€ wXx"t„k j







¥T ?K T ^ Y ^ [”„[TWV
_Z–X[ V K Y^Š^‰KY VVYX\P¥[T K  ;[]T K\ "R! Y g^ „VXTWVV K 5OJK # 0^uT T ^(V”_TWV  KK ^V K T  K ^Ž[ ¡Z7KK"[]XZXV\ K Y$ ‰K [ V YXY\PIL[K Y  K ^‚\ KDT ]Y V ^ š[^ [;KK
VK [V ‰$K*) \ K  K—K [¥ T K K Y ^ „Y TW^‚V T ^ K [V %”TW V gK"VK  ,Y+ ;K KV Z YX–\ [.^-5K T K V Y KV_] ^&Z ­[ KY ^.^ ^ K YXV \ ” TWV \ LK"^DK _ ^0Z / Y ^‚^ T $4^ K?K \Œ Y O ^ ;7Y T ^V Y [”K ['^
(Y $ VT  \Œ
Y V "[ V K¡K7\ ^ K1$ [  KDYX\ ^ $ T K ”T K Y ^ „TWV [Z7K ‹Y „T [ VL^ $ T \Œ) V 7T ^‰TWV Ž[ 2—Y „T [ V3^ K*  \WO
# [ ›[ Z7K.74K YK } ^?TZX^ \ K ;_R.YT 
‚–KK,"^[ [  V K 7K"T K^  [”[[”TWV
}[Ž
[K5Y T ^«; ^uT^*YK  „T [ [ V Y Y^ Kš[ —Y "^ Y _`VY ^ Y ­[K&_ ŽK Z–68K K V 7 K9” YX;T YZ Y K –V:Y^{ YX^ \W_ O<[";«[ \[ $4K"Y K IV K  ^­_KY Y ?\ K T ^ - TWL V;^  Y K7VZ7K YX^VZ K T K ZV 4—\ADT ^ OO
) ^ # Y VYIK Ž [ –KT K ‰  [ ^ [  Y K ^ K.4 T K>[X$ ['
_ Y VK 0 ^ K K"[ [ VT K  ^ \ NY ­Y K ­K&Ž K>K –¨$ K YV K=— K ;Y V:Y  –KYX_\g–[ Y V \ NK Y ^ Y*Y V\  - 
^ \ T[ ^ „TWV TWV @T  K f? ^V KILKgK O V
ŽKDK[ ILY ,K^ K"I^ K 7K?TWDVZ [ ^BVA $ KgŽOT[ \Œ «_g KDV YY K .^  KU–YXK.Y \Œ”4 ^ ZX
g_?\O TWY V V Y ­?„KT TY^ [ ^ V‰K ^ KDDY[ YVL I^ K XY(V\ [K"K K V [^  ;Y TWVVY ¥ Ž2[TW‚
V 2K — [Y Y „^}T [ ^&VšKG T  ^ X ZVY–K VY^ ‰K V K VY K V YX\ $ ^ K [?T ^ ¥
¦TT KZgT ^—Z7KYV  ^[ „OD‰CFTWV V HKE  KDK K Y ^Š^u¥ ^ T YTWV V O
[ K ^uT [;V ?YXT]) ^ \ŒK?o$4\ Z7 [ KD$2[]
HZXT \Œ$¨\ K Y TWK^,V V  K*7[ ) T V ^ K¡ Z –[–[[V  Ž K Y˜^.^u?ILT T[[]^JV\ XTWVOGV Ž L#[ KDYX5K ;\ ^ [ Y „YT [K7^uV\T T^JK"IY IVK#  K7Y\ T Y{K"ITWVK¦Ž 7[ Z T ^›5–;[T ^ŽYK „^.T^u[ KT [ VV!KKYXf? ^ \^ ^ [¨$$4Y[T K 5^B
A TW[ V [( K ”TWV T K K YK ^ TWV„”TWŽ T V [K H5;  Y YK^ ^u„„TWTT []V VV
¥ T K LK ^–K Y ^T ^ „K TWYV [\ T \K  ^ O T Y S [ \šT ^ K.[4”‰ $OZ7K K V  "T K _  V YK IK&K P Y [ ^ [ V K"#–K []V \ŒYK I K Y $ K"YK ¨V K TWYV ? Ž [ \ Y K 5; K7[¤Y \ „A ZT [ [ V¡; T TW^,?5V ^ ^ [ T K Y V –K[X„T ['^ 7N
^BOMAY L _ VT Yu
K¬VT YX^R\ŒTWLQ V IL­K[]^ \K XKDV YV K ‹KDYXK \¥ON[4$ S [ [ 2^
K _
[8K"K  V S X
VV  [K $; \ OTK  {; KK}V [K _ ¥T K ?T ^ Y
^ V„TW[V ‰$ \ K $¨ Y ^HK  KY IL^ K7\\ [T  Z7KT ¤^ TWY V V ‰K [ ­$K TW­V K ^  KDYT „T K U^ YT ^ VS4$ K7 \ K?[\ X‰ HJKXI O T I” O37# T}^ V K[”IL['K
($ Y T \Œ^
K K K M$ K VU'VWVWX ­K ^ KY Z ­[*†- K ^ Y ­K= X V K  Y V [  ^ Y V¥ TWV ^ T K V „T ^ ^ + ^* Y ^Y –[. O
}…l*`:dZ\v*[[Naus*]_cyq n^0cefB~B`brzadn aBcep†fga0]2fgn ]5n ]icjzh]ih]5n cejB€c\aƒ0‚adadk*aBc‡l&qRpylR]5j.mMj.n ncon~Bcojk*fBl&sBl0lR`b]Waomzp'f0c\aBl0j0q]‡lRƒ*c2l.~gq`bv(r*n aBs*f0k.f.~daGn a*tuv&|yadadv8€.vR‚s*n ad~gfBaBsuv>q]hau]5jBvHjBlgaMlRp'f*wGaiqˆ0„zsBaB`x]`:mBl,]5n fBj0vRrMsgn aG]ypyn~u:n sBq ]5cjBk.]2l.nazfBcer,aon fzvJv*]5ad`‚jBnc\ˆ*aMn rRn f0fBfr%a\s.{0]5]yf0jBvHaGsBv*nn fB]vRc_vn ]2ƒBn ncelRcci]5fJƒB`‰„G|adcKv*lRlRf&fRqŠ „g]W|_~B€j0s*s*fB^.r.lRa*q l.hRr&]5n jBadac
vRn fzn azŽ~uf0sBs*cfB]2~gn fBn s*rHqRn]5fB`blRvJƒ*ƒBcek*]5q au`D„>c5 pyn q ~Bj0s*fBr.aMvJ`…s*w%sg]2n ~gs.q „B|K‹jBad~BmMlRƒB]y„ulRƒ*`'~dlRw^0s*fg„JŒKj0sBc%n ]k*adaBfcelRq vR<l.`‡n cn ]%k0s*f*m0`‚ƒ&^g]_l*`






 

  



 











   

 







 




 

 

 

   














 


 




 
















 

  





 

 









 














TΠT



 

  





 




 










 


 
 
 





  














 
 

 
 

 
 
 











 

  

  
 







 


 


 



   














 



 
 















 







 











 













 





 



























 













 

 







 







 







 
   



 














 



 





 

 








  

 





 



 
 







 



 
  














 




 









 

 
 















Q K*
‚K K.4”Zg[\ Y V Y,O„,T [ [VL ^ S Y –OK / V [ Y Y ^ T [”[ [   O Y ^šS T ([ –# K"[?YIK _>Y'ŽK* $K D[ KDY  ^ [®Z7[”Z7[ K ¦…ŽKQ V \ T ^ KšY O(V H ^„T ‰"[ K  \ T – KDY T  Y _ „T"[ [ V” _
$$ T \ŒK –V K[ „ T K–K# ^ KDY Y ILK V Y[ V $4
[ V5
‚[K $‰ \ K [   K YX\ŒYILK K V [  K DY K T \ ^ ;[Y . –KUK  K.O;4”ZgH \ Y V Z Y –„K T ^[ K VLV ^0"! _ K.47YK }­K Zg\ TK ^N^NV TW[V*^^ Y['„‰T ^ K(GY Y –KD[ Y ^
KK.4”DZg[ \ Y V !Y „;T [ [ VL ^0K7! \ !

V [V $‰[ $‰\ K \ K  K K TWV TWV K K ^ [XK['Y
–_ KDY ^[ $4O KIL# K >Y;ILKžY 2\
‚K&K  N^$ ['T ‰K YT ^Š ^* KK ^^ „$T [ 7V T ;Y 2
XYOILK # XV[]^ Z7Y K „T ^ [GY $ [ T K
Y [ # YILKK ^ K}YT K – KDY [TWV ;YK
‚K  .? T–^ KgO K*4 [ K 7T K ^   YX\ T Z7[ ^.^‚T \ KY V Y TWV K ­K ^ K  TWV "[ 
['[?ITK ‰_ K –VK*$ ^ TY VK  V¬T ^ K KDY „^ T [ [ VLV ^D_ ‰[ $[ –K[ g;V YY
‚;K K T V YXK \;K Y fO K RT YXY \ _ ‰\ Y [ V –KH ;Y Y K _ KK ;–Y [ „T^_«^ T +G [ KDPY ^\ K ^.Ž^[ ;V Y K*$ KY;­YK„Y T ^ ^0/[ 
Zg#g\YK Y M”^ KK TWV IL K K ­‹[–YXK Z\7^ Z7‰KKD¦[]K˜ZXTWY(V\ K \YXTWV\ŒYWKgOILO K #  `D[ K?[  \ŒZ7K—$¨ Y Y ‰V KG[ $ [ V T Y K TW?V ;TIL^ []K;\ ILI[”K T[Yšš
KTW_JV S¥T Y–K T K\XYK \ =”T [„? TWV K TWŸVV7_¥T T –
‹K YX
Z V ?\ Y T  OG#J Y¥$4K O [^u[ T  :V”\ A  _ O \[ T
‚£K Z ­[;[”[K  ^ ­Z7KKY ”T TWYXV \ŒŸ_
T$¨WVY ^ Y ^Z V T ­
‹K"Y I „Y TT [^–[K V .O8Ž['E{ O­K QP7O
mT [^ OR «Q [”K"[[
‚
gK O K"#‡_  $$4T [ \ ^ [ [ ^\ V K1[$4\ T 4
‚[ K M 2
¡ZL[Y [ V Y Y¥
LT V‰T [K $‰VL—\^uK T S [ V K K \ K YX^.\^ _ # Y YV ‰V YXO^ [\ ‰^uT Kš^^[.  NK[— Y¥T KK T YXY \ ^ „TWVTWV ?$¨T ^ Y ^ [”['K
Ž:[  K0[ K ^ Y K˜^  :Y  –K1[ []ŽQ [^\ S Z  Q  K¡ Z7[HY ^ K V ^ K"[ KY  VQ ^ [¤Z YX \Y ^  [Z7[ Ž^ [ K X^ Z7"[ [ [ V  \ –mYXO YZ 7T K YX^ (K\ ‰$ [ KT \ŒV V ILKO K V „­T K[ ‰KVL^–[7K(ILŽ[KY ­TWKUV YX\  \ ^ K[ V V K.K[ 4 –KgK O^˜K ¥TW VT „?T [ T ^˜V K TO ^ ;‰Y [ ¥^ TWV”\ _
YK d V; #ŸY Y TK \XV Y K [ ^uT K ––K^.Y ^D_ [ KND[ Y Y V "[0Y V V [ KT $ [ VTK*4XY Z7YK TZ7‰;K K}VK V Y =^ Y ?V [1K Ž-†V?[ [ T _TWV
$
‰VT „K Y TWV TWŸVUY¥_ T O}K [ ¥Z T „–A[7TWV IO ŸTWV _ ‹YX7Z T ^ ?T [”Y ['?
gT O1\ T #  _ "L [  Q Y
IKV [# $;V \ KK  V K K _




 
























 





 

















 


  
 
 


 

 
 
 








 
  

  
 

 




   


 






 
  



 



 

  
  

 

 
  

  


 
 
 



 
 
  

 
 












 



 















 



 
 





 







 





 











 











 



















 















 


  
 

  






   
  





 










 









 
  








 










 



 

 

 








 
  




  

 
   


  










 

 



 








  





v*lRfB0aM€:kdj0„Msgˆ0ceao~gn …aBlRfgƒ*]2nfBcevH]cyagn `‰]5lRj0waB`Wl0w%]5j0saBl.``‡ŽJwGaBq nv*c]ecus*| m\adcKl.`W^0`blRk*q aBw%c_n fM]5jBax~dlRwwolRfHwolRv*aBq cKl0"]5jBadc2as0`‰agsl*`‡fBlH`badceaus0`b~BjMpNsBc
[]Z T

  


_]e @g@?@ _

fO RY S K T


  





wLn?i"v"ˆt,¦“–noi"yŸˆ•u"ngtUx¬•u†n?n7xowoy˜ˆ„• €m:t"€‰’oq ˆ"l‡otDyWj ˆk„iy–j jk„’€ wXx"t„k j 




  

     






     
  
9     



–Za K H^ Kz^uY T P^ H \ O_Y&$ aŽ[ ^mH }^*zYXP\Œ¬H Z Y –^ Y Y ^m„T­^*K" YXI Zg\¬T Z7Z
8[   †–KZ7[ [ "^ K ! ^K _ ?–T [0K [ ^ MVKDY –Y []\K ^ K YX^ V7\Œ $T ILK [ K^uT ZY IL+ KN–\K T Z ^ ­KD[ Y 'XV”K TW$4V [ $45
—TW[ V 2Y
,JM$[ ” 7H T Ž[ K I T [¥\ TTY K„T K YX^ Y \ ^ ^ „Y TW^‚V [ T
^ \ –KDKDKY ILK*Y IL^ K7[\ [ V7T T^ ;/ O K V # ¦a YILH K zTWPV HŽ[ 5‰[ K V  „TWV a  H K ^ zR[ H^* Y ZgZ7[ [  K K ^ ^ K K ­­K K ^ ^ KKY Y K $4^ [ 5+
Ž[^ ,"K.K47Y Y^ }Y Zg\ K [‘_¨Y a VH  zR[ H  T ^
^ „T \Œ ^ Z7?[T ^ V^ [[”[ TW
—V \ T ^ ^›–K^ I '[ T ‰
KrQ ^ [ – K ­^ K K^ Y KY [ K V ^ ZX$ \ gV [0K Z P–[ I'K?\ [ KrT K / ­O [ V KD[ $L#^ [ ! Y V Z7[”[ –K ^ KDY $4[ 5
_L^*
Y [^ V Hr„\TWVS0 K T \Œ ^&K  ZX ­Z7'[ [ %! 7K T [NT M –K ^Y KYK V?# T I`K [ ^‚T $ _ŸT a \Œ  K "K V KM –- [  «KgMWO #xE&!!Y V ;Y V ‰[ K ^ O ž[  \ Ua H zRH
H$ ^
[ Y "
K [ V [YX$ ^ Z K7^ ^ \  [$ K K,[$Ž[]T \Œ\Œ["[ Y $ ­^ K TW
V "\[  ” K_ YXK ? \ ^ ;«„ T [ [ \ Y$ V^ KrYY Y VV V ¬KIL[;K  Y
‚K K [ D¥[ T K  JK Y [ ^ $ $ „TW–VV[ V [Z ­VY [ V \  LK ^u^.[ ^T [ V ZoV\ Y I ‹YJ?‰T [ ^¨K V "K*K[ $  ^_L
[^*V ‰ [K $ Y [^ K,ZgY T\ V XDV [ #V K AK
¥Y T Y .‰ YXK \]KZ –[_ ) Y +GK0[ JY ­\ [K^ŠY0B^ /K [  O #KQXTILK ¥V T K K Y ^ K „TWV†_  [ Z ­D[ [ ' 
„VT [ [ V$ # Y JV ["[ "V [ K  $
V [[ $
V [ [ «$ Y V "[ [ $ V ^HK $ [ ([ YX'*\ ), +.\ -/Y - 0 K L^ K K^
YX\ R [\ Y VL„^uT [ T  VK ^ [ ?T R^ K I JT }[”ZK –[7\ KIL2K  1LY ­Y I ^ T „^TWG_ V  Z Y V[*T ^r$4^*[  "KDKY ^Š^^  Y \ # [ _ $¨Y ^ IK ¤Y „T ILK TWV‘a H zPH –K ^ KDY O
a H K zUPZoH Y ^*„T ZXT ZLZ7Y[ K K* TWV*­K ^a KDH Y zRKH ^ O4[ 36 57 ),T898;K":=K ^ <>+,Y ?;V  <.+>YX@A\ ^ @B[ ).C7[”) [ X
¡? Y V V ?DY <.)F„T ILE>K G U­U [)H\ K 89? TWV X G )JK IK+L–K89^?DKDGMCY U I VB N [ V@>K +>C70

















 








 
  
  









  

 

 

 

 

  
 








  
    



 



  

 
  

 

 




 

GMC?D<.)O: V P' - XRQ






  




 

 





 
  
 




 


 

 



 


 








 

 






 












  









 




I















 













 



 

 



 

















  





 









 









 



 
 







  
















 
  





 
 
  











 
 
 




 

 







 





 

 


[]Z T

  


_]e @g@?@ _

fO RY S K T


  





wLn?i"v"ˆt,¦“–noi"yŸˆ•u"ngtUx¬•u†n?n7xowoy˜ˆ„• €m:t"€‰’oq ˆ"l‡otDyWj ˆk„iy–j jk„’€ wXx"t„k j






   

      

WTZ7S V [Y $4K V –K 0K ^ Z7šK"[ TW[V  ZgK \ K ^ K –[Y^ IKY ‰.^ LKXY ^ TO9  # #V [$ –KT +g\Œ^ # Z7[ K []VZ7TW^ V KK _ D–# [[ ¥ _ YX\ K \Œ K K V K –KDKY Y L ^ K K<*_ #][]Y
ZXV Z7[[ $ V K7K \Œ$ V TWV ^ [ [ K ^ K [$Y –K / O Y $ T \Œ[ ^ KK8:$ Y T [–K LY¡^T K ILK ^ O9KK T# 
;V{[ [ K z$4) KILVY K V _gK  T [ –[ ^ K Y $ "_ T Y #VX$ V  T[ \Œ ^ Z ‰–Y [7V[ IL K K7$ \ ^ K K+†T Y–yKV‰IL K [ # K7 \ [^K (Y V V$¨[  Y VZ ‰‹Y KY Y V„V T¦K ^ g^ Y Z7Y [ –^K YY YV^ #]K YQ  [V V¬$ \ T^ ^ ­[[ \ VT ¡ ^ T Y^ VT KY V
‚„K T^0) /K _NZ Y –TWK KV V T TZX\ K K ^DO_
^ [  Y \ KD []Y ZX\ K K7Z YILK*YX\ ­^ K [ *^  *^ \ ^ Y K V ^  K  K7\ŒZ Y K # ”TK K \ T Y ŽK ^ „TWTWVVL(^* TW–VY V L^ K(Y UVZ"–! [ [ ^ Z7K 5[”O [  \ Y&$ "K K Y ^ KS :[Z d
Z7K[ V Y K V ^ K}^ [Y –KNILKK  ^ K LT^ [ L# ^ YY ILVK} .K ‰4”Z7KD[Y ^V K  O^‚# TW V ^K '[ ^.^ ‰ K ?K TWV Y – K"[”K K ^^ [YXZX^ KZ7ILK K V ‹YX[\ TWV‰”K T I _ T  K YXV \ ^ "Y[ ­”K _ TWV K-†K"[­KZLY Y  K  _
^'[ ^  \ D O Z XV7T  ^ [ TWV UK ^  [ _ "[ *^  Z Zg­Z7K"[IK „V TWV *^ K T K V  –K0[ Y V ; Y K V?V T ”Z TW V \ K"Y K „TWVTWV Y KV  TWVZ –L[ ^ ‰[ ¦„TWY V V KY TWV7”TWT VK Y Y :^ ¥„TWT V„T [ V TWVDYXd \
$4KDYX\ [ O K ^ Y
‚K¦[ H =GY  T \ _ # YILK _«TWV GY "_ Y
uK V [  Y¤\ T ŽK TWV&^  ‹Y V K:Z7[]\ T O #  ^ [ ‰K 7TWV
 [XK ^ YXZXZ7K V [S‰K _ Zg\ KY ^ K ^ K V Y Y V
"[  Y V $4[ 5
H$4K?\Π [ V K Y  [S TGY T \ O




 



 



 

 

  
  
  

 

 







 



     

  

   


 
  




 

 
















 















 










 







       
   


 

   


   
   
 
 


 



 
 
 




 

 
 

 
 

  


 

   
 


   
 


 







 













I TŒ





 

  
  
 
   
      


    






 









 


 





 








[]Z T

  


_]e @g@?@ _

fO RY S K T


  





wLngi"v"ˆ‚t,U“­noi"y ˆ•u"n?tUx¬•u5n?n7xowoy¡ˆ„• €,:tD€¬’oq lLˆ‡7t"y~j ˆkŠiy–j jkŠ’€ wXx"tŠk j j




       



  


Y ^ ?
‚T K ^ Ÿ_ [”Y ['^
$4^K7\ŒYXY ^ K    Y K ^ ^ „Y T [ ^VLK^ T K ^ Y [‰#"$¨Y Y „^ T \ K  ^ T [ [‘L^ Y Y VL^ $4[ K  [ ^ K7\ .^ O Z7K T?) T \ K} Y :K  ^ ­„K T ^.[ ^‚VLTW^V Y K ^ #K  Y ILK K ^ „T [ KDVLK ^DV _
#PK ­KYXY \ T ^ KK¬ [ Y K T; } Y Z7V [ Y [V TK¬;[[  V \ K ^ K K7\ –K ^&A  \ ^ _ L# ^gA YILY K [ K T  ¥K T K d [=Y ^ ;„TWVY
‚K $4K ­KK  ^ YTIoK Y V T „\ YT ) \ KYX\Œ [ TWV K,[ $ ­KT  K O
$¨^ Z['Y ­TVKY   X[S[V7 T‚
K"K??Z[T ^— TW¥V K ŽT K[T zd 2— ; Y Y^ [ „„V TWT V[[]VZ7O[]K \ šV P¥[7TWK VILKDK Y K L ^^? KšO
V [[;{ ‰$ [$4\?K TK ^DIL_ K K # ¦A _ TWYV IKK ­K K K T ¥^ T T K YKd  Z7Y [^ $4„TWY KV *…  TWV\ K L–^[ K ^ ¦Z$¨Y[VY  TWV”[[T I ¥Z T T'–^.K^ ILKYXK \ ^V TWV$ Y [KK
?[”T [^}
TWV T Ž^ [  5;šY Y „T [ KV*N T ^ Z [9[:$ Z T KUY ?T ^‰[XTWV['Ž
g[ O 5; Y Y \ KD„YT [ ^ V¥K _ Y KUV Y  ‰ I [T ^ ­K K  _TWV Y[ V KšQ VZg\ Y \ T ^ Kg(O T ^  =$4KY
*Z7[ TWV O ?T ^




  

 





 

 

 




 









 

   





















  
 





 













 



  

  



  












 
  


 








 

 

 











 



 










 
 


 
   

 















 




  





 









]5jBaM`b€ai‚s*q auaBw sB`baBceafBq lR~dlR`bauaumgc_sBn fBvTs*r>fBwov1…l*„Mwo`~u„Gˆ0l.lR~d`xqblRƒ&adwzfgc\]^*w%adlRaBfBaB` v*fgxc]a0c††fB~dlR]aHlHfp†^0^ `bn l&]5jl07 `b|"au[sBv,‡]5‹j.[Sn coadk.vRlRn ]lRl*m ` s*ƒ*q "`…s*q lgp'aB`†s.f0v R]aiˆ0a v*ˆ0s0`‰v*„g|G[†q celh^*q agsgc2a8`‰agsgv










 

T4







[]Z T

  


_]e @g@?@ _

fO RY S K T


  





wLngi"v"ˆ‚t,U“­noi"y ˆ•u"n?tUx¬•u5n?n7xowoy¡ˆ„• €,:tD€¬’oq lLˆ‡7t"y~j ˆkŠiy–j jkŠ’€ wXx"tŠk




  




TWV?”TT ^ –K \XY DZO žK K T _^3 KK ¥$ T Y [K \ K  [ K Z7¥KDT K []ZX\Y K9^ „$ TWV [ TWV'YIK^ IL[]_`\ ^XV [ KD K \  –K  K [ YT }V
*Z  –[7\ILK [ ?T ^ K ^ K [XTW['V
¥T I¥TT ­K  YX\ \^ Ž[[
Z –[K T # K ^Š"^,[ [ V K $¨^uT TY] V V „O T [ V[ ^ [ [:V K V T  Y V K K [ ?KT ^  $4 YX[ \ 5T
˜UY [V  7[ T ^ Y[”IL[K
U"[ Y  V V Y‰K K¦
VZ [TW$;V \ KK  KšK [­K  _ Zg\K KY ”^ T K K [ Y V ^ „YTWV
‰ KXO
 
1«1¨+

:V <AC :V +>C7898 V C
X )L-/GMC.) C U
oV EB)L' ?  )7' N GMC
 +H'*0  '*+>C  G/- )H0
:V 02'*+>C>-M5BC X




 






 
 
 
  



 





 








 

  




 





 





 

 


).C>G 89) )LG  )7'

4T















 





 



 

 
 


 





 

 










[]Z T

  


_]e @g@?@ _

fO RY S K T


  





wLn?i"v"ˆtmU“–noi"yŸˆ‚•„"ngt(x¬•„5ngn7xowoy¡ˆ„• €,tD€¬’oq lˆ‡7tDyWj ˆk„iy‹j jk„’€ wXx"t„k j






  

 

 

  

Y ?^ T„^ TWV [”K [V
¥TWT ^TV KD”K T I  T  K K ‘^ TWK V [ [ V—$4T ^y[® ZLK Y”T ^ Y O K  K<[ ¥) T K ^ d (Y ”^ T „^ TWV L^.^ ^K Z7^ K T )K ^ Y ^uT KT V ^ KgOT K V K K ”–K T K d 7T Y –K^ „ TWV m:^ Z7Y K ”TT )K
T ^zK¥ T I ? T  [K T0‰TWV [ V[ \ ^ AKILK K7‹YX\ T K\ ILK  YXZ ‰K [  ^ K?Om\ ^ Q¥gY ^ K „T [ YXV‰Z e K ”T ^ T ^zL¥^.T ^I K T  ^ K $ 0TWV [ ?T ^ ‰–K"[K  ^ K?K \ T„^ T [ $ VL–^R[ I£V ^ K [ „T [ gV V –> KDY  ^ K [ ^ V Y T \K K ^ 
K*Y `P VK—‘[ K ^ ^ K –[ „[ ^;T [ ^ TWVV [žZ $ –^K$I [T [ $ YL ^ ^ K.‰ 4 [ KT ^  K7K [ \ ^ –$ K K*?Ž"T[ _ –K[ — ^ YT KK u
KV K K _ K? $¨ YY ‰TWV KIoAYX[ \ T  [ [_ ”Y VT K  K Y [ ^ YX„\? TWVZ  ­\[?YOI„KT# [ A VLY^ ILO K¡K # Io YX[ \YVT ”IK KT }7;[T ^Y   ^ K[ T K^ V­K[Y Kg$ O
Y# VK  [TWZ7$ V K Ž T [ \Œ 5; Y YY"IL„_«K T [TWV V Y [TWV  KK  ^ Y K ILVYX[ \ T V¥  T [$ K ¥TWV T „T K¡[ V¥KK _«^ ¥ V Y T [ K V \ TK¦^Y ^ [„;  TWV K V7T ^ ['–KD$ TY T \Œ X V7K [ T V TDK"O O K Y  K\ KY ^ ^‚K TWV ­KK Y  ^ Y T K V[  K $  T \Œ Y KUY \ K K7[ Z K K 



 













 

 















 

















 

   
   
 

  







 
 

 

4 TΠT

















 





 






















 

 

 



















 

  







 











 

 





 


 
    

 



  





 






 



 

 










[]Z T

  


_]e @g@?@ _

fO RY S K T


  





wLngi"v"ˆ‚tmU“–noi"yˆ•u"n?tUx‰•u†n?n7xowoy¡ˆ„• €,tD€¬’oq lLˆ"‡otDyWj ˆk„iy–j jŒk„’€ wXx"t„k j 






  



    

$4Y [ ^ „ TWV Z –[ K [ K^ V ^Š;^ Y–[ K ^Š^ ^ # 'Y # V^m ^T $ [ VK \T[ —Y K [V V XY V?–[]T T\ YXK\ V K [ V Z  K Y V \ T  Y[ „TYX[ \ VT TWK V T ^¬  ^ YX[K \ T \ [¥ —$;T K [#  Y# ^ K„K7TWV \ XTKZ7ILKTWK V^ K L „K^ TWV–K T [^ Y ›–Y K ZoYXL[ Z7^uVgK TWVV ^rK TWV„Z7T [”[”[ VT K O
HrKDY \Œ^ K [ ;  Yg^ -5K*[ _Y V— Y Y‹Y TVWV ^ KŽK ^ [+ŽI T Y K K K # ^ V T K K V V „K T )g/ Y$4V[ Ÿ†\_ =‰L[ ^uTW–VK T } Q Z7 [ [ YoV L  \ Q_  _ K $ Y KL#^ K PT K Z Y ­[ ^ 'K  T mK T^ ^ IL?KT
Ž [  YX"\L T [ TWV   ^4 [K?\  Y ^‰KILK\ KT V K ^ ‹YO ‹Ya K V H ^ zY P„KTHT [ 4$ V¦[ [ T†^1\V  „ TW V–\[DKO  [KNZ [ –[ ' ZLKY „T [K.4 V Y [ VV  Y*[ \ [V $ –[] \¥ [YX \ T SU(T $4–[ [ ^  [ Z –[ !MPK ^ŠO ^ ž[ fK O>Lo[X[]['Z7K
[:[”[ \ T  K [ ‹YV K K ^0¬/ ^&K ZXa Z7H [ z„TWRV H Z ­‹[ Y V‹^ YY  „^ T [ Y V –K  ­['–K"K(^&Y  V YYUILZ7Y [XT \ [Y \  K¦ KYXIL\ TK 1$4$ [  K –ZK0–[[ V K ^Š^ [ K<fO4$ K Q O Y V K –YXK \Œ'T ^š+ V [K
[–KD>Y L^ [ V(Q  V [ a [ H  z[ PT H¬O O Y \ KY ^ KM†- [ TWV ‰ K TWVUT } Z –[7I TWV ¤a H zP H Q ^8 ‹Y V^ Y „T [ V ^& ZXZ7[ „TWV K L^ K


   


 
 
 

 


 


 




 

 








 





 





 














  

 
 


 




 



 
   

   
 
 

   



 
  



 

 
 








 








4LI







 

 
  
  
 










 
















 



















 





 



 






















  

[]Z T

  


_]e @g@?@ _

fO RY S K T


  





wLngi"v"ˆ‚tmU“–noi"yˆ•u"n?tUx‰•u†n?n7xowoy¡ˆ„• €,tD€¬’oq lLˆ"‡otDyWj ˆk„iy–j jŒk„’€ wXx"t„k j







  O



YYXZXT KYZ d TW­VL[XY^ Y ^ „¥[TWV _ $ K K ?V T TW”VTW'V LK"K^ Y ^ ^ T K ^¦K"YKIL^*VK Y [ V Y ^ TW[V^}ZgK7\ YZ7Zo^KY „‹T KY ^DV _\ K [ Y VZLY[ V \ [[}$ Z7T [ ^uKžT [ KK V —¥K TWY V KD¥K K T K T dYXQ ^ \ ^Y O^ [”„[TW›V \ ^D\ KD_;Y T†[^\ }_TWV ZoY V V?K K"T KK A ^D _ \ [Y : 
:KYYXTW\ V ^uA[
–K7K ZX­\ Y K?ZgK \ Y K š$Y T ^ @T K ?5V ^ „T )T K V YXK ZXZ –[”[gK Y ^ $4O¬[ 5Q:
4 A O£LHr^ K \Œ^ K Y gV []?5^\ [ ”T K T KV ^K  K"IY K?^¡\ []V Z7[ K UY TWVV ­K V KK ILV K yD$ KDTY \Œ:^ $4Y [ –5K
A* K V ^ KDK T K [
TWZ V Y ^uT \ YXK\«Y \ &Y_ $ ^uT ^ }Y ZX­\ K K^ ;Y[ VX$ V V K O TW V [ ,7K*T 4o^ YN[XZg['\
gK O;_ Hr\ŒK ? K¦[KT;–[ [ ^ VA [ Z687Kš[¥\  T Y ;‹[Y2K7\ I^ T [Y \VY  K ^ KN;YI VT []ž\ Y Z„T [ V^‚^ T [YX \
¥\ &Y T $Y ^D ‹_]Y*^  K  ”Z T –K [Y ^ Y  ^ „K KTWV^ ) ­K ^K V V”gY TW^ VV (K"K ^ Y KQ ^ [-†Y [ V–K¦ T \^ Y&K˜$ [^[ZgZ[Z7– [ [ '^uT K K—5K ‰[;[  RY­K4 YXVT \YT   _ T $ ^ Z O?–T [)  Y^ ­ŽK K [ 5 ‰K [^ –K K T _ ['K }*K ZoTWVY ? V [D?OM T ^ # ‰V [ [X[ V['A
gK O Z68[ 7
YXV? T K KIL^ K Y V?”T ^TWV Y T  _ K*K KU[ K V V [” TWV T K"^K ,[ ^ 1K  ¥K T K ^uT VY ^ „7TWT V @  K  ^‚YXT ]\ T V Y Z V– [ 'Z  ­[ ^ K ^.Y ^ Y Y –K( K TWV?^Š^ T K V  „ T YX\WO [ ^ O K ^ K*:Y L­^DK _
Y ­K K¦^ YX\T ^ [ K ¦TWV TWV –[ ;'Y  K K  ;O Y  „[ T YXTWJ\ VLŽ^ [ 5Y  V ŽK [ _ [ $,K ) @[ ^  „TTW‰V7T K TWT V K ?T ^ K IL^ []\ ‹ YX‰Z Kg! O [ S ^ Y V K V &K $[ [ K V K7XZ VgV ^ K Y V^ 0^ T  KK Y ^ _
Y V $ K Y ¥mT K^‚Td K¡Y ^ [„ TWV ¥0T K TWV 'Y ^ ^„TWV T ;8^ YgV 7 TWK V K [ T ^ TWV YXZgYZ –[]–KZ IL[]T Y \  KH„T [ Ž[ V¥«_ YY V ^  Z7K 7T T ) ^ [”Z ­[ [*
-†K T ^ ZLO Y [  T 4O ! V K ­KY ^ [ V
+ TY ^ [ K V K TWV –KDY ^ K[ V $4[ Y†\ 9V/  Y K V^  T M K K7\ ¦K Y ^‚–T .K  Y [„TTW[ V V / Y [ V }
Zo Y Z V7‰T K T ^¡^ *^  Y Y ^ K J [”[ K V \ K[ 21
[ V ­[I $ T ^ + [$ K ?[ T YXK \ ^ H\ Y”T KK
YY ­V [  gV ­K  K L^uTWV K T }Z K ­[ 'K  g„V T [][ \V [ ”T [K ^^ Z^ O–K ^ # K *V T ^ K * TWV ?[T Z7^ K [X'[ Y
g3MO #”T K K7d \ T YK"I^ K K ^ ?T $^‰TT ^\Œ . K¡Vž[ V &^ \  T$¨Y ^uT . [ Y „
‚T [K"K7VLZ ^
K ¥T K Y ^ „TWV Z –[ŽK ^.^uT [ V YX\ ^ Y V K TWVL^ T ^ K7\  _  –[ K TWV ? \ K* ¬TWV K 'L^ O A











 
 











 
 
















 

 



 

 
 
 
     


 






 
 




  
 
 
 

 

  

 





 
 


 
 

 
 



 
 
 

   

   





    




 
 
 




 

 
  
 
 





 



 









 












 

 




 



 



 

 
  
 












  
 





 





 


4LI TŒ





 

 



   


 













 



 



 

 










  

















 








 



 


  


 

 

 









 



 







 









 

 



  

 







 








 
 




 











 

 













 



[]Z T

  


_]e @g@?@ _

fO RY S K T


  





wLngi"v"ˆ‚t,0“­noi"y ˆ‚•u"n?t(x¬•„5ngn7xowoy˜ˆ„• €,:tD€¬’oq lLˆ‡7t"y~j ˆkŠiy–j jkŠ’€ wXx"tŠk j j




 







>g>gO~O e> VWX J5.K IK^‚K T?9]TG }VV KC Z7"[ ! Y VV  K K—^‚T[] V K–K  'M TW‹VYXZ ! Z P­[[ '^  O¡„TO˜[ VO˜O¡[ O˜^ O¡^ O˜O—O—O˜O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O—O—O˜O˜O¡O¡O˜O˜O˜O˜OO
>g>gOO c L; TWT V ^
[ TWV T YX\ KRY Y –
[ ­[ g„VT [  V O˜PO˜[ ^ O—O˜[ O¡O˜K O¡Y O˜–O˜[ O¡ O˜O¡JO˜K O—^‚T ]O˜V O˜O¡O¡O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O—O—O˜O˜O¡O¡O˜O˜O˜O˜OO
>g>gOO b a? # V ;K K ‹T YX\YXA\]MS T [   K7\ Y\ ^ „T [ O˜VLO¡^ O˜O˜O˜O˜O—O—O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O—O—O˜O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O—O—O˜O˜O¡O¡O˜O˜O˜O˜OO
>gO A R[ V \ L^uT [ V O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O˜O¡O˜O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O
ee O~O +Le>8 G I # V  - –5>Y[ ‰G X  T ^ „†T ),[ 7I,VT  <>#¤+>O¡C>M O˜G I$KDO¡8 Y O˜^O¡O˜–KDYO˜^ŠO—^ O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O—O—O˜O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O—O—O˜O˜O¡O¡O˜O˜O˜O˜OO
e O e O~> KK 22‰‰[[  VV YY TT ^^ Y VO— O˜‰O¡K O˜O¡Y O˜V7T O˜^ O¡O˜[ V O¡K?O˜Z O—^ O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O—O—O˜O˜O¡O¡O˜O˜O˜O˜OO
ee OO ee OO e RQ [V KV ­[*\ Q J [] \ Y „‰T [ K V _ O˜O I¥O—OO˜O¡O¡O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O—O—O˜O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O—O—O˜O˜O¡O¡O˜O˜O˜O˜OO
ee OO ee OO cb RS [ [}‰Z K ­V K .^.^uT2\ K Q  [ $Y [ O—V O˜O¡O¡O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O—O—O˜O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O—O—O˜O˜O¡O¡O˜O˜O˜O˜OO
 G N )7C.8 G V C>+7-  C>+.- 0H8 G 8
 O~
> # V –[  „T [ V O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O˜O¡O˜O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O
 O e K¦Z –[ K ^Š^ K ^‰TWV ¥T K Y ^ „TWV O˜O¡O˜O¡O˜O˜O¡O˜O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O
 O e O~> ¥T \Œ TWV K ^ [ ,^ \ K"KILK O¡O˜O¡O˜O˜O¡O˜O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O
 O e O e M [ m^ \ KDKILK O¡O˜O˜O—O˜O¡O˜O¡O˜O˜O¡O˜O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O
 O e O  E XVgV K ^ ^ K2O˜O˜O—O˜O¡O˜O¡O˜O˜O¡O˜O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O
 O e O c T K YI T #O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O˜O¡O˜O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O
 O e O b # V K V^‚T ) Y „T [ V Z7K T [  Y V  JY  K O¡O˜O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O
4 T4





 







  



  

 
 





 

 



 







 























 



  















 







 

cb




 

 
 
 
 

 
















 






  C.?D'







g>> e>



>> c
>> cc
>b
>>
>



ee @>
eege>
e?e c
eA

CONTENTS

M Z7K T YX\ [Z T ^ O¡O˜O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O
O~> # ^ K  [$ TWV ”T K Y ^ „TWV (T ^ .  \ K V # O˜O¡O˜O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O
H ”T „T [ V YX\ V [ K—[ VUV: ‰K T YX\ ^uT   \ Y „T [ V O¡O˜O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O
 O  O e T ^.^‚T ZLY „T [ V K*P`K [ V K KNZ7K ‹Y . –K T ^ K O˜O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O
 O  O  ‹YI T š&K P K ^ O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O
 O c Q ^ „T —Y K ^ [  K „T ‰K ^ YX\ K ^¬TWV ¥T K Y ^ „TWV O˜O—O˜O¡O˜O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O
 O c O~> „T \ T LTWV 0^ K  "T ¥T ‰K V^‚T [ V YX\gY V YX\ ^uT ^ Ž[ Y ‹Y K T ^ „T „T ‰K O˜O—O˜O¡O˜O¡O˜O
SUT \Œ K Q ^ YXZXZ ­[XY O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O
Y
­K ^ K V YXZgZ –[gY O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O
 O c O e K –Y „T [ ^ [ «ILY T [ ^ „T ‰K ^ YX\ K ^ O¡O˜O—O˜O¡O˜O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O
 O b M T  T \ Y T NYXZXZg\ T K  [ T K YI T O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O
 O b O~> «[7ILK V?TWV K   Y „T [ VL^ O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O
 O b O e JK ^‚T ]V [ r:Q 4”Z7K T ‰K V ^ O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O
 O  M  T;Y š[  ¥T ‰K V^‚T [ V \ K ^.^;V   K ^ O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O
 O A M  T;Y (O¡O˜O˜O¡O˜O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O
 O  6  K ^ „T [ VL^ O˜O˜O¡O˜O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O
 5BC X + N )7C.?9+7- 8 V   G @B)  - V :
c O~> # V –[  „T [ V O˜O¡O˜O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O
c O e V?T ILK ^ YX\ T }[  K¦\ [ ^Š^ [”K T K V ^ O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O
c O  H ^uT }ZX\ K  [ $ TWV Y ^ ‹Y T [ V ?T O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O
c O  O~> :Q 47Y }Zg\ K ^ [  K YX\  \ Y „T [ V^ O˜O˜O¡O˜O—O˜O¡O˜O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O
c O c XZ T YX"\ R[ }Z7[ V K V ^¬TWV 3K E XVgV K £Y V  {K V M ^ K  ^ O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O
c O c O~> K V  O˜O¡O˜O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O
c O c O e  [ VgV K „T [ V O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O
c O c O  :Q 4”ZLY VL^uT [ V ! P[ V ‹Y „T [ V O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O
c O b Y_ „TWV *T YX\Œ [ [ K K O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O
c O b O~> M”K T K ^ P[ VgV K „T [ V O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O
c O b O e Y Y –YX\Œ K?"\ R[ VXV K „T [ V O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O
 - V : GMC @B)7C 2<>+>CAC7)7- 8
b O~> # V –[  „T [ V O˜O¡O˜O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O
b O e XZ T YX\ ¥T Y ‹Y  ^ O˜O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O
b O  ;  ‹Y  \ T 1  NZ O˜O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O
 O

 O

e
e



 








 








 

@



@





 









 








7c


A
A

c@
c@
cge
cge











 
 



 



cA

cA
c
b@
b>
b>
b?e
b?e
b?e
b?e
b
b?b
b
b







 





   
 

 













 





 






















  
  






 

 



5BCAC.)L'  ,) 8 G U C

O~>



 

 

   

>














 





  

 









>







>




























#V O~>g–O~[ >  R„YT [ V
&$¨O˜Y O¡ O˜JO¡K ^‚O˜T ]O—V O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O—O—O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O˜O˜O—O—O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜OO ]]>>
O~>gO e R [ VXV K „TWV XVgV K ^ K '‰K V ^ O˜O˜O¡O˜O—O˜O¡O˜O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O  e
O~>gO  E K ^‚T ^ Y V KO¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O  
 












 









[]Z T

  


_]e @g@?@ _

fO RY S K T


  





wLngi"v"ˆ‚t,0“­noi"y ˆ‚•u"n?t(x¬•„5ngn7xowoy˜ˆ„• €,:tD€¬’oq lLˆ‡7t"y~j ˆkŠiy–j jkŠ’€ wXx"tŠk




@  G + U '*+ N +7-/I,5>- +L?DG V C.8

CONTENTS

AAO~O e># V –[K ?  ['„TT [ ‰V [ O¡VA O˜ZO¡68O˜7 O¡”O˜T Y O˜–O—YO˜ O¡O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O—O—O˜O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O—O—O˜O˜O¡O¡O˜O˜O˜O˜OO
AO  AO  K—O~> ILYX\ T # ¥^ T NK [ ? [K ‰? [ [V A ‰;[ [ V A K7¥\gT ILY YX\ ‹T Y# O¡O¡O˜O˜O¡O¡O˜O˜O—O—O˜O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O—O—O˜O˜O¡O¡O˜O˜O˜O˜OO
AO  O e HY \–gK V K K £Y ––K KDVY g!^ ”T –YKD;Y ^ K [ VK YPIo\ YK # T Y „O˜T [ O˜V O¡O˜O˜O¡O¡O˜O˜O—O—O˜O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O—O—O˜O˜O¡O¡O˜O˜O˜O˜OO
{Y K}Y ­KY˜IoY T Y „T [ V O˜O¡O˜O¡O˜O˜O¡O˜O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O
 O  ›Y T Y „T [ VL^ [  K {Y K˜Y ­KY _ O¡O˜O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O

A
O
AO c AO c K O~> ­&K Ž[ 2;K K  –*K ŽZ [ 65
7 ;”T [Y  K7–Y \— O—O˜O¡O¡O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O—O—O˜O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O—O—O˜O˜O¡O¡O˜O˜O˜O˜OO
AO c O e Q:47YK  TWY V?TWK˜V Y ­KYNK &K ^ P []K \  „T^ [ V O¡O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O—O—O˜O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O—O—O˜O˜O¡O¡O˜O˜O˜O˜OO
«Y K\ gVK V K ¥–KYXT K £\ Y [Y–KD^V Y„TW!\V ”^‚T YT [;;VLY ^K ?K –TWR[ V &KK P K.K 47Y Y ^–}Y O˜ZX\O¡K K}O˜TA^ „OO¡c T OO˜e K*O—P`KO˜O˜O˜O˜^ O¡O¡O˜O˜O˜O¡O¡O¡O˜O˜O˜O¡O¡O¡O˜O˜O˜O˜O˜O˜O¡O¡O¡O˜O˜O˜O—O—O—O˜O˜O˜O¡O¡O¡O˜O˜O˜O˜O˜O˜OOO
S ­Y K ?[ TWVV ¥K T „^‚T [T V K¡K**K P`P`K K +e$¨O˜YO¡IK O˜ŽO¡[ 5O˜;O˜Y „O¡T [ O˜V/ O¡O˜O˜O—O—O˜O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O—O—O˜O˜O¡O¡O˜O˜O˜O˜OO
Y
AAOO cc OO c Y [”‹Y [ V^‚T K K V ^‚T ]&K V P *KK P`K ^ O˜^ O—O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O—O—O˜O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O—O—O˜O˜O¡O¡O˜O˜O˜O˜OO
AAOO b JK ^‚3K T ]# VVKY VL­^u[ T ) K ^.Y ^ „TO˜[ VO¡RO˜[ O¡VLO˜^uT  O˜K O—‹Y O˜„T [O¡V O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O—O—O˜O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O—O—O˜O˜O¡O¡O˜O˜O˜O˜OO
AAOO A M6   TK ^ ;„T Y[ VL(^ O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O˜O˜O—O—O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O—O—O˜O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O—O—O˜O˜O¡O¡O˜O˜O˜O˜OO








 





AA cc

 


 





 

 

   
  
 
 



 









 



AA



 









  
 



>


>
b


 











 




 





 


 





??cc
??cc
gb



























AA 
gAA A


























 



 













2'PG ?DG IK+.-
- V :  M- 5BC U )7' )L- V IHG ? 0




V



„
T
V

#
–
[
[
¡
O
˜
O
¡
O
˜
O
¡
O
˜
O
˜
O
—
O
˜
O
¡
O
˜
O
¡
O
˜
O
˜
O
¡
O
˜
O
¡
O
˜
O
—
O
˜
O
˜
O
¡
O
˜
O
¡
O
˜
O
¡
O
˜
O
˜
O
¡
O
˜
O
—
O
˜
O
¡
O
˜
O
˜
O
O

O e K ? [T‰[ VA ‰[  K7\ ^ O˜O—O˜O¡O˜O¡O˜O˜O¡O˜O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O 
O e O~> {Y K Q ^ ‰[  K7\O˜O—O˜O¡O˜O¡O˜O˜O¡O˜O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O 
O e O e –KI T
Q ^}S [  K7\¦O˜O—O˜O¡O˜O¡O˜O˜O¡O˜O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O‘>D@>
K ^   Y –K ^ [ ,^ \ K"K"IK O˜O¡O˜O˜O¡O˜O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O‘>D@>
O e O  –KI T
Q ^ T  \ Y %‰[  K?\JO˜O¡O˜O˜O¡O˜O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O‘>D@ e
O e O c SUT \Œ K Q ^r^   Y –K<‰ [  K?\O¡O˜O¡O˜O˜O¡O˜O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O‘>D@ e
O  K—ILYX\ T ¥ T N[ K ? [ ‰ [ VA ‰ [  K7\ ^ O¡O˜O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O‘>D@ 
O  O~> {Y K Q ^ ‰[  K7\O˜O—O˜O¡O˜O¡O˜O˜O¡O˜O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O‘>D@ 
O  O e –KI T
Q ^ ‰ [  K7\ ^ O˜O—O˜O¡O˜O¡O˜O˜O¡O˜O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O‘>D@ 
^   Y –K<‰  [  K?\ O˜Q ^ O˜O—O˜ O¡O˜O¡O˜O˜O¡O˜O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O‘>D@ 
#…}Z –[7ILK {Y K ‰[ K7\žO¡O˜O˜O¡O˜O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O‘>D@
O  O  SUT \Œ K Q ^ ‰ [  K7\0O˜O˜O—O˜O¡O˜O¡O˜O˜O¡O˜O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O‘>D@ 
cO  OO c K=OO~c> E K*Ž Q [ 5‰K K –Q ¤^K*Ž ‰[ S 5[ ‰[   K K?K? \N\ + ; V:O˜[ ‰O˜K7KO—\TO˜O˜YXO¡O¡\NO˜O˜‰ O¡O¡[ O˜O˜K?O˜O˜\ / O¡O¡O˜O˜O˜O¡O¡O¡O˜O˜O˜O—O—O—O˜O˜O˜O˜O˜O˜O¡O¡O¡O˜O˜O˜O¡O¡O¡O˜O˜O˜O¡O¡O¡O˜O˜O˜O˜O˜O˜O¡O¡O¡O˜O˜O˜O—O—O—O˜O˜O˜O¡O¡O¡O˜O˜O˜O˜O˜O˜O‘O‘O‘>D>D>D@@@ ccc
O c O e JK ^uT ]V Z ­[ K ^.^ O˜O˜O—O˜O¡O˜O¡O˜O˜O¡O˜O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O‘>D@ 
O b M  T; Y (O˜O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O˜O¡O˜O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O‘>D@gA
O  6  K ^ „T [ VL^ O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O˜O¡O˜O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O‘>D@gA
O~>





 








 


 


 


 







































 



4J4 T wLngi"v"ˆ‚tmU“–noi"yˆ•u"n?tUx‰•u†n?n7xowoy¡ˆ„• €,tD€¬’oq lLˆ"‡otDyWj ˆk„iy–j jŒkf’¤t wXx"t„k








[]Z T

   


_¥e @?@g@ _

fO RY S K T


 

 




2).C7?DGMC V U H0  89? „) T N V  )H8 G U C
O~> # –[ [ O˜O¡O˜O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O®>D@

CONTENTS





O e O e K ~O > ? [Q¥TY ‰ \ [ V+ KA ‰O / [  ‰K?[\ ^  K7O˜\ O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O—O—O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O˜O˜O—O—O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O®O®>?>?>>@@
O e O e SUT \Œ K Q ^ ‰[  K7\UO—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O®>?>g>
O «K V K ‹YX\ T ^ L^.^‚T [ V O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O®>?> e
OO cb E K ^&K¡ H\ ^ V YXY \ V^uT ^ O˜T ^ O¡LO˜^.^‚O¡T [ O˜V O—O˜O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O—O—O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O˜O˜O—O—O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O®O®>?>?>> b
OO A M6   TK ^ ;„T Y[ VL(^ O¡O˜O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O—O—O˜O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O—O—O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O˜O˜O—O—O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O®O®>?>?>>
 











 













 





-/+ N @>G C U V *' I$) +7-/I,5>- +L?DG V C.8



























  
 





 


H¬H¬OWO e><.+L? ME K*ŽT<7K )"­;KDK¦Y !R89š>=? +>[+e MEA­['-/E G 8 K&< ŽKN –Y K")7VK0C. ?$Z7#$ [ 8 ^‚T &T „TI,[ K G )7VLVU^C.V ?9O˜[G 89O¡? K 8 ^BO˜/ &O¡+KO˜O˜0 O˜O˜O¡O¡O˜O˜O—O—O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O˜O˜O—O—O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O®O®>> e?egcb
H¬H¬OO c EE K*K*ŽŽKK ­­KDKDKK e O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O—O—O˜O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O—O—O˜O˜O¡O¡O˜O˜O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O˜O˜O—O—O˜O˜O¡O¡O˜O˜O¡O¡O˜O˜O®O®>> ee 



 






  












0  L) -/+,?DG V C78 <>G @: G ? <  G ) 4+L89?DGMC U !R89?9+>E>-/G 8 < N ).C7?
 
 )7C.8 G ?P0I,<.+>C U ) )&% ),I$? 8

 OW+>> CBC # VV – [ - V : T [ V O˜O˜O¡O˜O¡O˜O—O˜O˜O¡O˜O¡O˜O¡O˜O˜O¡O˜O—O˜O¡O˜O˜O¡O˜O¡O˜O¡O˜O˜O—O˜O¡O˜O¡O˜O®> b 

 )  )7' )7C>I$)

 













 

!





[]Z T

  


_]e @g@?@ _

fO RY S K T


  





wLn?i"v"ˆt,U“–noi"y ˆ‚•„"ngt(x¬•„5ngn7xowoy¡ˆ„• €,:tD€¬’oq ˆ"l‡otDyWj ˆk„iy–j jk„’€ wXx"t„k j




 





  

>
















   &

# V[ V YK ‰ –KKUY3K V ŽK&$"K/ Y Y ^ V; Y ;V Y V ” (T K [ Y ^ K „TWV ”T K [}Y ^ Zo„YTWV V7T K ^ ['}YILZLK Y V?T[ K V^ K YYILVK
K"KZ V(+ ^ J[][X\  K +†M\ K O.1LY Y Y ­I  T \^ SY VK  YXM \ –K7YJ\  "_
;[”Y []V \ Y Y K ­[‰'K  V O ^D!_ ! S K ^ K \ Y‰O / K O Y  Y ¦^ T ^0[! ‰Y K–K ^ +e$ K ?­T KY¡^ T[ ^ V‰!L^ [ ^ Ž[ \ ?K¬T ^}Y ^u T .['Y‰„[T [ ?V T #\ K TWM¥V'[‰^ K / \ YO ‰Y K¤K Z7YX[”Z[ ^
KKS–K  TT ^}^.^‚^WT V ['‰K
V ?[TW$‰V \ K  [ Kš[K ^ K [$ \ Y T [ ^ O YX\ a  K\ ILY K K K?\K3K ^Š$ ^ [ K V V K Z ­Y [V) ^ ^ K"K Y –KY;Y  K(K Y gVV  K †[\ $ TWV [ – KDK Y ^‚^ T[ ]VV*^š^ T [ ^
TY ^¦­KY V [ Z –[[ K"^ I K ^ V WT$ V [ T \ŒV O K S K[[  N–K"TWZLV?[7YTIL VK T _£K T [mO Y Y [ [N YKZL‰Y V [ Y VLV ^ T ^ ‹YY YX\ K \ K \ Y [[ž$ K Z –[ K¦KU Y Y KU^&. Y YX:\«^ Z7Z^uK T .T  T KU) Y „[T [ rZ VU–Y [ VT ^  Z "K­_{[ G'V Y [ [ V K Y Y TWV K KY ­K
['K }–K ZoY T ^ V UY \ [”[[ }
^ ZoY Y V 1$ K 7­T K  K  ^u[”T ]K V ^,^&+u‰ []\  H [ ›?Z TWV­[ _ K ^.^0K¡/¬Y TWV  [ [  †K $ T [\Œ ­K K<‰ [ K –K K K V [ ^ ,\ Y ^  ^ [*K;\ KY Y „T V YXY \Œ D[ O> # 
TO
 [XYX\# ^DV _ Y [ ^  K¦Z7K [ K ^ŠV ^u¥T[ TWV \ KTKD[K + NMe @ Z7 K L^K[ $ \ cKT Y@ V [ / [Y VK  [ TWVX\ KVV YK  L^ „T ‰‰T K K[^\_ ^uST  V7KK T )^u”T ]TY KV V \[Y ^ „+ TWV KU®> TW[!7V^e L[ [^ _¬‰Z [ –[ N–K /57 O 89? „T [N[ –K V Y '+ ?T KKY ILK [ K ^  K Y^ [K^
^–K 'TK K  V  K K ^ ! K?T[^ \ ‰T ­K?K TWZgV / \ YY Y K VTWV  K [ 'K L ^ KK \^.Y ^ 4$
˜K [ Y 5[ g
O ­[K  , ?K ^T ^^‚T T]K V[XV „O['T
)  [ T ^ Z ZLTWY V K1)T ZL[YX^ \ ^¬„TWT VK;ILK[]–K_\ ILILY*K[]( \ \  TWV„TWV T
[ V*K KTWV$4” ”K"T K KT K V Y Y^ „^ K TW„V TWV [ ^Z –[ =Y V$K  ^Š?^ T [K
[]K\  ^uT ; VU[ T ^¬K7^\ ^Z7_ K7$ \Œ K 7 T [  ZgO\ Y 'S  Y K V V K*$ K [ ¥ V T K K7Z Y ^D^ „_ TWV žY ^ KTWV [L ^V¦^ T ŽK [ V „T ;) Y V Z TWV  K T ZXY \ K  ^K _ ^DY_ ­Y K ­K(TWV Y –V [ YX\  K K   _ O K T K
K –[ ^ Y ­K¡K*4XZX\ Y TWV K  Y V K¡[]\  ;[  K7\ ^ Y ­K ^& Z7K ^ K  K  O
Z;{–K K ^‚?T  M [”K K V T^:K V V [[ K¡ MT ^ zK?4\ [”T KQ[ ILŸ_ K _ –K : YK ;V T —\ žT K^˜Y –KVVg[ V T [^ X  H V ^ K*K­K? & \\ Y TWTW„VV T [ YVL^ K ?‰ T  ZK"[XK „[ TWK{V &[$4› KDTWV[K V ¨?5ZXK®^ \ Y \ T [ VK V YXD\KA A «Y YXK"VZ[  K $ TK.+ E Y>KD K /  K_[  a[”KTK H Ž ^ [ z5$ R‰ T H¬K O
KTWV ¦K [ Y ”  T 7KK T K"IY K [ ^ ^ „TWTWVV [X[­K;  Y Y ^ K Y 7^ TW„V TWKKgV Og^ {;Y O K Kš ^[ ILY K7T  \ TW[ VL^ T Y Y V _ ZgK K\ _ XV Y K L K ^ ^ K Y¥T KYK ‰ [XK K K ^¡Y ¡V V [TWVK"K Žg[]^ K\Œ [[ $ [ V a IK HK  V zK„TP [ –H KDV YYX^–\ K K – K [OST[;{T; K ; K V^ K Y  VT Y  „Y T [„T V[ Y ^V _
 



 





 
  
 











 





 

 



 














 





 



 








  





 





















 

 

 












 

 




 
  

 






 

 
  










 










  




 





    
 



 































 










 

  



 













 








 
 





 



 
 





 








 







  




 









 
 
   



 
    
      
 

  
  













 









  









 

 



 








  



 
 


  









 




 




  

  







 


 



  
  






 

















 


  


  
 




 















 
 



  

  
 
   


 
 
  

 

   
 



  






 
   
    
  



 



WT­VK K [ ['Y T^Y ‰K TWV?K TWVVK  Y „[”T [”K[ ^[VL^;V [ ^‚TWY V Ž^ []„K TW\ŒV [?$ ^ K O (?;«IT ^K T [­T K\^ Y ['K T T;‰Y K Y V VV  Y „$ Y T ^‚[ ­T[ V¥V _ ^ Y O1VT K ";{V ! „K [ T ) T ^ [ Z T K TWV ¡^D_ T V Zg[ \ K Y ^ ,OO[=T ^ ! Ž[]V \ŒK K [$^ –KDY[ ^  [ K \  V K.[ 4”K V Z7IL^&K K  V „T K"[ K V ?Y YX^ \
‰7[ T ^‰ K?^ \ ^ [ I  T \[] \ Y Y „TWV.‰YX^ \Œ T K ^V „–T K) V Z TWKV V T ZX\ K K ^ T$4 [KDY  \  Z Y ­m[ ^' T K KV XK V –KDY YX^ \ T ^Io„YXT \ T ¥–TK ^&DO \  ^ O K  GY K V¬^* Y ‰­K [ ^* K?\ \ ^^ [ $ ?T _
YX[ ZgVZ7I KTWY V TWK V ?T [” [_
Y^ V [  [ Y ,KY ­^DK¨_ I T [Y \ Y 4„^TWV rT K ^V T K K V  „[”T ) K ^ Z YTWILV K¬T IoZLYXYX\\ T^ ¥Y T VD O S K5O>–K*E Ž[ K"–K K 0 T [ ^ V T [ $4[ + TW2V
^ K [  Y \TW V Y ‹Y .V  YXK \Œ^B/
[ TWV ­K;KY Y ^ K [?IK;K K.¥47T YY }‰ZgK \ K K T ^ TWV  [  [ K V K‰[[ %TWV—Y –KDV Y˜^ [K %;K [  K7Y \ ^ K—ILK7Y \ [ Y T –K‰NK Y ^ ‹Y $ V T \Œ Y VK (TW[7VšILV K K"–KK * [TWV   [ YX­KZ „K T «[ AV OO
[ [ ­ K Y ;K TW_ V0T K¡^ Y [ V [ \ L^uT [Y ^;VL^DV _ [ –K ŽV[ gX^DV _ šY ^ V [ !  [ «Y ^.&^ Y  ^ NY Z ^‚„TWT [V V^\ K O ? [K  $ ‰–[ [ V V \ A‰[ ^  K K? \ ^0‰! ;[  K K7\ [ gY ^ YY ^ KDYKIVK
ZgYX\ Y \ '  \ K Y  „T [ VK ^_gTWVc / L^ XVg;V K Y ­K ^ I ^ > / K  T „ T K ^uYXT \]^ V¥\ [_X$!:b / ZXI\ KgVV mK ^ ¥^IK?K \ [ T  K _7^uTe:/ V”Z_ 68K 7 C”O T Y –KY^  K _ TW:V / [ ZX\­gK V K ;[¥T YK7‰\ ^ K Y K­K
Z [  K ^ †Z7^–[ KD^YY K;^V [ *[VL£TW^ V Y VL–^ KDY $4Y K^ K ?5TW^ V ZT K –V[ K K  A    K [” ^ K „^¡TYX[ \ VVLT [^ DO [$4 [ K2
g^‚TO ] V}TWV<K Y ‰^[  T KK7V\ ^ „T Z) –K ^ ;K VY VXK V *K NTWV $ 7?T T ^ $ [”T [ \Œ
˜­K Y ^*–K \ mK TWV ­K –K Ž[' K K
‰gV [   !K K?†V\\ ^ TWK VŽ[ –KTKD}Y ­^Z K[ ­Y [?V ^ I [ TWZ7VLV KD^ []ZX @[ \ K* YX$ Y \ T –K _ TW?fV –^ K 'T K K V TW”V K T A@K \”KDYTY  ^  „VTWV„[ T ‰:K‘$4L[ Y^u2TWV
*V  K Y ^Š^š––KK 'T ^  \ KD[TWY V —_ [ Y Z V
u­[KSK '^; [ [ „V T [ K \ DV O \ KD[! Y ^ V V K O Y K ^ K [ [ ;–LKY ^ TWVK
^K7\ T T  K V TWV KY K—[šKD.K Y 47Y  [TW V K $ K Y [ TWKV ­[KY}^ Z7KN[ Z V ­K[V) ^ Y [7›T \ T Z D–[O '  K „T [XVV K [  ^ \ B!oTWV ^ ‹ZYXZ—†YZ7–[ K;^ K—Y V [  7[ T $ ^ [”[ [
TWTV7T  [ T K‰K7[ \ŒZ
K ¥T K Y ^ K [UY ?T KILK 7T ^ Y K O

Chapter 1. Introduction









 





 







 









 








 



 

 









 




 









 

 









  
  






  

 

 




 





 

  







 


























 

  


 



     



  
 

 
   



  



   

  

   



   

 


 
 

 
   
 

 
 
 

  




  
 




 



  




   
  






 



 

  

 









 
 




   








 


  
 

 


  



     






 





  















 


 

 

  













 "!#$ &%'
((!)* +,-./0/

P['[”[ }K V ^:Zg‹\YV T [ Y K [0–Y Z7 VL[]X^ VZ \ Y  „\ KYT [ VTWV O K?[ \ T K*[  _^ K.Y ^­KY‰ K®K „Z7T [­K K?V \ Y [K„R TV [ YHVLY ^Ž K*?K:$ T Z[Z7 K TWV K K–V KDY Y ^ ^ K"K K¡K TWZ7”V [ T TWZ V –[–^K}) [>g^ O~O>,$ K}Z K K ­–[ K˜TW'V Z  –[–„KD) TY [ ^ ^V K Y T–[^ K˜^ BYZgL! \ [^ ‰–[ YXK ­ZK
[]^Y ^Z7–K YXYS–Z˜Y  „YX T [ VV V0 ^„TT m[ Y VT­^ K [–VK* ŽK K \ –KK K  ^ K  ‹[NYXO Z”Y ^O‘H2K K ;\ TWŠ? V YRTWKDV 4 YILT K ^   X‰ V K „V\ [ T [ ^.VS^ [ [ ^ uK A ^ O ! T^ V K$ ^ K K‰V K [ YX­\ŒK?K \ Y „KST [ Y VL—V^  Y?T;ZK YRT$ 4YXT \  K.V V K Z K ­[^[ ) K  ^ [ [V[  Y  K
$ Y ^ K V [ YX\ŒK.4 T ^ ˜K^ — ['‰Y K*K $ T YXK\ ­K K [K ‰ $4K KD^ K VZ –[ K  ^ K ^ $4+ V[¤[ K*^4 ‹–KYX;ZUK [^ ,O Y V SXZ
T TWVYX\Œ / O _ Ž [ K K –KD”YT
‚K KILK Y V ^ „Z7TWV [ ‘TWV TWV+ 4L^ Q YW/ _
Z –[K ) ^‰–KDTWYV ‚
KILK K V ¥ Z7T K [ TWV Y ^ „\ TWT KV ^($ TWVT '?L TW^ V šYK –K}–Y Y V [ Kš [m e  @ b :O 7”A b Z –[ ' G+ [ egb d gb ^ –YXZ / O XZ T YX\
–K7\ Y „T ILK Y V K TWV Z –[) ^ 2143 V [K*\ $ Z Z ––[ [ '  Z7Z7K K K K V V 665 5 44Q Q Y Y 5 B87:9‘B<;;
.+ >gO~> /
    
  


 




 



 

 
 









 












 

 





 











 





 
 





 



 







 



=?>A@CB,DAEGF   





















 



 





  









 



















 


 
   





 





 







 


 









 












 




 



  





 



 











 





 
 

 
 
 
 
 









d~ l*`‚b}ZIadHy€ ~dN]jBn ]yazn fMk*s*aBs*ƒgq ]5fglgjB„pLl*s0`K `bp'MOauszNlRƒ*l0q]5"v1jB]5aGqj0n m\aMs*aoƒg^0]5]`‰jBl>lRl*~dŽ`adfBc2p'cov8lRJ*woƒ*q agq lRv,sBv*`xa\f>aB{&q n^*s*fBadk.r ~ilR]†eƒBƒ&]y]5fBj0aiv*a%ˆBaBa0lu`bf>cpK]efBs*s*aBfBk.`vJlRnƒg]fBlM]Kr szd~d|lRc5fBn c5fBnrRv*q aBaM`w%]ll&v*n fga0ˆ0qad^Bce`b]yadc2n fGaBfg]5]5jBq „8aGƒ0c]celRad~BvHmGn fza\{0]5~0jBj0azs*fBn f0r.vJa*ƒB|0c]5H†`‰„MjBa0]5`‰j0azsgn]_cyn sc
]5^.jBl.adc2c2c5azn k.v&n q sdn ]‚„B„Gcg]| l,wGs*m\aGwol*`‰a%^0`‰l0ŽJ]c†]5j.n c‡pNsi„B| a0`‚j.s.^0cW]5j.n cKn cN]5j0aG`bausBc2lRf%]5j.su]Wcelw%s*fg„%vRn a_~gsgce]2n fBr>~dlRw^0s*f.n auc‡c2lRq vn f






[]Z T

  


_]e @g@?@ _

fO RY S K T


  





wLn?i"v"ˆt,U“–noi"yŸˆ‚•u"ngtUx¬•u†ngn7xowoy—ˆ„• €m:t"€‰’oq ˆ"l‡otDyWj ˆk„iy–j jk„’€ wXx"t„k




P

Section 1.2. Designed/Undesigned Scrap/Cost

profits

breakeven
point

%

}

20

invesment
cost

{

0

0

78

~65-75

}

23

no
scrap

100

80

maximum
profits

%

scrap

0

%

”T ' –KU>gO~> Io K¦Z –[) ^ Y ^ Y( XV „T [ V [ K¡Y;[ XV [ K ^ –YXZ
100













 



 



 
 
   ! #"$%&"(')  +*,)- . /0)123'4
5 6 %"(+78%9
:;<1=.>. /?"@ A-;BCD/? 4

90E
F1=GH@IKJ(+31 L %NMON/GP
QR E9S TVU R>W

3YX[ ; 55 CCZZ 5 OB 7:9®B8; ;1 B Z4\ ]^
X

H+

1  %,. /_13'4
5 6 %N>"(+78 G $.4`,/a-C`,/b 4

90H;"
 =#"c121("(
% ')H<dO4e f /_1gh74! #"e

TWV   ?T ¥^r_ T ^  Y¡ ILK ?T &^  KL^›Z Y –V [„) T YX^\ O”T P`K –K V KXO K –K*Ž[ –K—Y=


  
 

  




€

‚







 7T K –K ' „T [ VšTWV}^ –YXZ $ T \Œ ­K ^* \

  











 /* I%( Gƒ„#  /* I%(# †…" 
ƒ3‡ /0

^^ –[ YXK  –Z \K! Y [ –K ^K@& I —K*>) Y / V V K  [  Y ^ K*^K ) YXV?\ŒT „Y T [ VLK1Y^ ‰V [K  KrYX^ \K?–\ TYX Z¥Y TWoO V ¥Y T ¦K ŸKV _ [ Y VK .^˜ 3e:VD / d K&[ )  V7[ T ^ „K T[ [ V:K¬Y ^&7YNT Z Y K –V[ [ V [ \ O K KH¥K T TWK–V7KT  Y Y –T^K „K TWV$4O [< TW
VTW'VKg) ^ ^ [^ 
TWV:T ^ –K*ŽK –K  [ K ­KNY ^ K XV K ^‚T ]V K 0^ ‹YXZ _ Y V K ^ K [ VT ^ ­K&ŽK ­K  Y ^8 K ^‚T ]V K 0^ ‹YXZ”O
 Y ‰T ^ K ¥T P`K –K V K # # ‰T ^, K ^uT –K V [ [ YILK ­Kd-†K „T [ V [›Y V (ZoY + K ­Kd-†K „T [ V}^ [  \  K
TY=}K $¨­Z7[ Y[ / ^.^uY T V \Y K _ [ [  K K7[\ T  [ ^TW^ V K Y $ T }K T \ŒT ^šKVKS[  gVXTW V?VK T K^u T T V K ['K  }O ZgY \ VK ?K7T ^˜\ ?T_ ^T ^NY  VT ^ žTWV?TT ¡ K TT ^ XY V„K T [ ^uK TV ^‚‹TY ][V \ KK [ [@^ ^  –Y YXVTWZ V7 ! T  [ ?T ^ T K^NO TT ^;{^—[^u$4TK KK ILKK TWVU^u_«T ]^*T V˜K T  ^
b wLn?i"v"ˆt,¦“–noi"yŸˆ•u"ngtUx¬•u†n?n7xowoy¡ˆ„• €,:tD€¬’oq lLˆ"‡otDyWj ˆk„iy–j jŒkf’¤t wXx"t„k
[]Z T _¥e @?@g@ _ fO RY S K T











 


 
  


 

    
 
 








  



     


 















 


 





 





 
 









 









 


















 



 

 





 




 











   




 

 































 

 


 

 





i j+p q=k9} rul=i ix ~m#q(nok9lop p juqVm#roi y s= jtluivi w9x yzk9jtx {ui
|

^[ –YXK Z ! [ [ ^ K}O Y \ KK ”[ T K  K Y ^K „5TW V TWV KK1V $ ”TWV Y K"rK o^  [  ^ \  ¥TK ^ „ TWV [ V ?K˜T ^ Y V K $ $4K"Y K V Y VXKV ^ [ K $4K [  ^ [ V ‹YXKgZO [NZ7[ V K V ^rTWV
^[ \ [ $ K M ZXT K\[XV V  K KWT V?¨TY  ILV K7T \;[ K YT
‚K‰¤K¦Y Y Y V^‚T ¨T ]Z7V?[ T ) –K [ –^uY K T V DoO ¥K7 T P\ T 7 K T ­^ TWK V V;Y „KDK TWYV  VLŽ^[ + ŸYXK*\D4o‰Y Y[ NY^ gTZgm/ \ K Z7Y _¥[ T T–,[ K T ^u^ V T Z7‹[Y $ ^.TWV^‚T T‰\Œ \K K V K š[ ­KTWV YX \ KK  \ Y ^ Y K V[ ˜^K—\ KDY KILT”„K TWT V TWYXYXV \\
$¨Z –Y [ ' _  $4[ K ^ ¥X+GTKVP`IL K K K –V^‚K T V]Z7V X[ K .K[ ¦47JY^Z }–[–ZXYX\ Z K  ^ T ^ [^¬K? TW\ TV} K ^ ^uTW['VT ‰Y V KKK * OY ^ ^ K ‹7^BYX/T Z ^ !Y –[K [ Z ^ T [ YV $ ILVTK@\Œ ^gK .V* ”TWK VT ^uK T  [ V  K [”([ ^ K ‹ YX TWZ VYX! \ T [ 0^ YXZ Z –[ KY'IL K Q,Q^ O KDOMK # V V Z 7–K T ^d
$^ K T KšV\Œ _ ILK Y K V O „TW V K K ^ ^ ­YK ‰^ T K^ K „YXT \ ‰^  [ K K _^uT –KKV 'O<Z7 [ # ^ŠK ^uT ?Y T VK \ T KgYV^u T K \ Y ^uT Y¤VK K Zo^UY ‹[^ Y$ ‰–YXV K Z ! K oY [ $ ^ ?O,T K H –KV –KTK*^ '4oYY NK Zg^ T \„K}T [YXK  \  ^* K K ^u^uT T]V VY:K :ZoYK7^ ‹\ [Y‹$ ‰YXZK $ ! K?[T ^ T ^
Y:T?T! \ g^(Y ^› T Z0^ K*Y 4 V Y –K ^ ^*K  \ ^—KDY WT V^‚T \ YY Z7V[X [ Y Y[7^IL„KzTWV $ 7+.T \ Y Y KNT YT ^ ;[ –YXXZXV Z7K [ OzZ7# V[ –[ ^‚K‰T \ Y /  K O­O Y ^ K K}_ Y V KmYX\ Y T^‚T !^ [Y  ^ Z –K˜K ^ŠIL^*K  V ­K
^ T^ „T KYX \   K K^u‰T [ V V^ T K?–Y \ ”TWK V ^ Y Y ^ YXY \D; [K ^‚^ T ]V K  ^  Y‰K Y –K [7^&IL K \ ^_ K ^ —YXT „\ŒT LYYX‰\  [ K g^‚V T ]V [RY Y VTSK  V K ^u–T YTWV V ‰- K ^ V YO ! [7VILKK Y VK
YK‰^u[ T XV V Z7K¬[ I^.^‚K T V \ KX- OL^ a [Y $ [?I[ K K Y KT „T ^ YX\ Y IKK ^‚T ]KDV‰K V^ [ Y ?K T KILKK ‡^‚T I]V‰\ K ^.^ ^ ‹–YXKiZ-5K ! „[ T [^ ¨V^ T ^ + ­XK V  K ^‚K T ] V K [N˜Y ^  ‹YXTWV?Z T /  Y  V 
\ K ^Š^ ILK V r^ ^ K 
IL[]\  ‰3K +  K ^‚T ]V K ¦^ –YXZ / O

Chapter 1. Introduction





 











 
 





 
 



 







 



 



 

 













 



 
 


















 





 

  

 











 



 














 




 





 
 


 


 

























 

 

 



 







 



 

 


 



 






   

 



 





 














 





  
 
 
      



 































  


 







  

 










 







 
 

 













 

 










  









 

 
 







 





 

  








 









  &%  # ("!#  +, ‡ /02   ((!#  ‚  /* I%"


# UK T ^N^ Y [ gVK  Y [ [ g K V „TWLV ^ ['Z ‰–Y K f„O T K V Ž[ [ „.T XK V Y KK?\ _ [ ^ K¤[‰Z –K"Y IK „T K Y ^ [ Z7K Y [T ^˜}^&Z  –[ ' „Y T [ V K[ Z T K K*[[^ [K
ZV [–[ '[  V ^ Y K0–K Y  .K  YXK \ 5  K TWV^uTK  V Y V^ [Z‰­K<[ '
 TWV„ T [ [V {Y[ILK^ ‹^Y O K  Y ^ K K  2;[ V[ ­K _ Kš7ZoT Y ^˜T  $4KYK T T ^ YX\ ZX^ [ž\ ^ Z7K †K"Z7[K ;. K Y NK  Y V
T­^ K K ^ Y K Y K IR[ Z KY T ^ KTWV  $ –[ K[ ^&Z   \ [T^ K¦V  –[Y [ [ Y^*¥IL KTWV Y Y˜V [Z –Y K K0„^uTT Y KgV O.G # Y V YX\ [ [ K(^uY +ŠT Q Q V^ \ d‚ZS Y –VYK  „YXZT \ Y&­K[ $ _ 'T­K_ ILKL „VTbT [ YJV Y VK [  ^ S0^ OK—T \ŒZ# K—–†[.T> -5^ K JAK7\/T T ^ KO IL) K ;{V7 T K ^ –K K YŸT _
V [[V[^ K V  K  K YXV \ K  ^ \ Y [K ^ ^* K¦Y Y®.Z  ‹YXY \ „T [ K^ Y [–‰K Z –\ [KDY I „T T [ V”­K _ ^*\ K \ ^0YX\ TW[ VV K V [ YXZ \ L ^ \ Y „Ž TW[ V K KUK Y .  K YX^‚\RT ]Z V¥­_ [) Y V^  O $ T K
TV\ ^¦TW[V
TWV T TW V KD Y–K$ K ?T$ K ?^‚TT -†][ V L^ [[ ; \Y
‚K KKDY [Z ^‚^–T [\ ) G+ K ^ VK(? Y K?d VZ\ T  T $ TWKV ?/ Y TO K  O [ M”K"V I[ K –O YX\  YXZ K 5K ‰^¦[ –TWKV _ ?[ T ^ V^‚T  [”K [–(
Y Y \ ­K<K )  V K Y ” V T YT YX\K  [ ^ [




  
  

 



 



  
 

   
 


 







 






 




 













 





 











 

 
 

 









  
  




 





 




 

 



 
 



 












  

 





   






 







 

 


 

 



 











   


















  







  







 









 








 







+/0  + 
&$%(,!




^Y K"V TIK K ––YXKDY YX\”^ \¥Io„TWYZ V T ^Y T ^ \ K [­^ K?$¨[\ YY V „KT IK? Y\ [ V TWV ^ [ Z7KDY[”Y
TW[ TWV V Y–K Y‰^ KDK IY ”K Tb S O>Ž[ ;{ ”K YXTV I \ TWT KV _ YXZ Y\Œ –^ [ „TWV KK ^Š;^DO _,Yg -†TW[ V[ P$ Y 7?T Io^T Y –VKDY YJK ^  ^[ K V TWV „TWVK K –
‚K K gVTWV Y ^¡K V$^ [ T Y V¥KDTWKV VK
[S  Y V ˜K [ ¥ T K K}Y Z7^ KD„TW[]V ZX\ K Z TW–VN[ T }K ^.Z7^ [ $4K Y –V K VZ7[ [ N^uT „^ T Z7[ [ VVL^^ TW[ V –K  K ¥žT K Y V Y ^ „[TW V ¦¥TTWK VLY ^ ^ „TWV &^* TWP VK^ „†T . ­['K ^0! $ Y ^Š^ Y [ mT T ^ Y „
T [V [V$^ O
Y ^ K ? JK –[ T Y „T . K A $ ?T ¦T ^ ILK ¥T  \ [ Y V KXO ?








 

 
 






 













  



















 
 













  


 










 





 



 



 



 













 





  
  
 
  
 

 


   


 









 KH)')I51*<G  L %N') "V

yjBaMw%aus*f.n fBr>l0"]5jBaz~B`‚n ]2n ~gs.qv*adc5n rRf>s*fBvs*k.l0ˆ0aGs*fBv1k*aBq lgp9~0`…n ]2n ~us*qv*adc5n rRfzp†n q k*a%vRn ce~BƒBc2ceadv n fM‹j0s*^g]aB`

H



[]Z T

  


_]e @g@?@ _

fO RY S K T


  





wLn?i"v"ˆt,U“–noi"yŸˆ‚•u"ngtUx¬•u†ngn7xowoy—ˆ„• €m:t"€‰’oq ˆ"l‡otDyWj ˆk„iy–j jk„’€ wXx"t„k






Y[  ^ „TWV :K T ^ T YK ‰A KS O SYXK \Œ[YX –\ŒK"” [?T I”YXK T \†YX_ ;\›Y Q K V:V  ”G[TWY V V K".K – []^ \ŒTWV TW[ V HZ # Z7V–[KL^ K ^ [ ^ŠVX^ T V YXY K7\4V\gQ [ V V ¥TWK V ­KDK K&K Ž–[ K^ ­^OK KDY  K ­ K KX^ 5VKD‰gY ^[ ­K K7_ \ T YK"7^IT K^ [ [Y ‰K K:YY K ^U”T VK T [K
^$4* [ †VZ  T K ^ K T  K Y ­K Z7T ^ K"[Y Zg–\ K7K \ Y TW„V T [ V^ Y7T Z K‰[K  $4K"K K V—­K^ [^ K;Y Y V ¡ XK V–”[ TWVV K"[  Lg^ V; [  KK7T\ ^£[$ $ ?VT ­K ^ KYYILK OKDK ! V V Z K –[ 'Y VXV K [ 
YZ V–[  ­K ^.K‘^ [Z7K ^ [ K VgVXK7V\  K [ ^ V Y –V[]¥\Œ TWTWV V (T ^, K K ^ –K ^ TKDY K  K  g­K VTW”V TWO V O H ?T \ T [ K;Yg-5[ —Z7[ TWV ^ [ K
KILK V 4^ ^ K  K ^uT ]V ­K  ?T –K‰K V ^ $4K –K ^ .”T K  ^ ['‰K –K ^ KDY K ^_ Ž[ `K.47Y}ZX\ K;M  L^D_
JK TWV?T
_ Y V ‹YXZ7K ,Y V [ K ^ O K ^ K‰[  K?\ ^D_ [$4KILK _ Y –K gV –KDYX\ T ^ „T Y V [ V [ Z –[7I T  K0Y
–Z7KD[ YXTW\V T ^"„_ T Z K}T Y .T  –K¬[ [ } Z ­K K ^.^u–KDT ?YXT \\ T –DK O 7`T K–K"‰_ K V K *^ [Z –Ÿ[7[ I  T  K}K˜Y Z K ”^uTWT VXYXV7\TWV ^u*T . TWV Y „‰T [ [?V‰I ^‚TWVTWV K K K ”T K T V Y [ ^ –„K TWV KTZ –;[ YgK-†[^Š^
[$¨Y Vg^ K TWV Y ^ ­KYX\ ^ ^ T K V KXO
$[4?Y9T !  K*TWV?–TKD[  Y  K ^ K I[”K?K \[ [  –K T Y ^ 7[ „TWTWV V g^ ^ K  K7Y \Z7Y K Y V
¥^‚TTWY ]V V?T ) [[  V Y  V K ^uKT ]YXV Y \ŒV [$¨‘YK ^ Z TWV–[]Z7Y K KU„T\ KT  K^ 7–KT  K T TW^‰V KY YX‹YY\ ^V [K K*$ O [Zo Y Y K:K K(VK.4 IL[ T K7^ \ [ K  V T ^ K O
JK TWV?T
+ {K TWV7T
?>  :e / \ TWV
‚K  K Y K¦IK?\ [ T [ K  [ $ ZoY K V + Y '[  T Y „T [ V / Y V  Z ­[?I T  KUY
  YX\ T Y „T ILKZ ^uT YX\P*K 4XZX\ Y V Y „T [ V Ž[ ?T ^ [  ­K V KgO®:Q 4XZ7K T ;K V YX‡\ $4[ 5
+ S Y T K 5> A c /;^ [ $4K 
[‰XK YY ^ [K(\ T  ZL7Y T [ „T ^‰.\ ,K K-5YXK \"^D_  _ Y[ \ V$T
u KTWYVL[ V^uT  Y KK ˜[  \ T  K T ?K T ? Y^I Zo_ T Y [„TŽ$ [ \ rK TWV*K-†K4oY O N–!K"ZgK\ K ;_ K +Y PTW–V K[ ^ ZoKYY IoY K;K KV^JT^ I YX \W„Y O~T > \ T?[c K V „/ TWO V TK H [ $¨^Y Z – K K [›^ $K Y V V "-5YXK_ \"[ _ YK
+d TWV7T    / –K  ?T ­K  Y KrILK7\ [ T T ^›^* ZgZ7[ K  ‰K.4”Z7K T ‰K V YX\oKI T  K V K,$ 7T ¡T ^ –K7\ Y K  [ K
 [ $
ZLY K VL^ HO ;{[ $4KILK _ K V  ;K T YX\XILYX\  K T ^ gV
V [ $ V K Y L^ K K˜.K 4”Z7K T ‰K V ^ $4K –K0Z7[”[  \
?5[^ []V \'#ILV K A K K0 Y \–Y ŽK [ K˜›V [ .KA?47@ Y Q ^g}Z Y ZXT V \ K YXH _ \ L+5[M^ .¥‹ YXT K \ T 5Y
‚V K¦Y ^ Y„–TWV [V   LZ ‘O + YX›\Œ YY I TKg^ >> A b / /4&^  K ¥K T ^P K K ­ K V Y „ T YX[]\Z „ K TW V  Y „T [ K¦VL^Z 687 Y ¥T Y YIL‹KY  KDŽK [ V
¥YX\ŒT K Y K ^ „ZTWV –UKI TWT V[ L[ ^  ‰K [  [ K7\ ^ YX\ K \ Y  K T ^Š^ KK  Y K¬K IL;K7\ Yg[ -5[ T ‰Z7_ [ TWV K ^ Y [ K—Y –KKDY}YYXV\   \[ Y „T [ K VJ^ ZLO¤Y ‹H Y ^‰K$ TK \Œ ^ O«K H ^^ $ [$ T V
TW–VKDYX \ T DYXO Z K ?4T ^A _ ;[ KšK7H \ L[X^ '[ ‹
YX\ T–Y [XV [ Q¡^ TW‰V [ ” T K K?\PZY ­^ [ „'TWV  ¤K TWV TW'V L^ [ –=K Ž[ –K &^  K:\ ^\ Y ^ Y ;V egb Z "–K K¥Y T ^ O `­K K V"g_ ^ [ V [K ZgZ7[Y ^uV T [K V \ [
$4TWV [ [V †K ?%T  $ ‰K ?Y T ^ V?T $4^4K?\ŒTWŸV K ^ KrY K\Y T ^†\ ¬K [  ‰7K T ^ [ K  V .+  ^& ZX­ZgK\ YY VK  KK ;¥Y T KV Y ^ „K"TWV[ [ / V $ \ 7TWT V $¨K—Y \ Y^}TWK V ^ K"–[ I'K V „TK K  ^
Y V  $¨V Y „^ T K V K ­[ V KD[ L^ \ T ^J}V ZX\ K ‰K  V K  O ^Š^uT ^  gV ^ V”TWV T V V £TWV ^
^ \ K KDKYILKg^O K {\ Y HK K¬$¨K > Y ^‰ gK V @ ^ [ T GK Y –K GK  $¨T \ T Y Y KW$ [ T  ‰‹Y[  ?\K7T T ^ \ -–K ^Y }KDY Z Y TWV Y K –K KDY¥^ >O [ K;{PK¡^ \ KDYXK\ ^K IL[ K, Y Y K"V I K?\ []YXZ7\Œ K K Y  ¡gKT K –[ ‹VK YXK":Z [? $¨;Y^ K IL‰K A[ _  Z K?–\ [ K$ Y?T [ \
[”K[
;–gY [”-5[ [ ;TW¥V T K K Y ^ TW„VTWV L^ TWVL^ „TTW.V¦ ^ K Z .^ T ! K}Y ^Š[^  [ T Y K(„T G[ Y V^ YILY K GV ?([ C7) Z  )L' \ T ^ : VK ' H877O T ^ ! GV Y K O Y VS [[ V­KD\ [7IL$4K [ _£Va K H Kz$ RH
Y V –K I [T
K  ­['TW V^ „! T .7 T [(K ^ M Y [ V K „/ TW:V $  K [ [ ^  K X VgV {K7Y \£\ Y K Q ^K ‰*^  [   ^K7\g[ K"IK;V [ YJV K K [ K =K
­V K K*^ $ KY Y K ^ {Y +Ž[ 4K .K Q ^47Y ‰}[ ZX \ KK?_\
T ^ [ YX\Œ ($ ­[ V O
‹Y Y^ V T ^ K ŽVK K„T_?) .TW V YXV?–Zg[ TWV Z­ [XZ7Y K [  TWV $ K[ ? T¥T ‰KZ K –VLg[7^uVI T [T  KV K YX ^ \‚YYY V V gYX”V?\ TWTV Ž^‚[ T ^ 2$¨ YXY ZX^ ^ Zg\$ T K K  ;K V Y [ Y ,Y –Ž[K [ .¥O¬TXK Q V?T „
‚Y TWK^ V „"TWV _ .K 4”ZZ7K K–[ GTY ‰K ^ŠK ^ K V O £YX [ &\ 7$4T ‰^ [ K[5
z^  K$ Y T V \ T ^ KK Y K

Section 1.4. Historical Background

 g
 +5+*, P
 


 

  
  
  

 
  

 

 
 







 

  



  













 

 



 




 



  





 

 
 


 
  
 






 
 















 


  

 

 


  
 
  


A







 









 


 


 


  

  


 







 


  





  


 

 
 
 








   


 
  



 








 
 

 
  


 



  
 





 



 









 









 



 

 

      

 


   
   
 

  
 

  
  



 


 



 




  

  



 

  
 
 


    
   
  
  
 


 
 



 
 
 
 


 


 
 
   

 




  
  

 
 
 

 
    

   


  
 
 

 
  
 
  



  




 






 


 
 



  






 

 














 
 

  
 





 











 

 










 









 



 

 











 











 

 
  
 



 










  
  



 
 
 
 







 
   
    

wLn?i"v"ˆt,¦“–noi"yŸˆ•u"ngtUx¬•u†n?n7xowoy¡ˆ„• €,:tD€¬’oq lLˆ"‡otDyWj ˆk„iy–j jŒkf’¤t wXx"t„k




[]Z T

_¥e @?@g@ _








  
   
  
 



   





















 
  









 















 





   
   

  





 
 

 
  







  





 






 








 



 


















  
  

 





 



  

 

 

 




 





  

   
  

  



  





 



  






 

ausBvs.k*lRƒg]†]5j.n c_n f>‹j.s.^B]aB` |



fO RY S K T


 

 





Y‰K . YXY \ V?^uTT .^ Y Z „­T [[ VLK^¡^.^TWV K ^_^&K  ”T K Y ^ Y )P^ „\ŒTWVTWV Z [­[ K ^.K ^ O YI T T ‰<K $ VL^uT T [ V \ YXT  \]?Y T V YX‰\ K^‚T ^HYX\ KY ‰V [ VK^IoY –Y  KY ^„T [ VY ! K.4 ‹K Y †„7T [ T V
[;{ [ $4KKILK Y T _ M –[K  †7T  K ‰‰K [\ ŸY _ V7T Y ^ V Y K ^  KD[ YX\ K $ YK
uVK V®TWVK [ KDYY [ ‹XY V VL0^ ŽKTWV T ^ K Y ^.^&YX \ ; K \ Y „T [ [ VL^ K [ V K K\ T ”T K\Y KgO
–Y VL ^ Ž?K T ¨^ Z Z ––[ [7ILK K ^. ^ Y + V K*K 4 ^ []K7\ \ŒT ¥K T V ) Y []„ZXT [ Z7V[ Z.X­[ V?T K ^.^0Ž/ [ O ?5^‚T }ZX\ K A ‰[  K7\ ^ [žZ ­K ”T K;Y V ZoY ‹Y‰K K ^
[TWV  Y V K&K $+ R”Y TT K duKS Y Y ^ K^ „T 5TWV> Y ?Z b  ­[ L/ ^ K ^.­^[”K _ [$ V ;K ?K T ž*K P`TWV$ K T \Œ K [ K TWV¥^ T Z ^K T ‹L–Y KD^.„Y^T [ K V„ T [ [‰V;[^šZ–TK ­^([ .V  O K \Œ Q \ T TW”V
‚T K \ ?&KgTQ O ^^ $4 [X[ ['5
g
gK OSO, ;{#K"IK K?–K \ Y []^ Z$4‰[0K"K K K*V V*4oY^[} [ZX$ \ K VK^
e:‰/ [T „$ T K?YX\ K^D\oV_gIL*^K  V K¦Y ILY–KDY ^ Y K : [[  VV [ K?^  Z ^—K[Z – [7I V T K KDKK gg^ VXV [KTK ; K gYK -5^‚[ T ]^ KV¥' _ 7OZXT  \ #gY V V V K7K>T ^ Ž¥[ TJY [”>‰[/ K
_ K ;K Y YXVK \(^‚T ] [\VLY ^ „T [ [ KVL^DV _ K*K¬ $ ILTWV7K TV [ „V TW V  NK7Z ^ g^ ^ VXY VKVK 
 K ^uT V”_ K Y –K  K ^ T K  Ž[ 1K ) ^ „T ‰KgO

Chapter 1. Introduction









 

 



 














 
  
  



 


 





 
 


 

 




 
  

 





  














 

 

 










 



 

 



 













 
   








  
  
  
 






 
 



 
 

  



 









 

 









 


 







    








 

























 



 






 







 



 



 

 





 



!  +. 8
…
!   +,/



­aK Y ^ ^ K‰Y K K"K T V K YX\ ^ Y ^uY T  T K K }\ Y [ Z„ T„[ TWV VL[ ^ V [ YITK˜}K Z ZX­\[ KK";K \ KV K  V Ž[ [g VK^  [ \ T ”[TWV T ) [ KY ¥„TILT K[ K V;Y TWV^ „LTW^\ V K&¥  TWZ V \ –[ TWV †K 7^Š;T ^  YOoV P[[ $ VY ^‚–$ KDT  Y?K ^T –Y ¡$ T7\ ^ K T
­K V ^ [KD\ $KY Y V  YX\;^$4[NY [ V Y 5
^
MM *KK7G\ ^Y [ V V Z Y –[V \ KJ []\Œ^ K +g†; >  Y > V/ LH ^ K 7–T []^ Z7
[ V [\$‰[ ^\ K >  K4 Y/ OV—SU^uTWTV  Y T K4\ Y K K YX \ TWV Kz[ )PV K,\Œ TW[V  Y VK‰ Z T [ VK KD^ K []–\K T ¥ T )$4[ Y 2„
T [ + VS0[TWV Y T K K _
T‰}Y[ I Z  T –K?[7\ILLK TW^uV TWV K )K®V?\ TTY  ^K Z ”­‰T[ P`[ K \ –K K K7 V _\ Y$¨K8V Y ‰ ^ K [¦Y [Y^ K   O[ ;[ gV V K Ž[ KYX£\Y;+g; Y[^Š  ^ K T Y –YXY „\WTVLOW[ > ^ V ŽK g[e: /[”LK ^KNK \ T  T ?K TV KG ) O ‰V?K TJK¨\YXK\WK7Y O \†K\ ‰_ K K—V 7Y T ^ ‰['‰K [T  [Y K7„ \T [ T [V^
TW‰V K $¨Y [ T „ TWV $¨Y ^ [   K ­K K?JZg.K\ Y 4”ZgK \ [  K  Y 0­KM YX$¨\ T ^Y „ T TWV ‰Y [  Y K7V \ Y [ V   K{^ [\Œ TK zK +5M$¨KSY;TWY V ^.Y ^ Y–Y V VL^Y ŽVK  oJO [] \Œ K †K > Q V / YXY \ŒVZ 
[ K  ^ ?T [\ K ^ V:.‰K T KYX\ )P^u\ŒT TWV  \ YY „V T 0[ V ^ []\ [”\ T [¥
T ) ^ ILY K„T [ V Z Z –[­[  T\ ^‚K TWšV O _ YX\Œ K ‰K [ ?^ +) V?T K ”T P`K –K V K _ ) V7T K
K7\ K K ‰ K V T K?^D\_ ”[ TWV [–KDXY V ^ [ Y V Y ¦K7\ K \ K –‰K &^ K  V \ ^^ O K / ¡*^  P`K  ­'[  ^ KILK ‹YX†\ ;gY -5[  –&Y $ Y
^ Y Z –KILK V  –[ 
K‘K ­\ KT  ?T ^NT  V [ ;K K"YX[ \WO  +d‰Kž[ \  K7\ / T Y VY N.K^ 4”Z Zg–Y \ Y"KTWVL ^ [ V K KDK Y ‰[]‹\ Y VL^ ŽK Y V K K $4KDKK V Y 9K ‹Y ‰[K \  T ^ „$¨T YX\Œ[ ^  Y V K
­ KDK7KYZ7Y K VK g^ ‹Y^ Y VL[ ^ VŽK YXfZ O K '  K"TWK[ V ;¥K T P K K D­O K ^ V [ [\ TK ”`T *K TW) V 4oY Y N„T K[ZgV\ K _K Z VL! –[^u^ T K [ ^Š^ V K K—K $4K KD$4K YXK"V N\K V+ ! K‘^ SK \[ T  ‰V ?[K—T  \ K Z Y YXV Y \WOW^ > K:Y K V/›žTWV^ ^ [][Y \$4T <K K  $ Z ?Y T Y^ K
Y K [TK ;VK  ‰T YXK \ ^T [YX \ $¨^‚TY  ­K \ +Y S „T [H V ;S Y H / –K  ?K¡T ­.K K 4” Z7K) T ‰ \ KTWV V YX$ \ T ­K *^  \ ^K O KDY ‹Y V^ ŽK [”K T K V [
H ^šT $¨Y ^ ‰K V „T [ V K  KDY  \ T K _JT }T ^0V [ \ KY %$ K V K\ T  ?T  ‰K YX\  [ $ ^ Y ^ Y ^ Z ‹Y Y V 



 




 





 










 


 
 
 
 







  







 



 
 



 




 







 

 



 



  
  





 



 






 







  









 



 

 

 

 









 






   

 

  

 



 







 













 

 















 









 
 

 




  

 


 
 
 
    


 


 
 
 




 


    
 



 



 

 







   





 







 

 

 









 









 















 







  




 

 

 




 




















 



 











 





 

 





  







 

 











 



 



 
  


 

‹ lRfBfga%]5Ž`…sBfBvRv*n ~ic†]]5l.j0`‰„>sg]_]l>n ]ypKn cWj0]5sgjB]‡aGp‡ausgsBcoc\n adk.ceaB]†q n ai]ˆ0lMad~0v`…n sg]2]Wn ~%]5lRj0fBsgaz]yclu]epKsBr.fza*p'| l*`‚mzl*`pKjBaB`baMj0aopNsBc_n fgˆ0lRq ˆ0adv|
[N‹lR~i]5wƒ0s*woq aB„u`bh~g]5n s.jBqRai„l*`']5sg`…n ~gadsgv,v&]aBl8wG^0n ~_`bl0ˆ0ˆBaBa%`bc5]5n j.lRsufB]Wcu| ]5jBazcel0b]‚pNs0`‰aMn cWp'l*`xmgn fBr,ˆ0aB`‰„Gp'aBq |








[]Z T

  


_]e @g@?@ _

fO RY S K T


  





wLn?i"v"ˆt,U“–noi"yŸˆ‚•u"ngtUx¬•u†ngn7xowoy—ˆ„• €m:t"€‰’oq ˆ"l‡otDyWj ˆk„iy–j jk„’€ wXx"t„k






$Ž[ ›K \ VUY T K¦ Zo[Y $ ^ [Y  ^ [ K V )P„TW\ŒV:TW V [ L „^ T ‰\ T K 7_TT ^ ONY Q:['4” Z7KT K T ‰ K + V RY YX\"d‚$4S [ K 5T
†> Yg^Hb Y  / KO ;[ VL^ ‹Y K  Y K  [$ _
TWV [žK;ZY ­K ^.[ ^*g V–K TWV K K­K ‰^uT ^ []\ Y V YK I T [ TWV K:YX\ŒY T K [$['T[ ‰ K O T YX\[ ^_ K :^ ?Y T \ ­K  YXZ‘\ Z  ­\K Y ^.^*K   –K $ TTWV [  K YY
I TWTV
T ^ YI Z7T [”[  T \^ ¦Z7K [”^ „[ T  — \ šY K K ^ „T —Y VY  K  YK ^–K*$4Ž[ K7–\ŒK WO K Y –Y K T ^ „T  [$=[ KU\ T  ?T  ‰K YX\ TWV K‰[]\ 
Y –K K ­K   [? $ T ­KTWV  YX\Œ[}Y K ?T^uKT IL K  \ Y Y8„T [  VL\Œ ^¨T .^  Y ^.^&  \ K ‰V K   [[ $—O K  [. ŸK.:47 Y\ K}V Zg\ K _g[T$— OM;«K [ $4[K"$ IK Y _ „T ‰KK‰K V Y V‹˜Y V ^ ZoK Y [K
Y¡YZ u
TKšZ7KMY $ X T VgV K K $ TXZ T YYX\ \ K V [ V”T „[T [ ¨ VY ^›TW[V8 ”T K >D@ Y ‚^ „TWV }[:T ^Y \ Y? T KILTWV K Y  y + Y \Œ .  YXK"\Œ IK?T \›[]TZ7^ K Y¡ ZX \ [ ¡$ O [ $ T /{T $ 7T T \Œ^
TWT ^V G Y ^ TWVK Ÿ _ [\ KNY †ZL\ Y ­K^ [ ‰ [KUZoY K ¥[T ^. ^uT ZoYK „T [ [V $ Z T –^ [ \ YK ^Š^¡TWV TWVY 5OmH K TW”V?TT „„TT [YX\V YX^ \ŒY _ K ^ K [ ^ T []—\ T T ¥^ T ) YX\ ^ Y [:„T Y3[ V GY Z –[ [ K ^ŠTWV ^
Y V ¥TWV K  [$ ­[' Y .  \ K V + TWV Y ^ K K  [$ T ^ .  \ K V g/ [UY*\ Y TWV Y  [¡$ O
^u ” T T  Y K –\ Y\Y T š„T ? [ O T V Y ‰ VK¤YXV \«[ ILK7\ YX[ \ T  ®\ Y Y K  O # K¤V K–KDV YX\–T Y V K ?T ^ [ ILK7\ [ K T X VgV Y K ^ T[ ^ Y K ^.^& YX‰ \ K  ! \ Y TWV K  K „T \ VT T WV‰ K ZT 68YX7 \
J#  \ KK¤.Y Z†\­[_ Z7\ K‰K V [ „TK K K?^ T\ ^ ^&YK. 4VgTV ^ [NTTWV  5 K ^ K YT  –KK[^}$ ^uY ])T .^ K?K \ Y Ÿ „_ T [ [ $ VVL^ TY ^ $ }K V T ^ K ––[]K Z KST ‰K [ ['  ‰[K?$ [ \ K VY Y K"V[  LKK ^ ^^š$ TWV TT [K ^š 4$T T \[  Y d Z K Y Y ^ V KY KK7[\ KTW$ V#
+ ^ [\ T 7 d \ T  7 T   [$ / K O
 + YX\ŒK KDK Y ['K.T4 ‰ –Y K K T YX\_ ‰–[[   K?\ ^BK/ ¥ T K K9T ^,; K [ V YK V?T ^  [”T ^[]\ YTWV ^Š^* \ T‰  K7 T   +[ [ T \gK [ †¨$ Y ? ­K K / OM\ #Y V ‰ [X[ [^ \ TWV ‰ A[ O K?# \V ^
Y . YX\ T _”^ [‰ KšZoY [ K KY T ^ –K‰ [?IK  [ T \ TWV KY ‹Y V^ Ž K fO
” T ^Š^uK T ZoY [?„IT [ K V V?TWKV 2 K  TWV  Y „T [ VTWV ^TWV YXK \Œ ^ [\ T ”K T ) V Y ‰ „T K[ V T O YX\, ‰ K [  ” K?T ^Š\ ^D^u_T ZoYr# „YT [  V Y&K¨$ 5Y –K T ^ [ _˜K V K ‰ \[ K ^ ¦„TWVT } Z7[ K
K 5 TWV Y Y ^ KXO
TWV K ! ^ KH[]V \‰ K,T ¥ [4$ T ) \ Ÿ[ V_Y $„TK [ ­[ V ^ V Z [$Y K^ _Y K $ _ Y­T KV‰ ( g [7TWVIoV
YXYXV\ZX[‰ Z $ –K []V Z  Y T [Y V7$ T K ^  ZoY KD+ Y K[”[]V ‹\ Y TWV + V[ ^ Ž ‰K [ K –[”K [K /  _ T[KK $ V –"[ Zo_ V Y Y K"[ ^‚K T  ^ V "/ \_N[7Y ILg„KTV [ ­VV?KTWYXV \ [ T ^  „K T\   ZZ Y –­„K[ T ^Š[ '^*V¬  ­TWVKK
Y–K V ^* \ –KD^—YX^ \ T ^ „[ T  \  ­K ^* K¦\ K.^ ”4 O8Z7›K \ KDYK  \  _ –[ 2  Y V $4[ V2
; T ^}K V T KDYXK \ ^‚T [  \ K Y „ T [ [ V V OK TWV  K K ^ 2KN‰ Y [ ––KDK Y _ ^ [ K* Ž[ K–‰ Kš[ Y VV ^ –Y–KDYXK \ T ^ 7„TT ^
K.Z7? 4 [–KDT TW^ YXV "\ T _+G[ A KV + –[¦K(TY  Y T {­K Y\ KVVY I TW‰ M¥V KY V T >YXK \ ?^ Yb:.I/ OT¥ T !K / ^ V Y V Y KšZ [­Y [?^ŠI^*K K ^ ‰ $ K Y T VŸ Y _ [ K T `K K K.4” Z7V[K $ ‰ T ‰T K ^ K T.V  YX^ \ ^  .\ KY ”V "T K _ ^ K Y[T ^.V ^&;„ TWV[‰  K [ K7 \ ^^‚_JT  Y V [¤\ Y Y T KK
 [$  [”K ^V [ YILK‰Y V —K*`P K [ V K ^ [\ T ” T ) Y „T [ V Y V [ [  ^ K YILK K T ŸK*X4 Z7K T ‰ K V ^ [ Y
?T ^ \ Y T 
+ ›YIK ¦Y V P[ XVg^ > A / O%›\ KDY  \ _ ?T ^ [ V ‹Y ”T „T [ V}^& K ^ ¨^ K"IK –YX\X[]Z „T [ VL^RI
P[ [ K K Y ­K T Y V K ; [  K7\ T ^ K?\   [XK ^¡V [ ; Y K 5O
! V K T ^ T Y V K˜[ K R[ V K T ^ $ ­[ V O
P[ [ K Y –K1$ –[ V O

Section 1.5. Numerical Simulations


















 




 











 




  

 





 



 

  
 











 
 

 










 

 

 



 




 





 











  
 
 








 







   

 







 







 


 

  



 
  

 

 

 





 



  













  







 

 









 


 
   

 




  









 


 













 





  



 

 

  




 




 



 















 






 


 








 







 

 

 










 

 



 

 
 
  

 







 

 





 





 







 





 

 
 

 









    
    
   
 

 
   

 

















 

  
 


 

   

 
  




 


 




 








 
  






  









 















 















 


 






  

 





[]Z T

   
























  





 
 



  












  

wLn?i"v"ˆt,¦“–noi"yŸˆ•u"ngtUx¬•u†n?n7xowoy¡ˆ„• €,:tD€¬’oq lLˆ"‡otDyWj ˆk„iy–j jŒkf’¤t wXx"t„k










 
 








  



 





 







 

  



 







 

 

 
 





 





 



  








 

 



 
 
 
  





 




   


  



 

 
















 

 

 














_¥e @?@g@ _

fO RY S K T


 

 



[ KYX\Œ ?T $  –[ ­VK ^ KDYY V "$4K K ;KK V –„K T ^[ KDV Y K  K K –^ K T ^YIY K—V K.K*4”4oZ7YK NT Zg‰\ K,K V $ YXK\]­Z K –[”[K ^ YX[ \  Y \ Y „
T [ VL^K Y V Z¥O K  ^ T ^ [$¨$ Y VV Y [ Y VK
K K YX\NY+ I T T ^ ¡$¨Y Y VV  Y ”T Y–K V K Z YX­K \W^.OW> ^* –K A /JT ^ ^ YX.Zg¥ZXT \ K T K   Y [ V [ K\ K}Z Y–I [ T DK OM^Š^r# V TWV $ K ?T T YX\  Kš\ Y \ „T T [ 7VLT ^ ‰K‰K Y YX \ T ^ [ Z7[^  Y –^ŠK ^*( ‰TWV K [
^Y‰.[^&Y –K } ; TWVZ K „T [YXT \]V „TK V YX\"K K K*T 4oY‰ [  [ TW V K?YK \Ÿ„TZ [ Y­VK I ”O T T UMY Kr VK*Y Ž^.K )P^& \ŒN^—TWZ V „K T [ $ K V [[]Y  \ TWK}VV [—K V Y KDT[‹Y‰ V K[$®KD[ + O  aY [K $ / \ K[ Kr^ Y \ K[”[
˜[YI Y ^ T +eD$¨O ?Y TR^^ Y ‰? ^ K*K [ 4X ZXK?[\ Y \”V TWYV K 7?TT A ^
[ K ‰ ^ K¤[$ Z V T IoY K K7–Kg\ O Y KUY IT [m\ Y ‰; [K g V T ˜YT ^}T ^ ; [YX$ \ŒPY–Y V K TWV K [ –K*Ž [ –K K V Y[ I NT T }Z7Y [ ^ Y [ V g/NKT ^ [ ILV K YILK ‹Y T „T K:YXK \P Y  ^ YX\$ T [ \Œ
\ T [  ?T Kš YX‰ZXK Z –YX[J\4 T — [$Y K7–\ Y KTWV ) + V?[ T VLK ^ K ~[*IoY Y „T [?VT KIL[K ,ILK []­\[* ‰IK K<V Ž[ Y ­K[Y¥VOH^ P Y [ V V ILK  K ^ VK?^‚\ T _PT /  OS;{KNK YV ^Š^*K  _ } Y TZ 4„TIL[ K7V \ [ T Y Y K^
YT ^ T Y  ^Š^*[ $ ‰^mK TWV˜TWV ^ Y‰ K K‰­ILK K7^ \ KD[ Y T ˜K Y ^ ^ ‰Kš[  \ TK? \W?O(T  # V K –V KDYXK \ TWV _ K K  [Y$=I T [ _ \ T  K(? T \  T  ;7T K YX‰\ K  [YX$ \ T ^˜Y –TWKDV Y T ^ K Y $4YX[¤\ yZ $ Y Y^ K
­? K ”\ [T [ LV ^gA Y Vž O=TW# VV ??TT ^^ YY ^^ KK T }K T ^ $ \ T ‚
[K \ K . YXV?\ TWV  \ Y Y „T [ VL[ ^H \ K<[  V  [ \ŒŸ[Y¨$ILKY  K 4 [7ILK ,[ Y  V[9 $ \ T  T ? T ž –KDTWYXVL\^uT T  K ^uTWV [$ K ^ Y K^
IK?\ [ T T ^—V [ [ V „TWV [ L^ Y V=”T P`K –K V  ­[' K YX\  \ Y K  O

Chapter 1. Introduction

    
 
  
 
  

 

 




  

    

  

 

    



 


 

 


  

 
 

 






 



 
   


 
















 


















 

 



 















 



 



 




  
 
  



  
 
  
 



 
 

 

 

 
 




 
    


 
   
 



 

 
 

 


 
 
 

  






 
 
  

 

 





 

  

 







 





 
 









 

 

 

  
 














 

- L­['^ „
HT )]VQK [ T K +XRK*K Y4oYY
uNLK ^ ZgK \ YK,V[ K  M¥^*Y VYXm\ > ^  .\Y A K/ O T ^ Y V K KŽ[ –; K g^ [VK Y K7Y \‚[K? -†K ^ uYAK ^. $^*[ T $‰K TWVK.4 –K KY ‰^ Kš[ PKIK?^  \\ [K"[K"$ IT K TD^ O . RV YŽ [ \ K
‚.KV X¥V Y YY VVK?  \ M¥_ Y YXKV \Œ
UZ# –KK¡^ ^ K"K*K KX4 V  Z7Y K ^ „TT [ ‰V”KY _ V YX7K \”T K^ ­IK -5T^ K K:K Y V T ^ K –K K ^*^K ‰YX\ [\ ^^ VL[ ^ –^ [‹Y Y K K  K Y Y ? Z7[”–K [K ­^&K A  T\ ^—^ [ V [gVK^& ( Y [ ‘-5YK Y VTWV!+ K S  TWV7Y TŽ?„[ T ^ YXK \ V\ YY[ VVTWV ¥Y T „MX4T I[ Y K VLVV^  gC^ .KO  V >:# V   \ K :V / K O
 [$ 4$ K –K K ^ Y‰ KCdCG$ ?T \ K¬Y ^uT } ZX\ K‰Y V YX\ ^‚T ^ Y V1 K; [ VL^ ‹Y K K ¥T P`K –K V K T ^ IK ¦\ Y KXO£Hr\ ^ [ _
[$4V [ K V K Y V T  4$ [ VK  K [  K [T$ ^ [\ {T  Y 7 V T  }Io$ YXT \  K˜[ K ­[®ILK K7T \ }[ ZgT \ K‰K [ V Y K „T [ .Vš:T ^  Y \ K V GY O  \  O T K ^ K –K ^& \ ^ [ V K Y V
  







 











 

 




 

 

 
 

   







 




 



 





 

 



  
 
 



 






  

   
 


    
 

  
 

 






 








  


 


   









  

    
 
 




 






















 

TZ ^ ILK ^u T UYXK Z7\ ?[]^‚T ZT .Y  \Y Y –„K T [ TWV V0K7\ TWT VK&K [ ” T YK K Y ^[ K „TWVV KU ;LTWV^K 'K&T ^ YX\WOT\ ^‚# OT  #¥Y  YVg\ Y V „[ T [[ V^ V^ KDI K}Y TW–V K.K4”K Y˜Z7 K ZoY T ‰V Y Y K V KDY Y VYX3\][ K"‰I [T  KrK K?VYX\ \Œ K Y ^*^ K Zg[ Z7K [ ^uKT „^ TWV V ZT ­$[K ^ ­[ \ KV  K
‰­K *^[   \ K?^\ ^ Y Y ^ ^ K Y  ­K[ YXV \ŸK"I K T  K­KV YX\«KCZ 7 O^‚#yT $4^3[ X V\   K \ T
‚^ K Y V[ ”TW^ V K"K O V V‰„K T \ T YXY \ YXZ7\[ TW V \ Y „T [[VL‰^ K _ #†Y $ TZ \Œ–[ ^&  K K ^ –KDYX[\ T ^ „T K
^*L^ Z T T [ ^ Y [  Y V V ‰K T YX\'‰[  K7\”Y V:T ^r^& ZXZ7[ „TWV KI T  K V KgODC 







 

 



 

  

 











 
 

 









 



 












 









 

 







 

















 



 








 
 
  
 


  




 H"`D„,n ]W„ulRƒ*`cea0q 'Žq JsMk*l0]]5q aMs*fBv>]5ƒ*`xf,n ]_ƒ*^0c5n v&azs*fBv,ceadaGpyj0sg]_j0s*^*^*aBfBcg|
Z  HyjBaGk.lRƒ*f0v&sB`‰„zs*fBv,n f.n ]2n s*q.~ulRfBvRn ]2n lRfBcWp'aB`baGfBl0]Nci^.a0q auvlRƒg]†n fo]5jBa%^.s.^*aB` 
 lgp'aiˆ0aB`]5jBad„%p'aB`baon wz^*q n ~gn ]5q „oc]esg]adv
n fzZ]5ZjBJa>lM^Bpy`badjBc2„zaBfg]]el8sg]2ƒBn lRceaGf| ]5jBaG~dlRw^*q n ~usg]ao]5ƒ*`xk*ƒ*q a0fg]%w%l&v*aBq 
]5jBa%ZxZ }gx‹sg~dq aun ]‡]5sBjo]5`xqj.„s*suq u]†celR]5]‚j*wop'n cWl8aj.pKƒ*sBf*`b`blRc\m0j_fBfBr8lgpNpKl.wzf,`bv*ƒB~dcucelR]yhw€Bk*pNao^0lRs*]5ƒ*f.jBqnaBvMau`bc†a*q n|p'miaWaB
B`bl*]alo`ƒBa\]ec\{.s.n s*mifBa†wr>]5^*]5jBqjBa.ayaBhJlRn `Wce^&adwo^.aol*lR]5`‰v*j0]5ƒ*aaBf.q&^0n]]‚s*l,„%^.~B…aBl*q`‡s0`Jnkd]5w „j0ao]5>j0`bƒ&adsg~d]_`‚…l*sdn `b]K„vn hc†s*€0fB~dv*v,l*lo`x~db]5adlRj.~iq n]dauf&| sBm†rR]5ƒBj.asu]"n f%pNpKl.`xj.mon ~Bkdjz„ ]5NjBaisg„ˆ0aiƒB„RceŠ ac
pyrR`bj*lRn ƒ*~B^>jHn€cyjBs%lR^*r.alRl&n fzv,]5lRj0fBa%a&| ƒgHy]5ƒ&jB`‰aia>„>q j0ausBsgˆ0vHaGƒBnc†fBc2]aBl8`‰]j0adsgvHˆ0awo`bl*au`bs*aGq n ^&ce]2jgn „B~c\f*n ~dƒ&c wox…aBl*`‚`n ~ga\s.{*qs*wowzl&^*v&q aBaKq cg]5|j0ak.l&n q n f0r,jBagsu]W]5`…s*fBc‚aB` yn fB]lz]5jBaBn `‡wol&v&aBq c




[]Z T

  


_]e @g@?@ _

fO RY S K T


  









wLngi"v"ˆ‚t¨0“–noi"y ˆ‚•„"ngt(x¬•„5ngn7xowoy˜ˆ„• €,:tD€¬’oq lˆ‡7tDyWj ˆk„iy‹j jk„’€ wXx"t„k






Section 1.6. “Integral” Models



&  %(



( /



–LKD^ VY Y Ž^ [ [ KV .[Yg V \Y K K7K –K\ &^?Š_ TW V \ ^K K Y V‹YX \‰YXKNK ZXZ ZT ­­[XYXK Y \^ K ^uVT  A „‰T\ ‰Y K „KXT [ O [VL ^ ?O [T  ^ Z K–KN[ ‰\ T \ [ K^? ¨T  T }‰Y Z7^ K [ \ K&YX \ Y  V [$!K [X”Y [TVK\ }TWV ^Y [^ 7„\ T TTW”^V T ) YXZXK Y Z V „–¥T[g[ TWYV VHKD—K [ T^ ^ V $ [ T K¡ZT K768\ K 7
¥TWVLT ^*Y  ­‹K Y^  _ [ Y V>K—”[T K  Y ^K „TW—V Y V7—T ŽYK ^ ?Y TW„V T K˜[ VLY ^ ?T[\ T ^& ZXY ZgV \ }  Y \ V)P=\Œ  KK;”Y TVK3 ‰[K"\ =[ DO>K ^u# T VV 7­T K ^, ¥?T T Y ­K‰‹YK  V _ ^ Y  V K K0V ”\ TTW V K"7KT 
‰Z –KK ;YXY\ .T ^U–8KTWV -† K–K"K TK W V Y O4! V KK TY V¥_ $ ILT K7\ [ T K ‹K7Y \ŒV Z¡[K Y VKNZ68K97 )P¥\Œ TTWY V ‹Y„T ‰_ K Y VT ^N ^ —YX \Œ„RT K\ T LTV W[ V  K.4”Z7[&K TZ ‰–KK ILV K V YX\
IoILK7YX\\ [  K ^T Ž[ Y ^ K ^‚[ T ­K K, Y )P\Œ[?TWIV K „K T ;KNY TWVY VIL YX\  YK K˜[—ILY K7^.\ ^&[  –T K,„T KY ^;['T }TZ –Y [7„ILT [K V Y KV   K7YX\\ [T $¦[Y  T „K T YXY\‚Io^ „YXTW\V  K O [} Z K–KILKY V K
K
–V [ [ ^‚$ T [ V V [ [  KK¤‰Y []\  [O T + ?RT ^ Y d‚$4S [}K IoT †YX> \  K?^ b Y Y / –K;O *K 4XZ7KK T ‰[ K ­V K YX\”Y;V [ : VK7[_\ Ž–[ K7\ T Y K‘\ K Z 68KD7 [ ”T T ^ Y Y–ILY Y  T \ Y \Y K ^ [ KDKY V
¥KT Y IL‰K7\ K[]Z7K K  YXY \V  \ $ Y „T T\Œ[ VL^K Y ¥V T ^ :LT ¬^.^ T K,^ U”TTW^ V L ^.^ YXK Z*KTWV RA O{YXH Z K «ŸAŸZ –O [  [ K—Y [?IK ‰[  K?\ T ^ KšZg\ XV K
$ ? T # .Y  [”V[7[ ^IL K‘[ YY ^ V „ TWV -?Y L^ ^ Y;­YK0Y V Z ¦[?­I[ [K '  K KK   Y K VT^‚„T T]VYXK7\rZo\ [Z7Y $ [–YTWV‰$ K7T K [ ^¡VZ7TW[ [”3V [ ”T K YY ^ V Y „^TWV„K TWgV ^ Y  –KUYIZ KN–[ Y ' T[ K„T^ OYX^ \` Z7 [  TWV K 5Y ‰‰[[ [?––IKKgK _O
TWV ?T–^;KDY T ^^ K $ K K˜­K Z –[ K}Y K \ [ ^uV T[  V7T T) YXY \ V [ \ ‰V Y K7VZ Ÿ^_ [ ZX\ Y Y ^TWV Y ILK^uT ]V? T )  YXY \ T V –[]Y \^ KX„O TWV ^uY TWVV ­K K ^ K K [ V K¡K?\ KDZ Y^¥_ TWV [ V K „T ‰Y KgV O
H Y 
‚”K T VN„T [TWV V YX[ \Œ [_ V^‚KT  K;–YY „TWV T [ V[ ^ ^ $ [K V}[Z7V[ K V K V [X^ [ +d^ ;K ^ Y [ 7TWV KK ^uT ][ V^ Y VKN Z [–[ K K ^.^ / $Y –T K—Y $V YXT \Œ\ K K  ¥Y T ^ V  ^Š^ YK IUK TWV [ KK
 YXY Z [ K –[ ^‚QLT Q [ V Y V K¡K K ¥[ T I V T [K  }TW[V  [ K$4[”T K ;Y Y TWV^ „TWV Y OK [ T K ^ P^ TWV
Y K*Z7[ ­[ ^uT UY V  Y .^ ! Y T ›K V ‹Y TWVDd
‰–KDK YV „T O [ V [ K0 Z7[Y 0^­[! ^uY T T JK V  K‹Y TWV[U‰K K V V ‹YXZgY Z7V K  KUY Y ^ K ^ T [  VK^ „ T . [K Y ^ Y(\ K\ YY ^ K0Ž[ ZL Y Y[ K [ K T K [ R^ I YX\\  Z7[ T –[ Y ^uV T DOKIo YXZ Kd
[Y ‹VY  „T IL[ K V V B+†!Y V Y Kš­KY Y –KD„Y¥T [ O V Z –K}[ K&KP ^ŠK ^ K ^ ^ C [/_ \IL K V T Y \ [ V Y K„TIo[ YXVLZ7^ [ ‹+Y \ Y „^T [ V ZX\ Y YIK K [ K"K V =K Ž)P[ \ŒXK V /_ [  T 4 K TWV TWV^‚ZT ]­V?[ T ) K ^.Y ^ KV ^D_O
K¬K IL K VT 4 TWV \ [ Y‰„KT [ V +Y B^ V?/ T ^  Y V ^ Y K ­K [ ¥VT I ^‚T T   K K &­K TWV Zo[ Y „$4T YX[ \Œ ^[ [V \ KIR^K IN^‚TWV K K‰‰[ [V \ Ÿ\ _  Y  V YX \ T Y „K T IK;^ .K [ 4”NZg^\ Y \ KDV KY IL„KgT [ O V M”.K 4[ T‰^ K O
ILK T V4 BTWV! Y Z ­Kr[ Y K­K^.Y^ K^4^ T G^ ¥YILT ^ K ^ŠK"^ K K V˜˜TWTWV V IK ^ „YXT Z Y K K  YO V  KY V V K 1K  [ VLT 4 ^uTWT V  K –Z K –˜[ ^ []K ^Š\ IL^ KK ^ OY – K,ILK K –K  ^‚7T ]T –V?KT ;) K Y V V J[ TWVV KK
‰ –[K"K\  [ K gK V?_T ‰  K K3+ [ TWV ?^ TYWV ­K Y^VK   YXY \ V  TWV: K  TWV Y ^ \ „TW V K I / KY IoVY 0 ^ Y  „ TWVK"K K K Y ^ Y„ITWV T „T KO ^ +ŽIoKY )  ^  IL$4K [ V „TWK V g/V?N_ T Y [ K –K^
[Ž]Y [ ­ZXK Z7K[L^ ^ .K Yg V?VŸT [¦_ .K 4 9[ K –­Y K&ŽT 4T[ ­$ K _ T K [Y  ^ K¦K TW0^ V?\! TT Y ?T T‡T  K –[‰ K K9YX \WO K T 4 ^ TWV [K 4^ Z ^ ­\ [ K"K"KDIKK ^.K˜^K KY ^ V YOš<^ Hr„¥TWTV\ŒK (T YH^ K I ^ T K ^ K ^  []&K \  Ž[ [„T ­TW[ K V VL^ ­KKY Y ­^ K K Y ^ K ^K YYXK IZ ^K T [\Œ Y‰KK
Y V  ‰[ ­K¡*K 4XZ7K V^‚T IK}Y V U^ [  \  K}YI[ T  K *T ,Z7[ ^.^‚T \ KXO
TWTWVV Y ­K K?K\ ^ Y „ [ T I;T K(4 ^TWV \ \ YK"K"IZ K K ­[ T ^[ K V Y^.'^ K?^¬T "T TW_ V  Y –K K  K [ [gVVX^‚[]T V Z7K KK ­–^KY _ „$ T [ [V K YX–\ K K [ TWVLVK¦^u”T ]\T „T V?T [ ?T ) VT  ^ Y ‰ŽV [ K oC $YXO \ ?  T [ $ K¡^Y K ILV K \ [Y „V T
YXYK \Œ NK}Y Y [T £ Y K TWV VK^ ‹Y TWYV ‹‰YK I K T V






  


  

 
  
 
 
  
 



  
 



 


 


 


  
   

 












 
 





















   




  
  



 





 





 


 
 

 






  
 






 
   





 








 
 
 
 
































 







 




  









 





 



 





  
   
 
 

   




  














 
 



 
 
 






 
 



   


 
 





 

   

 

 


 









 





 

 









 

   










 

 








 



  
 
  







 
  

 
 


   

 
 





 


















 




 











  



 







 






















 
   
  
 



 

 

  





 







 

 


 








 













  
   
 



 
  
 
    
 
 










  
 

 

  

 













  

   



   
 







  



 

 
 




 

 

  









 
 





 

 



 










 






















 






















 
 



 
 



  
 
   





u~ sg]ZZ adr.JJl*lRlR`‰w%w%„aa_kd„MpN`badl.n ce]`xagcem>aBsBq`bj02~B|sBjBcaB`bk*c,adaBˆ*fMn adp~us0`x]5…j0n ada1v~0lRjBƒgaB]KwGs*n ~ufBs*vHqNj0`blRausB^.~iai]2nƒ*lRq fB„zc pyxa&n q |rk.| aM`b^&aBƒ*q auk*sBq nc2c\aHjBaul0vzcef.lRn ]5lR`bfJl.|r.aBf vƒ*`‚n fBr<celRq n vRn ŽJ~usg]2n lRf ^0`bl&~daucec sgc








>?> wLn?i"v"ˆtmU“–noi"yŸˆ‚•„"ngt(x¬•„5ngn7xowoy¡ˆ„• €,:tD€¬’oq ˆ"l‡otDyWj ˆk„iy–j jkf’t wXx"t„k






[]Z T

   


_¥e @?@g@ _

fO RY S K T


 

 



Y([ \ T  K?T   ‰T 4oKK YX\:TWV $¨[ YIK¡[K¤\ T   7^ T  K*‰Ž[K –KYX\ TWV K˜Y T K T ^^ K.[ 4 ¡Y^ \ KD^ KILK Kg O OzPa [[$V^ K $  T  K V R\ Y _ duS K K T ­K Q ^ ^uT 'Ž[  2YX \”Y \T Y:T [^ V ŽK[ YK V
YX\  \ Y K K [ –K T „T YX\ ^ \ [$ ZX\ gV K PIK?\ [ T NY V ?T ^ $ T \Œ K ”T ^ L^.^ K (TWV  YXZ K O

Chapter 1. Introduction













 

‡









 





 







 

 







 



 


 

   
 













 

,# #! /* +,

# ¬^‚YTWILT V^ K Y V –KDKDK*KYX4 V\ ^ T „[ TTWK V –V K „K T ‰K TWV K Y TWVVK   Y K K V^u ¥T T KV7;TWVY Y V ^uTWV V 0K K*$ TWVX'VgKV ^ K X!V7T; [] K K\  ^ Y LY ^VYK1ILK Ž[ K KDK ”V K1T K Y ) Y ^ ^ K „„TWVT O;# K—‰Z –YT ^[ V KK ^.VK ^ ¥O V TWV K*S KD$ K Y V –K=ILY [];V˜\ [ ^ „ TY K7[ \ V ^
TWV K ¥ T K Y ^ „TWV *TWVL^ DO




  

 

 

 

 

 
 

[]Z T

  






  






 



  

 





  
 



  









 





_]e @g@?@ _

 

fO RY S K T


  





wLngi"v"ˆ‚t¨0“–noi"y ˆ‚•„"ngt(x¬•„5ngn7xowoy˜ˆ„• €,:tD€¬’oq lˆ‡7tDyWj ˆk„iy‹j jk„’€ wXx"t„k










  
€"O












  


 

  ((!)* +,


[S [  mK*KK4XZ7¥K YT K ^‚TWTV Y †K^ „?^ TWTV  [ ‰$ [K TY  Y V7g;T V?YT^ VOrOR KH 7V ^RT ^J”^ TWT[V^ ‰K" K KD¬[.^ !YV –K%K $K^ KDNY [ Z –K [[$ ^{TWV TW‰,V –[[¥^T K  7YKT ^ ^ „\ TTWŽV ?K¨T ^Y Y – [–XK¬XVV\ Y  Y‰
Z7TWK"KV [YXZg\"\ KGY K $^ Z7gK V[‰ Y K [–K4^ K*^ Y 4XVTZ7K¥K V TWV K^
YTW‰V ^ K $47K?T Y^ \ŒV7JY T Y ­K^^0Y! _ KD#WK Y ŽK"Z K7–\–[]Y ^Z7VLK ^–[K „4VT K Z^ \ –[ [ K ^ŠY ^Y K ^Š^ ^ „OM7TWT V#^
[V + Z7^[KK?$‰Z \  T YYXK \Œ [ Y —VgK YV ][ ^ VL$ ^ KT K0\Œ *-5Y[ ILYXTW[V\Œ [T  ‰K ^BK / O Y [ ­K ^ Z K  ­KK  Y K K ^‚TT ]‰7V TK ^  [
 V [$‰K\  Z K –[ KX†O 7K ^ŠT  ^
$> ?S[ AŸ$¨OKY#'–VŽK*[ XY V­[¤K *K :V 4X? ZoT ‰^Y TWK V –[”K [ [L
^ ?[T K[”8[Z –

[7^ V I [YT $;K}[\  Y NK TW\ KV [Y –[ –TKD\ŒY L ^ K –K „K T†IL?K0[”T  Z[ T
‰.K?.–K˜\ ?Y [T V?& T S^ CK0K #yZ $4Y [ V7^‚T T \ ^g¤^ A O ^&  *?T H¬^ K ^O
mOMYX[Z ;{YK­K VL ^ T KK^ YV Y O
Y
^TW[”V [ $4
^[ [* $ Z &^ 7 TY T^ K —Y  Y –[K š$— [ O K7  YX\# TWV Y []Z7$ K T[”[
gY †HO ?#Ÿ"T  [Y  ‰ $ K [ T \ŒV :Y \ ) V?V T  ^ 3K O ?‰T ^;[ TW^ V K  X^ V „ TWV K ;Y Y V V  YX"\¥[ Y  ^.^ $ Z7KT \Œ ^  [ K K [ [V „Z TWT V
K V –[KD$ Y V
$4[ K V  ”KDK7T YXZ ^ \ ^ Y $4$ V8KT $ PT [ \Œ V K TW„V TWTWVV K 7–KT [ ¬ ‹K YXK  \L Y Y V „K YXT [ V\ VLY ^ ^ .K O  ^ – K‰$ [7KrT K †V ?K $ T ?T \Œ^ ¬Y K VK   ”Y T I „Y TT K[^‚¦T V TW$ V [ T \Œ[ V "K.TWK74”V Z Zo­Y [ ^ TW'V  K–[ N„TWT V[ V K[ K 2 ‰V K.[ 4K  {^V[ K YV  „–T []T[ \V^ IMOOz[L7L7\ YY ;KK K
$ '[ T \Œ}R$4Z –MK K ^Š$ ^uTT \Œ \ K K  Y K ^ ^K ^ LO ^.^užTWV K ­‰&K  [ –Y‰TWVK V  .­ '[ ! K   KD YXY \ „TWVT [ V $GO L7T Y ^ \[ _ ;Y K V YX[]Z Z KT *^$  T \Œ K [  XKVYX \ TWYV ž$ \ Y T "K ^_JK V  [ [ V $
I T ^ K [ –K ^ ^ [ [ $ _?T ;^ Y [X7'[ TW
gV YO a K IL[K $=K K?\ K ^.^K _ Y K ^ NK Y $4–K K T }K7Z7\ T [K"IK Y V Y Y V *KT ‰¦T ^ Y –Y K  IoV Y[ K K ^.\ ^K K V „YT YX\ [ K X–VKDY K K ^ KY $ VT  \Œ








 
 
 



















 

 











 


 





   

 
  
 


 
 


  




 

 
   









 

 
 

  
 
  


    
 
  

 

  

  
 





 














 

 

 

  















 
 


 

  




 

 




















 

 









 

   

 

 











 


 

  

  





  

  



 

























 


 
  















 

 
 

 





  





 

 




  



 



 



 

 
    


 
 


 

  
 
 



 
     



 





n fB]5`‰}ZBlRHy€vJrRƒBjB`b~iazlg]5pm0`‰„>fBlglR]pya\f {0q adR]_v*]5k.r.`badlRaGailR]lRmdaBf%cg`|Š ]5cGj0s*sgfB]Wv ]lR^.j0n ~os*w%~dlRadw%cdŠaKk*l&`‰lRlRmuw cdhNH€a0…q &ad[a0qJˆ*]5n ˆj0sg']Kf.]5n j0ˆBaiaB„`bc\nsB]‚`b„)azH†a\jB{*aos*wzv*a0^*^0q adsBcK`‰]5l0woNa0]fgl&]yl1l0w
JƒB~Bq ƒ.jHn v w%sg]adaB~B`‚j0n s*s*qJf.‚n ~dl.cK`Ws*`baufBsBv v*aB `†ausgsgc]
H`…s*fBce…aB`p'aB`baz€JlRkg]es.n fBauvHw„ 8| J~*| Hyj0sg]‡v*a0^0sB`‰]5woa0fg]_j0sgˆBaoso~dlRfB~da0fg]5`…su]2n lRf>l0p'l*`xq v…l*`‚w%l.c]‡a\{&^*aB`‰]cKn f%]5j.n cysB`baus
c\ƒ0~Bj W`e| |8Hs0n ]5q a.hs*fBv,l0]5jBa0`| s*fg„l0"ŽJrRƒ*`badcs*fBv,vRn c2~BƒBc\n lRfBcsB`bak.l*`xbadv`‰lRw ]5jBa0`‰a&|














>

­KY  [ V K ^ K []Z T ^ Y ^ $4K7\ŒWO
 



Chapter 2. Basic Fluid Mechanics



#  +/ ! + … # & /0  &//

€"z€

^ [ \ ?KDTY Vž[ ^TWV ­K Y7^.I^ T ^K O [[”[KU
K \ T T  ^ TWV?T [ V‰K‘^‚T K \ TK YX­?\K ^ T  Y [ Y–KN^ ^ YY VZ ^*K* Y 4o^ Y^K NY ZgV[ \ K}K [K  ^*Y [ V^‚?NT ; ^&K [7 ILL K ^ ^g\ ATY  V ?[T KX V O1O®„TW;{VHr[[ \ $4L ^K"\ I<TWK V$  _  K V KUY K.\ T 4”YXZ7Z7[ ­T [J^ K4 ‰T ;K Y [YX\\ Y ^
 ; ; b  T ^ [ V „TWV [ L^ \  K*Ž[ 5‰K  $ K V—^ KDY ^ ­K ^.^ Y –K‰YXZg\ T K  O K,$ [\ K ^ K T ^ []\ T T¥T K Y ^ „TWV
Y –KDY P[ KDVYX^‚\T ^ K $ 4T Y \ T; Y7T  K T YX\ Y ^ –K Y ^ =„TW?V \ [X['[
V ^gAš^ K[\ T  [ : [' K Y VY ILK ^ K Y ^ [\ T Z 7T ^T  ‰O [?I TWV žTWV YUILK7\ [ T _  + ^ K"K
”T ' –K Q,Q:/ O   1K Ž[ K –K  7T –K  Ž[ 7T ^ []Z7K –Y „T [ V¦T ^ Z ­[Z7[ „T [ V YX\ [


+ e O~> /
! TWV [ K †$4[ g^D_ K ^ KY ^ ­KY ^‰T ^ Z ­[ZgZ7[ „T [ V YX\ [
+ e O :e /
 
V  K ^ KDY  ^ Y K [ V ¥T „T [ V Y V  YU\ TWV KDY PIK?\ [ „T ”T ^ T  „T [ VšT Y V K ^ [ $ V Y  1

Y V  K –*K Ž[ –K
+ e O :/
   1  
Y ?T ^ Y K ^Š–*^ Kš }Y –Z K „T†[ ?V T ?\ KD^ Y g^ Y Y ^ Y [ 8 [(K *K a 4 &K?$ T 7T [¡V7V T [Y VV †a ?*K T $ @O [ #V?V T Y V ?T ^ K [”Y[I T
<[ {$4Y KUV [ V \ K ‰0K Y V –K„T [ V V[ K  ¥T ^.^ 3K G^Y K 
TWV ? T ^ K˜[”I T['^
g[O ^uT T ^ YXZgZ –[]Z7K ¦[ \ T  7T  Y V ¤T $¨Y ^ Ž[ gV  Y K ‹Y „T [([  K}I T ^ [ ^uT [ K
 7K T V^ ^‚ZT ­[TZ7^,K T }Z7T[ ^  K XV V O „T [ V?T ^[ ‹Y „T K[ T ^K}YXZ7\ŒK K ‹ Y .
 TW­V K}K ;Y VY U„T ^ K I VT ^^ „T[ I^uK T [ _ Y V TKšZ K­K V ^.[ ^* K – KgO Y ^  O  [ R\ T  ?T  ‰K YX\
 







 





 






 





 

















 



 


  

 

 


 
 









 

 
 


















 



 








     


   














 





  












 


 






 



 



 
  
 

















 















   
 



 







 




 



  
   
 


  

 











 

 



 









 



 





 

 



 


U

¥T  ­K e O~> I H ^ Y;Y „T [ ^ KDY  [ $ [  KDK  [$














    "! $ #&%$ ( ' )%
* + '+ %(' ,'-! & ' 
.&
 <7)7' NV‡X 07C>+ N G I$8





K0ZL Y []Z„T YX\ ^K  [ [ V V [ K7Z \K^ YI[K ^ ^ K K^  ^ Y KVš O [ V K –[]\X[ ILV []­\ [ ‰\gILKg[]O \  ‰KK T^ ^ ^Y K? T –YT ^ Y ^ \ K[]\Œ„K T [ „V T [ [V  [m[ ZLXYV „–T Y YXT K \ ^^ OO
 aB`ba%pNafBadadv8sGˆBlRq ƒ*fg]aB`]l>a\{R^*q s.n f>n f,wol*`baov*ai]es.n q cy]5jBaM^0`blR^*aB`‰]2n adcl0‡q n /Jƒ.n vHw%ai]es*q c

žKNY


  





[]Z T

_]e @g@?@ _

 
 

 

  


 


 

fO RY S K T


  





 



 

   





 





wLngi"v"ˆ‚t¨0“–noi"y ˆ‚•„"ngt(x¬•„5ngn7xowoy˜ˆ„• €,:tD€¬’oq lˆ‡7tDyWj ˆk„iy‹j jk„’€ wXx"t„k




P

Y Y ­[ „T \ ^ Y V K \ KY[”I[K
gO K ^ K1^ ) K^ Y \ Y*V$  YX[ZgXZXV\ T K  Y T K[ ^ Y K V V ‰[ [?V IYKXO K7\ Y K ^„KTWV š$4^[ ^ [ KV  K?Z Y^ V $ T K \Œ $L^ K T  KK.V4 YK ^VL^uT IX\ K

Section 2.2. What is fluid? Shear streass
 
      

 

 







 

R U W @CELF W F  

W @

U=T
4U



T FOB





FWF
U F F



 

F

 




T

FOB





 







 





UW

!






 






K —Y K;Y „T YX\ –K7Z ­K ^ K V „T [ V [«K   Y T „T [ VNe O c(T ^ ”T ILK V









1 3 T AW F @E F W T F FOB

 

T
AF

 






 



FWF
T @W
R B
F F
T AF zT F8B
 




7

  

#






 

"

#$

!






+ e O c/




+ e O b:/
a [ K¦K Z –K Y.^ ^&4 T ,–K˜T ^ Y Y‰V IK K [”[   ­[ YX^ ZgZY „­[JT 4 T Z ;–KY ^Š„^*T [  V­K [}¥ T Y^ ^Š^*L^uT‰[ VK $ T Y .K 47K Y};ZXY .^\ K¡^,IT ^ TWV Y  [ V(^ Z Y  V } Z Ž[ ^ ^ Kš O ii rqw=noqqp rui pxqjjov,{ i joy {(p }xr~q={ j zxVi wVj=ii xwujtq({Vx i{ j
%'&)(

&

*



 


  





1

&

,+-



/.

%

(

10

 

  
   



(

(

*

! + . ! ! 

(

/+-

2.






 

GF

'& 



23




 

  
 





 



54

   

^) Z74oK K K ^u T ) Y [ VV UI[­T[m\  \”T ;^I[K­K&\  Ž$ K‰7–KK T  $¨Y [N;^—Y Y TW^ V^.^ ­[ K Y 'V  K K V  K ¨Y L]VO{ Q \ K Y\ K IKX=O # V O K K ^‚K T }[ VZg[ \VLK –^[]^ K \”~ILIo[]Y O I¥„\ OT [ ‰V T ^ K [_ $ %;O I3K Y V $4^.^ KšKY[ ­K*^*[ \ [”g—[V
^ TWV*^ KY Y ­K
Y V K¡ILK [”[  YXZXZ –[J4 T ;Y K  
>%9H' $etJ+e

 1 5

+ e O /

Y  KZ   ?T ^ $4 K–[ [¦  .K Y 47„Y T [ }VUZXK ^ \ K Y^ [ X[ K V^  ^uYT }K DZXO \ 1K Y Ž[ V GK ;TWY V ^Š^ K¦[ VLI^ [K \ ~ Io‰Y „K T [ V '[ O ‰K  ­'[  K ¥T P`K –K V K0[ H;Y ^.^ K ^ K TWV
 [  *K Ž[ 5;Y \ K O I¥O

 
 1

+ e OA /




A@CB

A@ED

 



 



IH

 





  
 



 







 

KJ





%

NAOQPSR=T U7TV

 


 



 












 









 
  
 

%YX
Z



 



 













 



ML



OWR=T U7TV


  

NAOQPSR=T U7TV







%

OYPR[T U7T

V

N

%



OW\R[T U]TV

%^X
Z

=?>A@BD E F   

_ ' ,1+*<G I
,
N1v
H  %L >IG>  ' D 2  +V""
`
 >I "F"( 1 F1v
A+' , 5" %t ' Aa>1=ve 1= >A'"z" (K"(+vJ;1 
 b
1  "E5Y
>1 "@1 3>c 5"(1@ "@1=v
1 

Q R E9S TVU R>W
c E@ 1
1= 
 b
K1 3.e B


Z  Y V [ K £K.47Y}ZX\ K


  

aBq aiˆBa0s(f,k*mgq nn v*fBcuv Œ'wGpyj0s.aBf `baMm0fBjBlgapyj0fTsBv,sBco]5jB]5aGjBa1]2n w%woa%sBces*]aBfB`†v,l0aB_f0aB~u`bs*r0q ~B„ƒ*]q l>ƒBcdv*h‡aiwGˆ0aBsBq v*lRaH^>j.s*nq c>&]5q jBn ˆ*aGn f0rRr(`baukdsg„(]W]5k*j.agn n fBfBr.rTcos,jBa>]5ƒgj0]sBl*cy`hNv*~ulRs*fBf8a*| „ulRƒ n w%sBrRfBaHjBaHj.sgv


>b

=lq=yk9y q=x jo{ui#{jt{i wuq  joj9p x {=rui q  x y 



wLn?i"v"ˆtmU“–noi"yŸˆ‚•„"ngt(x¬•„5ngn7xowoy¡ˆ„• €,:tD€¬’oq ˆ"l‡otDjyWˆk„iy–j jkf’t wXx"t„k




[]Z T

   


_¥e @?@g@ _

fO RY S K T


 

 



76 98
> : ?<



98 ;:=<
78



 


 #



 

Chapter 2. Basic Fluid Mechanics

% .  !





”TWV K „T ;K Y ¬T $ T \Œ Y
‚K [0K}Z K Y V
”T ILK V¦TWV Z ­K"I T [ ^ K¡K.47Y}ZX\ KgO


 



 

 








D





!  +. 





  

% .!











K ^ K [ V¤a K*$ [ V \ Y*$ [M‰[ „T [ VšT ^ $ T K V ;Y K—Y „T YX\Œ NY ^




D










D

1



  

 





+ e O /

7T ^ K*4XZoY –K „T [ V”_ [ [  ^ K _ Ž[ † ?T  ZLY „T YX\ K ^ Y V K $ T K V Y ^





 






%

N







1






%

P

NGO

V

 









 







1 









%

NAOYP R=T U7TV

  

%

O


!  &
 



+ e O :/

%

[ TWV ‰ [ –K¡K.4”Zg\ T ^‚T T Y V K $ T K V Y ^



  



R[T U]TV

%%

+ e O~>D@ /



X
Z

!

S [”š[ 3.K 4”XZ7VK  KT K V^g¥K TWV KD[Y  7TW7V T ^ [7}T ^ ZX;\ K.Y 4 K ;T Y YX\ K T ^ T YX\WO Y `K Y
‚[ K ¥‰T I[ K¬–K IK <Y Vš TW^uV?T ‰T ;K YX^ \ K TWV Ž[ [ 5;[XY „[ T 0[ V¡^ .T ^› ^ KK"KV  ^ [ [3Y‰IKK
$$¨K ^ YT K V V „T YX[ TW\ V7T
[  V [ $  K TW;V K Y ^ –KDYK Y V;”K Y TW„V T K YX[\ Y  T \K ^ „K—T YX?I\ ^T K^ OzV —#„TWŽYV [ <XK V T KYX^‚\WM O3T ]V#NYXOM$Z T #WT–\Œ[ ;ŸQ YX^ Y ZX Z K˜[”­[K Y
T Y –[ KDY [KTK&K.P 4‰[ K K7V\ K V^[ J ¥^­['T[ ^.^ –K>^ ŽK[ K –KDK¦Y [  Z ^ K K^$ ^uT[ [V^
^ .[  $ PJO [šZ ­K ^ K V 7T ^ '[ }Zg\ K*4 T ^.^* K$ T [  [  V?TWV K ­KY  K "$ T K.4 YT;Y K;Y „T YX\ ! Z ^uT ^
















 
 






 



[]Z T



@ 



  

 

 

 
 




 



 



 

 

_]e @g@?@ _



 


fO RY S K T


  





 
 



 





  

  


 

 






  

 




  

























 

 



 













 

 
  
  


 





 

wLngi"v"ˆ‚t¨0“–noi"y ˆ‚•„"ngt(x¬•„5ngn7xowoy˜ˆ„• €,:tD€¬’oq lˆ‡7tDyWj ˆk„iy‹j jk„’€ wXx"t„k
















 



! + .& .&











 



 &

 
 

  

   !"   $#&%' 
() *
+,() - .0/ 1 %
23.45 -  678 "
8 $#&%'  0
89  / :; <
=
>@?BAB !" 
 . ;
;
;;
8- %C
&
D
;.8E>
";
F
G   / - %IH*.HJ.; . ;
;-.'KLBMONQP?, 
/&. 
)R
83.4H0*.OH.C .8;
8- 1 %S
G 1T"/78-1U.S )!"  )>V)VV1W
8X     

5>'P'P+$0

5.89?9'P+7-MG +

YZ\[ ]_^ ` abc+d0e`&f b+^$Z"ZIZ"ZIZ"ZIZ"ZIZ"Z"ZIZIZ"Z"ZIZIZ"Z"ZIZIZ"Z"Z"Z,Z"Z"Z"Z,Z"Z"Z"Zhg0i
YZ gkjmln'o abeOn;p&p nCpf1^qc0f n'eOr8p&`&f ^stZ"ZIZIZ"Z"ZIZIZ"Z"ZIZIZ"Z"Z"Z,Z"Z"Z"Z,Z"Z"Z"Zhg[
u0v wvyx{z5|_}y}y|y~JS€Q+‚ƒ<J„€ƒ<}y‚ ‚)…8‚†v9v9v9vv9v9v9vv9v9v9vv9v9vv9v9v9vGv9v9v9v w x
u0v wv w ‡0J„€mƒ<}y‚ ‚ …8‚ˆv9v9vv9v9vGv9v9v9vv9v9v9vv9v9v9vv9v9vv9v9v9vGv9v9v9v wCw
u0v wv u ‰Š+~J~J‚ ‹Bƒ=Œ0ƒ=€Q‚ hvv9v9vGv9v9v9vv9v9v9vv9v9v9vv9v9vv9v9v9vGv9v9v9v wOŽ
u0v wv Ž |y‚9‘…0|1€Œ’v9v9v9vv9v9vGv9v9v9vv9v9v9vv9v9v9vv9v9vv9v9v9vGv9v9v9v w“
u0v wv ” •@~ €Q‚ ~Jƒ<|1–J‘€Q|y„;~˜—‚)‹Q|y„™š‘C~J™q‘›\€Q‚)‹œv9v9vv9v9v9vv9v9vv9v9v9vGv9v9v9v wC
YZ Y ž>o0n8ef rŸJ`Qb+o0f eOpqZIZ"ZIZ"ZIZ"ZIZ"Z"ZIZIZ"Z"ZIZIZ"Z"ZIZIZ"Z"Z"Z,Z"Z"Z"Z,Z"Z"Z"Zhg0 
u0v u0vyx¡•@ƒD€QJ‚¢J„£’|y~q™+|y‚9‘Cƒ=€Q|y~+$|_ƒB€QŠ0‹Q¤JŠJ}y‚ ~ € ¥¦v9v9vv9v9vv9v9v9vGv9v9v9v w§
¨ ™J™0|1€Q|_„C~‘}~+„C€Q‚„C~©~ŠJ$‚)‹Q|y‘}>ƒ<|y,ŠJ}_‘€Q|y„;~ªv9vv9v9vv9v9v9vGv9v9v9v uC«
u0v u0v w |yƒ<ƒ<|_—J‘€Q|y„;~š‚ ¬‚ )€m„;~˜€QJ‚G€Q‚ $—‚ ‹&‘€QŠ+‹Q‚‹Q|_ƒ<‚­vv9v9vv9v9v9vGv9v9v9v uC«
W HF®¯ °>±²)°³²O´=µ)¶B·R¸_¹Cº¼» HF®)µ½>µQ°=¯ ¾C¶D¹ ·J·\µ&µQ¿ °À)°³µ)ºD°>·\¹O¸0³@®¯ ¶B±²OÁ Á µQ¿  ¯ ¶)ÃD®O¯ ¾C®GÄ)¸_µQ°°=ÅO¸_µÆ¿C¯ µÃ&²)°³¯ ¶)¾°Ç È  µ<³²OÁ Á ÅO¸yÉ
¾¯ à ²ÁC²O¶)¿IºB² ³µ)¸Ê¯ ²Á °>³@¸\²O¶)°@² ÃQ³¯ ¹C¶)° ËÍ̹CÁ1ÎÏÐ;Ë>È
)µ)Ñ ¸*Å ² ¸1À K  Ò;ÈÄÄ;Î0K K M  K K)Ó8Î0H3®¯ °F¯ °3²O¶Bµ=ÔÃQµ)Á Á µ)¶)³5µ<Ô²Oº ÄÁ µU¹ ·ÄO¹¹O¸
¸_µQ°µ ²)¸_Ã)®;Î µ)¸_µÈJÕC±F¯ Á ÁCÃ)® ²O¶)¾µm³@®O¯ °ÆÑO¹¹C´²OÄOÄ ¸_¹O² à ®²O¶)¿SÕC±F¯ Á Á ¶)¹ ³F¿C¯ °Ã)Å)°°F°=ÄOµQà ¯ Ö;úm¯ °³²O´=µQ°3±U®¯ Ã)®G²)¸_µ¶OÅOºBµ)¸_¹CÅ)°&ÎUÕ
±>¹CÅOÁ ¿$Á ¯ ´<µ¹C¶OÁ À³¹SÄO¹¯ ¶ ³D¹CÅ ³B® ¹&±×¿C¯ ºDµ)¶ °@¯ ¹C¶²Á+²O¶ ²OÁ À °@¯ °à ²¶9³²O´=µ©»*Ã)Á Å)³R³µ)¸_µQ¿ ØÄ ²Oĵ ¸Ù°=Å)à ®I²)°³@®¯ °D¹C¶)µ²O¶)¿,³@ÅO¸*¶,¯ ³
¯ ¶)³¹²m¸_µ&²OÁ Ú²OÁ Å ²OÑOÁ µOÎ H3®O¯ °5µ=ÔO²ºÄOÁ µF±3¯ Á Á²OÄOÄOµ&² ¸¯ ¶¶)µ=Ô ³²)¿O¿C¯ ³¯ ¹C¶ ¹ ·0³@®¯ °3ÑO¹¹C´ ¯ ¶D²Æ·Ê¹¸*ºt¹ · ;Å)µQ°³¯ ¹C¶m³¹m³@® µ°³@Å)¿Oµ)¶ ³QÎ
Ë0À)³@®)µ<±Ù²<À&È8³@®)µ²Å)³@®)¹¸_°BºDµ)¶ ³¯ ¹C¶)µQ¿9³@®²&³¯ ¶Û5Å)°³@¸\²Á ¯ ² ³@®)µ ¯ ¸¯ ¿Oµ&²¯ °3±¹¸*´)¯ ¶)¾ ÎÕ °5³@®)µGÄ® À)°=¯ ÃQ°DÁ ²<±5°U² ¸yµ¸_µ&²OÁ Á À ¿C¯ Ü0µ)¸_µ)¶ ³
¹ Ú µ)¸³@®)µ)¸_µ Ý'Û>°3³@®)µ9Ä ¸y¹C¹ ·>³¹³@®)µ)¯ ¸5ºD¹C¿Oµ)Á È8³@®)µ9¸_µQ°µ&² ¸_Ã)®)µ)¸_°mºDµ)¶ ³¯ ¹C¶)µQ¿I³\±>¹,ŶO´ ¶)¹&±U¶"ÃQ¹Cº Ä ²O¶¯ µQ°²)°U·Ê²)Ã<³5³@® ² ³F³@®)µ ¯ ¸
ºD¹C¿Oµ)Á0¯ °3±>¹O¸*´)¯ ¶)¾ Î  ® ² ³U²"¶¯ Ã&µGÄ ¸y¹C¹ ·  ·ÙÃQ¹CÅO¸_°µÈ0³@®)µÄ ¸_¹CÑOÁ µ ºª¯ ¶G³@®)µ ÃQ¹CºÄ ²O¶ ÀG±²)°Uµ=ÔO²)Ã<³@Á À9²)°F¿OµQ°Ã)¸Ê¯ ÑOµQ¿Þ¯ ¶³@®)µ
ºD¹C¿Oµ)Á;²O¶)¿"°¹CÁ Å ³¯ ¹C¶"¸_µ ;ů ¸_µQ°F³¹IÅ)°µB³@®)µGºB¹¿Oµ)Á1Î

/

/

ßCà

Chapter 3. Dimensional Analysis

u0v uv u ‹&‘…0|1€Œ˜‚ ¬‚ )€Qƒ v9vGv9v9v9vv9v9vv9v9v9vv9v9v9vv9v9vGv9v9v9vv9v9v u0x
JpQ`&f Ír;`QnCpb Æ` l nS`&f ÍnÞp)eOrŸ nCpf1^©c0f nÞeOr8p&`&f ^s ZIZ"Z"ZIZIZ"Z"ZIZ"ZIZ"ZIZ"ZIZhY[
u0v Ž0v_x €Q|y}y| | J$ƒ<‚ $|>™+|y$‚ +ƒ<|y„ ‘}ّ ‘}yŒ0ƒ<|yƒm›*„C‹ &‘O‹&‘C)€Q‚)‹Q|yƒ=€Q|y9€Q|y$‚ v9v9v u0x
|y}_}y‚)‹ ƒG‘C—J—0‹Q„8‘  vGv9v9v9vv9v9vv9v9v9vv9v9v9vv9v9vGv9v9v9vv9v9v u;u
‹Q‚)ƒ<‚ €G‘—J—0‹Q„8‘C&’vGv9v9v9vv9v9vv9v9v9vv9v9v9vv9v9vGv9v9v9vv9v9v uCŽ
u0v Ž0v w DJ‚‹&‘O€Q|_„Cƒ„›3…C‘‹Q|y„;Š+ƒm€Q|y$‚ƒ< ‘C}y‚ ƒˆv9v9vv9v9v9vv9v9vGv9v9v9vv9v9v u;“
YZ žf Sf1Ÿ r;af ` Sro0o+Ÿ f n8cq`Qb Df n'er Cf ` Z"ZIZIZ"Z"ZIZIZ"Z"ZIZIZ"Z"ZIZ"ZIZ"ZIZ"ZIZhY
u0v ” v_x G„O…8‚)‹ J| +S‚ Š‘O€Q|_„ Jƒ v9v9vv9v9vv9v9v9vv9v9v9vv9v9vGv9v9v9vv9v9v u8
u0v ” v w ‚ ƒ<|y q„C› +—‚ ‹Q|_$‚ €Qƒ˜v9vv9v9vv9v9v9vv9v9v9vv9v9vGv9v9v9vv9v9v Ž8«
YZ žd Ír;a Sb Æc+f Ín ^ p)f b+^0Ÿ n;p&p9^0d +n apmZIZ"Z"ZIZIZ"Z"ZIZIZ"Z"ZIZ"ZIZ"ZIZ"ZIZ +i
YZ žd Ír;a Z,Z"Z"Z"Z"Z,Z"Z"Z"Z,Z"Z"Z"ZIZIZ"Z"ZIZIZ"Z"ZIZIZ"Z"ZIZ"ZIZ"ZIZ"ZIZ +g
YZ   d n;pQ`&f b+^pªZ,Z"Z"Z"Z"Z,Z"Z"Z"Z,Z"Z"Z"ZIZIZ"Z"ZIZIZ"Z"ZIZIZ"Z"ZIZ"ZIZ"ZIZ"ZIZ +g
YZ




















































&

'(

)



'(

)



"!$#









%



,

:<;1=>'>>?;A@
-/.102'3)4 516
798
2CBD3FEHGJI3LK$MON4L3

(*

+
+
+

PRQSTUQSVWYX%Z'[\(]^W ]`_
W \La%Q
b
cedf[W%a
dZ'gWihjZ\kX%Z'[`TlZmdS%X nocp S/qmb S
\rb a%]Dn



 
 

     
 

  








 
     


 


 
 
  

   !  "#   


 
&('   ) 
% +* ,
$  %  
'     -  +* 
  %. .
  

 + ,
 
(
 % 

/

   
(0* ,  '   (
 
   % /1















,
2&
" 3 4"


    (
 
5 .  
,
 
.  4






 
6* ,

4
4


* 8*  9"  *0*
71
  /
: ;
(  
      <  =   
 $
4" 

 * >* 









( 


%
? 4  4


@ 6*
 A*





 @ 


 B
 C
*
4
  6 4

"  









.



4

* !D
  4
 E  ' (

FD
       E

(
 G 
 
#  ;
(
          %    5  
 
  4



.





 @  E
'    
  +* :  ;



.

 
H
 
  A 
I %' ;
J
 LK   ß%M(N0à
IO M@PQ I1
      E   . 
.   F*
 ,
ßEQ   @<
  

 
O Q 


Q "  *  R*
yor wus=jtjtl9lu} iHr qz~r9x { {ui ru} l n=qq yr j 7i x y w=q l=y yj x jo{

% 

.
       
 
 
E  =k r ivj vk9p qy q={=i rui x jt{
   S 
   ( @  
  21 '   
.   EU4
 H S 4 .

   H  .
 @T*  S ,
 @
.
1
* %  '   
 
; 
 +* / ;
( 



.


G   EU4
 
1 2
,
F  
*
.










.


G   EU4
 V1
$
F 4
 '   V*
W 
%      ;  X*
.


'    '   <*
 


.
.



Y  '  ( * ;  
(

;
O P <D  
    H   




( 
* @ '   +
 <

.






K
K
 '  ( E
RZ[
 
 ßEM\N(Q


F*
 #





5
K
\ 3 , '   " *
 Q

 
S] , 3 4
D Z
Q 


^   '    > '  ( '   _ 
2` . a1 
 *
:D   K  *   
  Q b  7c 4
 3 4
 ß%M(d@N 




.


  feSg
] h1 + *  "  2 , S *
@
<B



K jilk m Q
m poqprts!{
%U
 eSgEn2oqprts 1 eg
uvwyx
uzsW 4
   
 6B
    n+oqprts   uvwyx
uzs H1 . ,
@  n+oqprts   uvwyx
uzs 
,
m uvwyx
uzs  7
  h
  h


 4, 

  !*
.   %U

 < ;
 K c 4
  D
.   %U
 
ß%M(d@N(Q +1

. 
  4,  

 
,
W . 

  V*

;
 |
.






FeSg


4,
2 *


?

N

N

4

4 .

7.

I

N

.

'I

I

4

N

4

4

.

3

@

-

-/.

N

.

N3jI

-/.

.

.

@

7.
3jN

4

76N4L3

N
Im3r-6

I--.

- I

7

6 2
E

N

I-
4

5

.

-64 N

N

4 .

=

I

. H4

Bi4

4

.

5'N
3

7%4

N/7 -

Bi4 N

4 N

4

-/.

-/7N

.

.

N/7N3

5.

76I
7
I

7 I

N3

7

4

.

5

-I

4

N

;

7.I

3J-/.

N

4

7 I

7

I
7%4 .

-

I
7N

4

N

EDMO.

N

N

2

Nm3rI

3jN.

;

3

6N4 516
7
.7

0mNm3)4

;

;

76N

76N

I

LE

4

? A
7

E

.

4 N

.

3

N

F3jNN

)I

N

.

4

3

M

I

I
7N

76
N

3 7 I

2

5

7

.76
N3

2N

0I3rI

@

2

4

N

Nm3J4

-/.

4

0m.

2

I

"Im33 4 5

N/7N3

64 -6

I

73j.

N

U@

2`76N

@

0m.

7 I

7

N

.

N

I

.

2

7

4

H6N
4

;

5

0f6
2 4 -I

0mNm3)4

76I
7

N

mN

I
7%4 .

@

/N

@

N
-7%4 .

?E

E

4

E

i3jI

3jI
7N

N3

I

E

4

4 7 2

D4 N

0I3)4

5e7

-7%4 .

.

.

k76
N

2U7.

64 -6(-/.

-/.

5

;

f0

-4 7 2(4 iI

5.

4 72 E

"I 7%4

N76
.

D513j.

.

H64

N/76.

.52

2Y.

5AE

N

3jN I

7%4 4 NH76m4
I

N

I
7%4
NN

Nm3jN



7 I

.

I
7%4 .

-/.

NN

N

N

4

76
N2

N I

H6N

1.

7

E

H4

.m7

4

4

.m7

I-/N

N/7N3

E

N

7.

4

E

.

7H0Im3rI

6I

4

`6
NON

f04

6m4 -m6`76N

3 7 I

4

Nm3 7 I

iI
7Nm3kI

N

N

I

0f0

7%4 I

I

76I
7

@

513j.

I

N

6If0
7Nm3FE

- I

76N

7

-6

0mNm3)4

H6N

E

7%4 I

/6.

E

3jI
7%4 .kE

7N

4 kN3 N

N

2N

7

N3 4 - I

N7 I

.7H6I

I
7%4 .

76
N

3

N

N

5

0mNm3)4

76
N

iI

8

N mI-7

I
7%4 .

.

4

4

5AE

4

6.

.

.

4 kN3 N

7

N

7H76m4

H4 76OI

N

I

E

5

Nm3

76.

7

-3jN I

@

-I 7%4

N I3j-m6
N3

4 7 I
7%4 .

4

N

7.

;

4

4

76m4

N

5ON

-N

5

5

4

Nm3

;

7

@

4

76I
7

7.U76
N

JN

2

4

Nm3

`4 76C76N

5

iI

;

I

I
7%4 .

5

3jN

4 7

516.

3

-N

7 I

I

.

N(3jN

5YI3 NC0m3jN

5'.

73 .

0

9@

7%4

I

N mI

3

N

3rI
7%4 .

4 7 2Y4 `5

7.O76N

0mN3

I

0mNm3)4

-I

3jN

.

7 I
7%4 .

7

76'3j.

4

Nm3

- I 7%4

I

4 N

N
Im3r-6Nm3

N

4 N

7.

/6.

4

3

3jN

4

0m3j.

N

Ni5'.

N

I iI3 NH.

.

-

5'.

%I

4 N

.7

I3$N/7

N

4 (4 Im3

-7

fI

5

4

.76
N3?4 O0m.
N3

7.

7

76
NUN

-7%4 .

.

N

-.

4

A ;

N

A

-I

N
I

O4

73rI

-6If0 7N3i4

4 N

7N

N7Nm3

0mNm3)4

N

"76N

`4 76i76N

4 N

-6

4 NY-I 7%4

-/N

7

4 N

.

64 -6

NH7.

I3

1.

?

7.

I3 N

N/7N3
E

N

N

7.

N/7N3 ^4

7%4 4 7 2

5O76
NU03 N

7

0I3jI

64 -6o4

7%4 .

3 2(4

N

If0f0

0mNm3)4
N

.

N

I
7%4 .

7 I4

I '4

76I
7H3jNm0m3jN

I
7N

6I

@

7 I5'N

76N

6.

0I3rI

`6m4

2 4 iIf0f0

N0m3jN

N

4 /N
.

6 2e76
N

@

D0I3rI

7.U.

0I-/7%4

76N.

G$.

H6N

I3jN

N

I

?

N

@

`4

A

76N

Nm3rI

N -/7%4 .

E

-/N

f6N I
7

7.

5'N

-/N

I

0m3j.

4 -

-/N

N

.

I

5

73j.

Nm3jN

N

0

4

I

5

N -m6I

N0I3rI
7N

I

N

fN

4 .

7 H76I
7`I3 N

0I3 7%4 -

N

5

(3 N

0mNm3)4

4

N 4 5

E

.m7 +

N

'3jN

N'E

6N4 516
7

-/.

5

2

I

I

4 Im3)4 72

4 I

0m3jN

5

N

76I
7

m76N

3

4

N/7Nm3

6
N

4 (4 Im3)4 7 2

^I

0m.

5

2O764

N 4 5

I3jN

;

4 .

.

N -7%4

7.

5o-/.

3^76.

4 NY-I 7%4

4

5

7(7.

6
N

N

-/.

N

N I

-I 7%4

>

4

6I

I

.

@

I r7N3A76N

76N

"I 7%4

0Im3rI

;

N

2

2 4

3

.

k76NHN

?.76
N3iI

;

4

I

76N

I

N f0mN3 4

76N

I3 4 2

mI

5

N

NY6
.

.

7

N 4 5

N

@

7

76N

N f0mN

5IY513jN I
7

D0'6
2 4 -I

N3?.

N/7N3

Nm3rI

3 7 I

0m3 .

N

@

iI

3 4

N I3

7D.

N7Nm3 iI3 NO0I3jI

N

;

N

0

0m.

.

764 `I

-6If0
7Nm3

4 ^-I

0

N mI

4

7.

I

I

E

N

76N/2

6.

@

@

N

I

?

O0 7%4

7%4

4

2 4

Nm3

76
N

IC3 N

.

.e- I

N

N

I

4

N

H4

4 NU-I

N

I
7%4 .

76N

N

I

.

N

3 N

I

3jN I

7

4

@

7 C4

.

N -N

Nm3rI

3jN

.

Im3 7%4 -

N 4 5

3

I
7F7N

4 N

76I
7HI

2

3HI

E

0Im3rI

0I3jI

N(764

N mI

-I

764

.7

I

.

3

.

N3jI

I

.

I

7

6
.?0mN

764

7

@

2 4 O6I

E

N^I3 N

.fN

.

I

N76
.

7.

3

7 i7.

.YI-64 N

H64

.

N

4

7N

;

4

F3j.

7 I5N H.

;

4 .

4 .

2OI

N

7.

73jI

7 I

.7N iI

.

2 4

4 .

6I
7H4

N

N

7

N

I

?I

5

I

7

I

.f.

N

N '4 7(4

-I

4

I

I

@

I

4 7

$.

I

4

7O.

4

4

4 .

76
N

76I
7^76N
I

;

I
7%4 .

Nm3FE

I

@

0mNm3)4

N

N
Im3r-6.

-

I

4

3jNm0

3 N

7 I

N/76.

76m4

E

N3 4

4 .

N3

5kE

.

-6If0 7N3`4 Y4
N

C

4

;

.

Im3jN

4

7.

I5'.O764

.7

@

Nm3 7

4 .

76N

m4 7

7 I

`4

-

`6m4

Y4

.

N76
.

N 4

-

7.

2N I3

NU6N I
7D73rI

BD3FE

-6If0
7Nm3FE
@

4 /6N

I5

2

7

4 r72
N3

N -/7%4

I

0Im3 7%4 I

3 7 I

2 4
E

76m4 HN 7 I

.

A

D76
No4 O0m.

I

4

73j.

76N

5CN
N

I-/7 I

73j.

A;

4

5

2

76
N

I
7%4 .
.

4

4 7.

3jN

-m6I3jI-/7Nm3)4 7%4 -

}=ÛÃ<³@Å ²OÁ Á À&È ~J¸_¹ ·XÎ €JÎ >Î ‚3(Î €CÃ)´<µ)¸y³D¯ ¶ ³@¸_¹¿;Å)Ã&µQ¿Í³@®)µm¿C¯ ºDµ)¶)°=¯ ¹C¶ ²OÁ²¶²Á À)°=¯ °3³¹"³@®)µm¿C¯ µ Ã&²)°³¯ ¶)¾ÍÁ ¹C¶)¾,ѵQ·\¹O¸yµºDµOÎÆÕ²Oº
¹C¶OÁ À9®¯ °UÂQµ&²OÁ ¹CÅ)°U¿C¯ °à ¯ ÄOÁ µOÈ0²Á ÁC³@®)µÃ)¸_µQ¿C¯ ³°=®)¹CÅOÁ ¿I¾¹³¹,®¯ ºÎ ·>Ã&¹CÅO¸_°µÈ+²OÁ ÁC³@®)µGº ¯ °³²O´<µQ°² ¸yµºm¯ ¶ µm²¶ ¿Í¶)¹C¶)µ¹ ·F½5¸Î
€Cà ´=µ)¸y³<Ø °&ÎÙÛ5Á Á³@®)µB³ÊÀOÄO¹°¯ F¶ €CÃ)´<µ)¸y³<Ø °DÄ ²OÄOµ)¸±>µ)¸_µGºÆÀG¸_µQ°<ĹC¶ °@¯ ÑO¯ Á ¯ ³\ÀFƒÊ³@® µ)¸_µ ²)¸_µºB²O¶ À ³\ÀĹ°t„Ù·\¹O¸±F®¯ Ã)®,Õ ²OĹCÁ ¹¾¯ ÂQµOÎ
… HF®)µm¯ ºÄ¹O¸y³²O¶)ÃQµB¹ ·ÃQ¹Cº IJ ÃQ³UÄ ¸_µQ°µ)¶ ³² ³¯ ¹C¶,Õ ² ³R³@¸Ê¯ ÑOÅ ³µD³
¹ ~J¸_¹ ·Î ,ÎËJµ)¶ ³Ê±3¯ ³Ã)®±U®)¹G±²)°FºDÀºDµ)¶ ³¹O¸¿8ÅO¸Ê¯ ¶)¾IºÆÀ
ºB²)°³µ)¸°³@Å)¿C¯ µ&°&Î
† ËJµQ°@¯ ¿OµQ°Gºm²O¶ ÀIÃQ¹C¶)Ã&µ)Ä ³@Å ²OÁÙÄO® À °@¯ à ²Áº ¯ °³²´<µQ°Qȳ@® µ"²Å)³@®)¹¸_°9® ² Ú)µ"²IÃQ¹C¶)ÃQµ)Ä)³@Å ²OÁºm²&³@® µ)ºB² ³¯ à ²Áº ¯ °³²´<µOÎ HF®)µ<À
ß%M
P

QS/T

QSVWYX%Z'[\

]^W ]`_
W \La%Q
b
cedf[W%a

dZgWDhjZ\AX%Z'[`TlZmdS%X nocp Sqb S
\jb aFWn

:<;
-.10/2f3)4 516
798

=>>'>?;A@

2oBD3FE

GJI3LK$MON4L3

:



;:





I<



Chapter 3. Dimensional Analysis

H 


.

76
N

I



N

 

.10mN

4


a

5UI

 

.m7DI

4

  
-

76N

0m3jN

 * 

'3)4 /N

0m4L0mN

1.

   
(




I

76
N(I

76
.

3 HI

N

E



 


D

2

D1

 4
SO ß  Z
4 5

  "

f3jN

AE

A.



NO4

7.

4 '  

76
N

6.

N

N mI

0

N

.  '   @ $ 

.

 4 K > 
RO ßQ 1









 @
%U

7" * ^*
  

@





.


Y





,
%U





*

4 
h1
    %  












W
a
S* ,
4  







R  ,
;  ,  *
EU4

W
* S 
 6
    
 W)
^
$  X1 , *W 

 *   @*
         
4  
' 
$  
V]   2* ,
E
* 
%U
 4 M(M ß
*
  
 S* ,  
 +   S  


 8   '  
@.  
    9    
 F  





.
#

.



,


 


*
(

 @
 a

  4 G 
  
   ^
 @F    

2* , 
E.
1 


4"
a  @F z %U

      ! 












 .

N/7

.

N

7 I

764

N
-/.

03 .

.

@

3jI
7%4 .
N

N

iI

7 D7.

76
N

N

0m3jN -N

-

4

4

I

.

H6f3 .
4

5

76N

-

E

4 .

4

.

N

5

I

-I

0

7%4

.

7(76N

@

3

.

6N

.

7.

3jI

76N

Nm3rI

-/N

>

4 7%4 -

E

7.

N I

-N

C76NR3 N
I
5

N

7

2

4

>

76N

3jN

I

N3

H4

76N

3

I
7%4 .

4

N

fI

3jN

F3j.

7 I

0

;

5

N

4

4

76
N

N

4

N

Nm3jN

-

-/N

I

2 7N

03 .

4

N

.

I

N

4 N

2

N

I
7%4 .

I

N

;

76
N

?I

4

I4

.

7.

7.

;

3 N

4

I2(76I
7

`4

N

NH76N`7

.

4 7E

3jN I

DI

7.

6.

N

N

H4 76

'3 76
N3

N

@

6I

NYI

Nm3"I

3j.

I
7N'E

-m3 4

LE

@

76N

N(N
7N

N

.

N7Nm3

7Nm3"76
N

N

6
N

7.

I
7F7N3 N

7

3

@

N/7 -E

4

N

.

E

^76Ne3 .

Ne0Im3rI

.7^N

N
I 4 2

AE

.

@

7.O.

-/.

'3jN

2U.

4 .

I

N

7N

4

4 5

N7Nm3

H4

N

I

N

.

N

2(.

7 I5'N OI3 N

-I

4

2 4 H-I

7F7%4

4

.7%4 -/No76I
7

N3

I

.

N N

4 I

NO76NU.

76NU3 .

5

I

4

764

76m4 DIf0'03 .fI-6
.

2

I

3j.

76I

;

N

4

N

76N

6I

76N(3rI
7%4 .

@

4 .

N

7.

.

6N

N

NY76NoI

Ne4

4L3 N

".

H6NO3rI
7%4 .

4 7 I
7%4 .

E

.

0

;

4 O3jN

LE

I3^6.

N/7N3

I3 5'Nm3J76I

76
N

NN

0 (7.

7.YI

;

7.CIY-
4L3r-

0Im3rI

N7Nm3FE

IC3jI
7%4 .
I

.

2e4 7

4 I

.

H4

5C0m3j.

3

N

NY4

7

-/7 I

6.

.

7.

F3j.

5CIe3j.
.

N'E

76
N

4

N

6N

4

.

N

^.

7F7%4

7.

76I
7

`4 76(7.

7OI

N

7.

N(3j.

-m3 4L0
7%4 .

4 N

5?6
.

N

.

4

NO.

4L3 N

i76Ne6
.

I2

N
I

3jI
7%4 .

0

N/7Nm3

N(- I

`6m4 DI

N/7Nm3

.

4 I

N3?76I

5kE

6N

4 I

N

Nm3".

7F7%4

1N mI

4 7(4 U3jN

N/7N3

3j.

I

4 I

;

N

4 I

76
N

76m4

.

IU73 4

@

76
N

3jI
7%4 .

@

N

0

4

Im3jN

A

0m3j.

7

4 I3

-/.

@

;

N

76NO03 .

4

@

N

4 7 I
7%4 .

Nm3 7N

7.

E

I

5AE

³@¸Ê¯ µQ¿³¹ ²)Ã)®¯ µ<Ú)µU³@®)µU°@²OºDµ²O¶)¿!#" ¶OÅOº ÑOµ)¸_°3¯ ¶³@®)µÆµ=ÔCĵ ¸\¯ ºDµ)¶)³°Ù²)°Ù¯ ¶m¸_µ&²OÁ ¯ ³\ÀD·\¹O¸Á ¹ ± Ä)¸_µQ°°=ÅO¸_µÆ¿C¯ µUÃ&²)°³¯ ¶ ¾ Î%$F®)µ<À
¿Oµ)¸Ê¯ Ú µQ¿$µ 8Å ² ³¯ ¹C¶,·Ê¹¸5³@®)µÚ)µ Á ¹Ã)¯ ³ÊÀ͸_² ³¯ ¹ÞѲ °µQ¿$¹C¶Iµ ;Å ²OÁ&,¶Oź ÑOµ)¸_°WƒºD¹C¿Oµ)ÁJ²O¶)¿Þ²)Ã<³@Å ²OÁ „<Î'$F®)µ<ÀS® ² Ú µ¿O¹C¶)µ³@®)µ
°²OºDµD·Ê¹(¸ #"¶Oź ÑOµ)¸_°&)Î $3®)µ ¶³@®)µ<Àµ ;Å ² ³µ ³@®)µBÚ µ)Á ¹Cà ¯ ³ÊÀ9¸\² ³¯ ¹IÑ ²)°µ&¿"¹C¶Gµ ;Ų
Á *m³¹GÚ)µ)Á ¹Ã ¯ ³\À"¸\²&³¯ ¹,Ñ ²)°µQ¿I¹C¶µ ;Å ²OÁ
#"¶Oź ÑOµ)¸_°&Î +¹ ±>µ<Ú µ)¸Ú)µ Á ¹Ã)¯ ³ÊÀ9¸\² ³¯ ¹IÑ ²)°µQ¿I¹C¶µ ;Å ²O,Á  ¯ °U²mÃQ¹C¶ °³²O¶ ³²O¶)¿9¿O¹CµQ°FÚ²)¸yÀm±F¯ ³@® ³@® µB³@ÅO¶O¶)µ Á8¿C¯ ºDµ)¶)°=¯ ¹C¶
ƒR²)°Æ¹CÄOĹ°µQ¿,³¹9¿C¯ °³²¶ ÃQµ ·¸_¹Cº ³@®)µ°³²)¸y³¯ ¶ ¾ÍĹ¯ ¶ ³QÎ „<*Î $3®)µ ·Ê²)Ã<³3³@® ² ³F³@® µQ°µ"¸\²&³¯ ¹°D® ² Ú µB³@®)µ°²OºDµB°ÀOºÑ¹CÁ °F¿O¹µ&°B¶)¹ ³
ºDµ&²O¶ ³@® ² ³5³@®)µ<À9²)¸_µ¸_µ&²OÁ Á Àm³@®)µm°@²OºDµO&Î $F®)µQ°µB³\±¹"¸\² ³¯ ¹°Æ²)¸_µB¿C¯ Ü0µ)¸_µ)¶ ³U²O¶)¿"à ²¶¶)¹ ³ÆѵBµ ;Å ² ³µQ¿Î

/

/

:<;1=>'>>?;A@
-/.102'3)4 516
798
2CBD3FEHGJI3LK$MON4L3

/

/

/

/

PRQSTUQSVWYX%Z'[\(]^W ]`_
W \La%Q
b
cedf[W%a
dZ'gWihjZ\kX%Z'[`TlZmdS%X nocp S/qmb S
\rb a%]Dn

/

-.

Section 3.2. The processes in die casting







    
 ) 

 


G
ßEQ $ , 
.
1



 ,
 
  
4"    :
   S*

.


  X1    
@
%  [
 
 W 4, *  
 > /  . Q  * (,
 . @



QO $ , 

2   \)Q $ , 
 .  *W 
P(Q 4 $



K
%   
   $
  Q
.  # 
/ 







%  %  
 



 

.




$
ß
  
O * F* 4
  "
 ;

  4
" 
E. 
E   




 
%  % F  $


 
S  
  
  
 *    
. @4
  W ' <



.

.



(
%
@% 4 4

 
@ 4

.







 V  X1 !" @ 

E 4 

4
  K 

   
G   %U
  % " 
   ,
 Q [1 H
. %  G
' 

;   [1
%  

F *    .
(


/

.







E
^
V*
 E  * , %

*
  












Y

4,
*  

'  
  * (,

. 

. a   
 EG
   *2 %  



 

7 *    % 
. @f
  

 



  
  @

-  # 4

(  
/  
.  h  @ G 
.


  

 G   .  *  



.      
 '  

 


EG
1



H6N

4 NC-I

4 kN3 N

-I

4

H64

.

3

4 4 .

-N

.

-/N3

4 N

0

;

N

76N

76N

6
.7

4

N 7N
.

7

@

4 7

513rI
N

.

5N

N'E

4

6N

.7D-/.

.

3JN mI

0

N



I

4 4 .

.

4

N

-I
7%4 .

.

N

03 .

I

.

4

I

5

.

4

6m4 -m6oIm3jNC-.
@

-6I

3

73rI

Nm3

0m3j.

7N

R@

N

.

4

-I
7%4 .

76N

.

.

4

-N

N

7.O7 I

4

5

576
N

0m3 .

76
N

2

. `4

4

-I
7%4 .

E

4

;

N

76
N

4

-/N

.

-/N

I

73 .

2 7N

I o4

N
I-6U0m3j.

$76N

Nm3k4

N3

Nm33 N

.

6N I
7

7i.

N

76N

3 N

0m4 -/7 '3jN

76NO3jN

-N

3?I`-/.

;

N I3

4

4

0m3 .

-/N

-/N

I(-

k;

6I

Nm0Im3rI
7N

-
4 72

0m3j.

7 `4

.m76Nm3

2

?76N

5Nm3

N H3jN

;

76N

.

0

N

2

/64L0

0m.

K

N

76N

7

E

0m3jN

N

'3jN

4 I513rI

'0 K

I
7%4 .

73 N
I

I
7

N

76m4

4

76N

- I

N

E

A;

6I

N

0

- I
7%4 .

2O6I
I

@

;

N -/7N

@

N

;

N

I-/N

4 i76
N

E

7%4 .

N

0m.f.

3

1.
.

N

7

N

E

4

76N

76
N

.

0

7 '3

3jN

76N(0m.
N

2 7N

.

0

76N

N^7.

N -I

4 -

6I O7.

73rI

N mI

f3

@

-N

.

;

Nm3rI

3

-.

-3)4 7%4 -I

6
N3 N
.

@

76N

N

N -/7

0m3j.

N 4 5

5N

-N

4 -

.

.

0I3jI

76N

4 72 E

3jNHN

2

.

76
N

0

N

.

@

-I

3

E

Nm3kI

.m7iN kN
-7

.

N

76Nm3jN

I

N

N

76m4 C0m3 .

7.

'0 73jN I

3

IO0Im3rI

-I

76NU- I

4

N

76
N

.76
N3"N mI

73 N
I

DI3jN

.

.

73rI

7.

I

.m76Nm3

f3jNU4

4 7 2

.m7

4 7 2

.m7N

4 72

E

E

I3

.

76N`-I

I3)4 2

N

f03 N

76N`-I

-

@

4 7%4 .

0I3 7%4 -

4

- I

-m3 4

1.

N

7

7.

-/.

.m7(73rI

4

N 4 5

73jN I

N

4

-

'3jN(4

Im3jN

K

0m.

N

76NUI4L3 5fI

.

N

4

`6
NO0m3 N

.

.

.

I
7%4 .

7N

2

4 7%4 .

F3j.

I
7%4 .

5kE

2

N

N

"3jN

7%4

R@

m-/.

73rI

7%4 I

7

7

N kN
-7

2 7N

.

73 N
I

76N
.

4

I
7%4 .

4

o@

N -7N

K

3

.m7

-I

N

I

.

.

N

7.

7

4

4 N`7.o6I

4 kN3 N

-6I3jI-/7Nm3)4 I
7%4 .
N

7.

0

76
N

N

4 N

73j.

.7

N3jI
7N

7

-/N

.

76
N(4

76
N

Nm3

-
4 72e4

N

.

E

H64

4 ^73
N

4

=

0m3j.

N

-N

I
7%4 -

3$76NU3

N

.

@

.

;

5

N

N N

I
76N

0

3j.

E

- I 7%4

7 f3

;

@

N

I

;

`3 N
I

4

N

;

7.

4 .

3"-/.

NN

-m6

N

76
N

I l.

7.

@

H6N

Nm3 1.

@

-I

E

6
.7

.

4

-/N

N/7Nm3

576N

I

0m3j.

5R0m3j.

7^0I3jI

4 72

4

7%4

7

N

I3 5'N

NN

N

4 I

5Nm3

@

N

-/N

.

73 4 -/7(76m4

3

N 4 5

.

.

N 4 5

73jN I

E

E

 !#"%$'&)(+*-,.(+/0&1,23*4*
54*

initial
stage

hydralic
jump

H

later
stage
bubles

air
entrainment

 4
/O   ,  @
4 5

1 2 *9 4
=

H6N

ß
P

1.

QS/T

F3j.

# 

<76
N

QSVWYX%Z'[\

I

f3 N

AE

=

4

/6.m7

]^W ]`_
W \La%Q
b
cedf[W%a

dZgWDhjZ\AX%Z'[`TlZmdS%X nocp Sqb S
\jb aFWn

5U.

N N

N

4

/ W  .

"76N

 . =



NH7.O76
N

4

.m7

/6.m7

3jN -N4

NN

N

. #;

N

-6

:<;
-.10/2f3)4 516
798

I
7F7N



7%4 .

=>>'>?;A@

 
4

2oBD3FE

76N



4 N

 

- I 7%4

GJI3LK$MON4L3

5

Chapter 3. Dimensional Analysis

?

A

  ( =  $  4 ? < * %  

% 


 .


 @ 

. ( E

6 * @S U4
   A 
4

 
   1 
 @


 
 

% 
*j
E *
  

  Q 
 .
    . K  $
 Q (  Q ,

k 

9kVj
 9k

  j  
 @
 k==jk      j 

 

 

 0q
(
*  ; U
      . Y ; U

Y $ 
   
 !
 "
  j $# j
%  
.

.
  
 a .   @
  @
; 
 6
   
  &' 
 !# j
( ) 

"   (* "(k


  j




;


.
0q
(



; U4

#  K
 ; . @ Q Y
k"

+"  $*   "&(
k  & j
9kok ,-

 .  )  Y






  Y


 
> U4
 *

4



.








*
'   H 
" *




%  
@



 H   4
  
     U
 

. 
1
8 
4

 @ EG
 a *
 
  @
 
  4  "  


%.
 H " +
%.
 f    / U
   
b  G







$
Y
 j/&
0 21

9k 3# j
 3   



H

4

%




E
'



E


@
&
  
 54   j   )6 7

 

. @
 W R    *
. 
i k 8 *

  





+k " 1'9#j,-,- ):
 H 4 a  a
  F *


 S* , 
  

 uj, '
;
19 j91 j ; j#
   " (  k  )<  j => :


.
=

.


i A5CEk D 8 Hc
 :
 @? B




=  E'  K ? C 8 iGF

      ;B
  @ 8 
K * IH QQ !1
 *
 
 
1
  . 
  
R @ !  $  

 
  . =  "  * .  
4  '
3 N

@

N
Im3r-6

-I

7%4

I

;

5

4

76N

0m.

7.

4

N
-I

3 7 I

4

3

7

N

k4

-/.

'3

N

N

lN/7

.

7

4

0I
7F7N3

I

-6I

5N

-/N

I

E

6 2

E

7.

9>"   & 
 
  " 
" 1<K  - +
  k
  jk
Lj"N     &   1( " &
   .%13M-  j 
   OP
  j7Q>  " 
-9#j,R 
  R   4 S
    =T N
 j
 K
   
; k  " 1 
4   j   ) .




V



&
t
j

k


'


"
W


L

"

U'  '" 
X

 # 
I
  1
&
  '" 
 V j
o j#$
  "
 
9#j,<v. jok   k
jN4   Y 

2

H6N

Nm3 2

6N I
7D73rI

4

.

4

4

4 7N

.

#

N -/7%4 .

N

76
N(-3)4 7%4 -I

3 .

N

NN

.

3

4

-
4 72

4

5N

4 HI

N

4

7O3j.

N

.

NfE

.

4

4

.

7.

H764 Y03 .

N

m4

N7 I

0

4

.

4

4

N

N/7 I

N -6I

4

E

@

5N`I

N

N

3

.

0m3 N

76
N

-/N

'3jN

4 NC- I

-I

- I
7%4 .

.

7Nm3

-

Nm0
76

N/7 I

7.

.

N

4 N

4 72R0

/6.

I2

C6
.

;

I2Nm3

76N

76N

76
N

5

6N I
7

NN

Nm3J7.

N

64 -6YI

7

I

4 7%4 .

5'N'E

I

NfE

NN

^76N

76NU4 O0m4

-m3 4 7%4 - I

N

7

73jI

3?I

@

I4 I

4

5

4

5

N

N0 76

4

N3

f3 4

5Y0m3j.

m4

-/N

N

7Nm3FE

N

E

76NC6N I
7H73rI

N

N

5

m4

N/7 I

-.

E

4

lN/7

f3 )I-N

N

I3 N
I

.

7

Nm3FE

-/N

iI

76
N

N

3J76N

N

7

.

5'.

7

.

N

.

4 5

4

-4 7 2

I
7 f3rI
Y@

N kN
-7N

76NU3jI

4

2

.

I

6
N3 N

4

H4

NY03 . '4

.e3 N
I

.

.

4 N

4 DI

76
Ne3rI

I

7

4 D76
N

I

I
7%4 .

-4 7 2

0 7%4 .

76N

2

F3j.

If0'0m3j. '4

N I3

.

5

0

5'N

76
N

I3 2

@

N -7N

-6I

3 7

1.

.

4

C4 YI

4

3jI
7NYI

I

-/7%4 .

04

5

N3

I3

1.

.m7

76N(4

4

I

7

6m4L0C4

4

76N

7 I

4

73jI

0m3j.10mN3 7%4 N

.

3iIC-.

f3 3j.

6N I
7

76
N

N HI HI

N

76N

.

5'NO4

I
7%4 .

-3jN I
NN

4

4

.

3jN

76N

76
N

-6I

N'E

Nm3

N3$7.

 * '  
(  * (,

K 6 
;O O Q 1
@  
%
    (

76m4

.

I

-I

A-m6I

5N

4 72

E

- I

7iI

I
7

0m3jN

N

7

N '4 72 E

J(+/0&1,23*4*
54*







 U4


N

76
N

5

4

-6I

4 7E

4

2O-6I

.m7NO76I
7H764

H6NO6N I
7i73jI

.

76N

NN

76N

N`7.(76
N

N -/7%4 .

@

4

76N

76N

.

.

-/Ne76
N

-/.

4 5

516

Nm3 7 I

.

6
N

4

I2oI

E

4 7N

.

N5?3 N N

F3j.

N

-I
7%4 .

N

76
N

3r-/N

`76
N

@

.

4

4 I
7%4 .

N

N

4 7 I

2

F3 .

.

.

76N

0

NC76'3j.

-3jN I
7N

0m3 .

73jI4

N

4

4 N

Nm3"7.

76
N

4

Nm3

-/NY.

If0f0mN I3

N

N
73jN

.m7

I

4 D-3jN I
7N

;

4

Im3jN

N

76N

I2N3

0

N

O0

I

3 7 I

5N3

3 4

.

F3 .

;

0

N

N

1.

7.

0m.

Nm3

4 -

@'@

76I
7O4 7

73rI

76
N

73rI

N -/7%4 .

4

;

N

N7 I

H6N4

N N

6
N
I
7

6
N
I
7^73rI

76
N

3jI

N

@

HI

76
N

-/.

6 2

7

4 N

@

4 .

@

N

4

6
N
I
7

N3 .

N(6I

H6N

I

4

I4L3

;

7

4

76N

0m.

;

7 I5'N

N

N mE

76
N

N

7i-Nm3 7 I4

0m3jN

7U3 .

I

7

76m4

.

76
N

0m3j.m7N -/7%4 .

N/7 I

1.

4 /N

@

No4 7O4

4 5

.

;

4

LE

4

0

'3jN

Nm3A.

N7 I

N I

N

E

N

H6N

EDMO.

-N

76N

5'Nm3

?E

7N

= 
S*
 
.



. 

N

.

.

N3

7D.

4

-
4 72

7 2f0m4 - I

3jN.

;

.

;

4

- I
7%4 .

N

N -/7

iI i76I
7i76N

7%4

76
N

 G   
$
  



S 4 $
%  

S

 @
y  !O X  

   


N

N

"76NU3jN 4

.

.

E

4

NY.

4

3i6
N
I
7i7.0mN

4 7 2

7 I

.

$76
N

-N

76NYI

-I
7%4 .

0m3j.

N/73rI
7N

-/N

.

IO7 2f0m4 - I

I4L3 5'I D4

.

7.o6N I
7^73jI

N3

3

4

N

I2Nm3

Nm3

4

 
  

 
 y  
2  ,



0
7%4 .

I5

4 7

76N(5'I



4

76NCI

.m7`0

4

I/2

I4L3 5'I

N

0'6I

I

I

4 O0m.

2 4

3 7 I

0'6I

N

Nm3A76I

7

4

76
N

NfE

Z\[2]'^`_@abaKc d<ce2fhg2i ij2kc dl+g2mVn/oo7fpm<lbe5qrfsd<l+g5dtd&lbouicvXwhcasxyod&gIizm<wb{-|>gX}~ocm}~e2f3d&c fzwbeXwhm-ij€{<o7bigX}~o6a
nzj\m<ig2nhm@eI|uxg5d&o{&cg2in/oie5q‚d&lbom-wb{<|>g2}opqrlbc}!lƒcm€„zfbe5qrfƒcf\d&lbom<}c o7fXd&c …/}pic d&o{!g5d&wb{<o†g2m
d&lbos{&ofbo7q‡g2im<wb{<|>g2}o@d&lboeX{<jXˆ
‰‹ŠbŒ

1
  4


  
.
k k
9
k 
9
k' 
j>
k  "  j!#zj j
 k ’- k   “- ” j 
 uj,h'    '4 "h

j
:
4

4 5

.

f3jN

N

@

7%4

.

N

5

;

3jN

4

N

AE

I/2 Nm3J764 -

I


"<# 
 

    H U4


V* R 4"
K
ß
E
Q
HO O  " 
 
   
(



"  
E' 
6 4" 

  7 U4
  *  7 U4
 
 K . H;
E R-   Ž‘

 %- 


H6Nm3jN

 j/ =j,R K
 " 
  j 5j #

 "

Xj 4   jN  ,$ 
= j ( "
#
!
 

%
9N j 4 

I3

N

0m.

76
N

4

7

H-I
.

F3jNN
4

Y@

.

.

I

0m3 .

N

-N

76N

If0f0m3j. 4

76N

50m.

I
7i76NO6N I
7^73jI

4

4

4

7

I
7N

N/7 I

I

@

.

N

e@

N3

I4L3

2

.

6
N

76N

F3 .

I-7

.

4

76N

6 2

I

5

4

I
7i76N

4

/.

76N

4

N(I

4



4

@ 

 + * 

: U4
  ;1 R 4 $
  *
@

 *
  

  
A Q

I
7.

3

-I

N(.

N/7 I

N/7 I

4

7.C76N

IY0

4 7%4 I

J7N

'3 )I-/N

4

I
7N

4

H4 76

7.

76N

N/7 I

LE

7N

O0mNm3rI
7 '3jN

I4L3"I

/6.

`6
N

.

0mNm3rI
7 '3jN

4 U-/.

7 I

4

4

@

N

N

7

.

I

E

•

Õ+® ² Ú µB·\¹CÅO¶ ¿I¹C¶OÁ À Ú µ)¸yÀ ·\µQ± ¹ ·5IJÄOµ)¸_°Æ¿Oµ&²OÁ ¯ ¶)¾±3¯ ³@®G³@®¯ °²)°=ÄOµQÃ<³QÎmÕ ·À&¹CÅ"´ ¶)¹ ± ²OÑO¹CÅ ³D¸_µQ°µ&²)¸_Ã)®9ÃQ¹C¶)ÃQµ)¸*¶¯ ¶)¾"³@®O¯ °
¯ °°=Å)µm¹O¸À&¹CÅm±>¹CÅOÁ ¿SÁ ¯ ´<µD³¹G±>¹¸*´ ¹C¶ ³@®¯ °F³¹Cį ÃÈ+ÄOÁ µ&²)°µm¿;¸_¹CÄ"ºDµD²9Á ¯ ¶ µOÎ
· —0ů ¿ÍºDµQà ® ²O¶¯ ÃQ°D²O¶)¿S® µ&² ³F³@¸\²¶ °·\µ ¸Ù²¶ ¿ÞÕ0²Oº ±²¯ ³¯ ¶)¾"³¹Ö0¶¯ °<®"¯ ³
– ÕJ® ² Ú µGºB²)¿Oµ °¹CºDµ µ)Á µ)ºBµ)¶ ³² ¸1ÀµQ°³¯ ºB² ³µQ°Æ¹ h
²O¶)¿I³¹IÖ¶ ¿Í
² ˜R¹CÅO¸*¶ ²OÁ±3¯ ³@®)¹CÅ ³Æ³@®)µI´)¯ ¶)¿Í¹ ·F¸_µ<·Êµ)¸_µQµQ° ºDµ ¶ ³¯ ¹C¶)µ&¿$¯ ¶Û3ÄOĵ ¶)¿C¯ ÔÍÛUÎR™¸3ÄOµ)¸*® ²OÄ)° ¯ ³U±3¯ Á Á0²Äĵ&² ¸F¯ ¶G³@®)µ
:<;1=>'>>?;A@
-/.102'3)4 516
798
2CBD3FEHGJI3LK$MON4L3

PRQSTUQSVWYX%Z'[\(]^W ]`_
W \La%Q
b
cedf[W%a
dZ'gWihjZ\kX%Z'[`TlZmdS%X nocp S/qmb S
\rb a%]Dn

--

Section 3.2. The processes in die casting

y

Shot
Sleeve

Temperature

heat transfer
to the air
process 1

heat transfer
to the sleeve
process 2

>;

 4
;O O 
f3 N

AE

N
I
7i73rI

 

Nm3

03 .

y

4 5

Solidification
layer

%   

-/N

N

/ W  .

4

76
N

6
.7

NN

N

(liquid)

shot sleeve (steel)

 
/O \  5 4 $
4 5

1

H6N

6Nm3jN

N3

4

/ 

@

G$.

5

N

 






4

4

4

insulation

 @

-I
7%4 .

.

S   .

76N

/6.m7

NN

N



7%4

N

% 

%

N 7%4

I
7N

  .

76N

NN

N

4

 
  





-3)4L0
7

I3 2O-.

 

p

.

 

I
7%4 .

 



76N

4



?E

.   %U


5.

p
*

'3jN

(solid)

l

Temperature

δ

liquid metal

N



4 7%4 .

U@

?E

.m7N

*

N/7

K O ßEQ
NN

 + 4

"  


y 

76
NU03 .?0mNm3 7%4 N



/  .

76N

N N

N

I

/6.

o@

N

7 I

76N(I4L3 5'I

N

.

/  . H

3$76
N

NN

N



I
7N3 4 I

LE

4

KO Q
F

?E

=



 

=

¶)µ=Ô ³²)¿O¿C¯ ³¯ ¹C¶I¹ ·>³@®O¯ ° ѹC¹C´ÎÕ ·>À&¹CÅG±>¹CÅÁ ¿ÞÁ ¯ ´<µm³¹$®)µ)Á ÄͺDµm³¹9Ö¶O¯ °=®³@®)µ±>¹¸*´G¹C¶9³@®¯ °BÄ ¸_¹CÑOÁ µ ºGÈÄOÁ µ&²)°µG¿;¸_¹CÄ,ºBµ ²
Á ¯ ¶)µOÎ

O
P

QS/T

QSVWYX%Z'[\

]^W ]`_
W \La%Q
b
cedf[W%a

dZgWDhjZ\AX%Z'[`TlZmdS%X nocp Sqb S
\jb aFWn

:<;
-.10/2f3)4 516
798

=>>'>?;A@

2oBD3FE

GJI3LK$MON4L3

Chapter 3. Dimensional Analysis

]

4



% 




.
K
 4 Q
 



 4U

6
N3 N

4

3jNm03 N

N7 I

.

H6N

5.




4

4


Nm3

4

5






76
N

I3 2O-.



 

N

4 7%4 .

s


H6NO5'.

.

.

-
4 72
@

4

4

 K 

4

N/7 I

^*

@

N7



N N

76
N

.

 Q

4

0'6I

N

K O \Q
?E

 ! 4







N

^*

N7

.

N N

"  
# U4
  []




? 
 E.
@

 % @ H U4
  . 
  
i    s      
    s 

 s

7.

/6.

76N

76N

-m6I

0'6I

s

4

N/7 I

4

N



@



N`7 I

5N

N

.

N D.

.

N

3k76
N

4

4

76N

4 72OI

4

N7 I

I
7 f3jI

4

N7 I

4 H5

4

4

4

.

4

4

0f6I

4

7Nm3 )I-/N

4

0f6I

  4


N

I

N -7%4 .

@

N



.

LE

-/.

.

N 5

N
-7

76
N

E

2

K O P(Q
?E



 

-I
7%4 .

4 7 2OI
7D76
N

76N

-7%4



4 7%4 .

?E

 

@[ 4  $ 
 
S 4 


@ H U4

   
.
%U
  = U
 ;*
.



Im3 2C-/.

KO O Q

 
 U


3$76
N



-4 7 2

Nm3

4 7 2O-m6I

.



-.

1



   

4

N

4


4 N'EYG$.

s



76
NO0m3j.10mNm3 7%4 N





7.C76N

  

6
N
I
7D.

4

  
   

  

 U

. 



.  




N

. 



4L3jN -/7%4 .

  

sn


I3

N

 

I
7%4 .



4 -




.m7NH76I
7

76N



N




I

G$.



s

 







NN



N

4L0I
7%4 .

I



 

6Nm3jN

4

.   % U


sn
*


7`76NC0mN3 0mN

  
   

 w rrBs

1

N

N

4 72

5YN

I
7%4 .

4

76N

4

N

 

`4 76

N5

N -7%4

 @
5Y.

 


76
N

I
7 '3rI

%.

?-/.

 

N -/7%4 .

I

5NO4

 



s 

j 
  
  "  jp  ,-  !Hj9j  &
 ”  1
 4
1
k 

9k$ j@k"%
& =j
   " 
  j
N9j" - #"
9kok   
  j
U4
 
 7j   (
  .



  
  

s


K O N(Q
?E

 B
     
(
 4   
G 

  ßQ $ ,  / W  . Q


O Q


   . 
$ 
(,
  . @  W 
. 
 Q Y   *  3 H"  *l;

 
K   W 4 $
4





  1 ? 


;

4
a 4 $
%  z
  . 

$  Y   $   
(
  $ 
  -  [* #"  *T
 =
  S
%$ ? 

. H  , K 
^  

=
#

  

R Q Y   ,
   

 


%

.






&

9k &Vj   OP  Hj9j  &
 ” 

G


A




A







4

(



 *
& =j  -  1

& =j *)


 * Q
 
 h1
 
@ 


7N '(
9' k9k    .
-     Q


* 
 

 
<    < 


2 "

   
 % .
 

(,
# *L h +
* $ ? 

1

 
   +1  

 1
 '  
"
>& "
 j'  0-,- 
( ( ( & ',

"
4 
  j~
  k" ! 
-
 #
`6
N

4

4L0I
7%4 .

-7%4 .

H6Nm3jN(Im3jN

4 N/7%4

5

N3 2

7%4

.7O7.
0

Y@

I

I

N

0I3jN

-/.

N

.

76N

4

7.

0I

I

7E

BD3jI

@

4

.

4

I

5

I D4

5

H6N

1.

3jN I

.

3

Nm3"- I

7

4

N

N

4

I

.

3 N

76N

.

0mN3 4 .

64 N

@

.

Nm3$7.

;

.

I

7

Nm3FE

.

76
N(6N I
7

H6NO6N I
7i73jI

3JN I

0

;

N

@

76N

NfE

76
N

H6N

0m3j.

N'E

I

;

2

76
N

?;

.

@

Nm3FE

I

N3

.f.

73jI

.

-
4 72

6
N
I
7

E

Nm3

@

N

73rI

4

Nm64

-m6

N
I
7^I

-I
M

N

@

6I

I

N

3jI

6
N
I

0(4

4 N

@

N N

N3

A

@

Im3 2

76
N

N

7

2

I2Nm3

7

0

73rI

Nm3

4 N

4

-

N3 7DI

. 
 ß Q  * * ? ? 

1 a * 

  F E  
. S*   *   
- K  
 +O P
 O N(Q W 

$ ,  
$  !
4

76
N

,.-""+*0/ , 1
,&*2


H6N

.

J76
N

6N I
7

@

N

I
7 f3rI

F3 .

.

2

4 -

0
7%4 .

.

0m.

N3

N

-I

I

76I
7

-.

76
N

N

I

76
N

I
7%4

N -m6I

0mNm3)4 .

N

5

3jN

4

4

76
N3

4

f3 4

N3$4

0

I

73jI

=

N

N -.

4

Nm3

`6
NO6
N
I
7

@

7

I3j5N

4 7^-I

NN

6N I
7

73rI

0

73rI

6
.7

-m6oI

N3 2

$76N

N'E

76
N

3 7D0mNm3)4 .

N

4

k;

5

.

4 7%4 .

0mN3 4 .

76m4 H-I
4

6
N
I
7

Nm3

4

7

4 7%4 I

E

If6N I

N

76
N

-/N

76N(4

I2N3

@

4

Nm3

.

@

Im3 2

7

4 5

7E

N

0m3j.

.

LE

N 5

N

7

-I
7%4 .

.

0(I

3 N

N

)I-7D76I
7

@

4 -

N
-/.

.

0m3jN

4

@

7.

76NU6
N
I
7i73rI

5'Nm3

N

I3 5

76N

0

.

76N

76
N

N

4

E

4

N -6I

N6m4

76
N

7O76N

Nm3)4

I

-I
7%4 .

2 /N

4

@

N

0

4

N

0mNm3)4 .

5

N kN
-7 OI3jN

N

I

.

I

-.

7.

N -/7%4 .

/.

k"X b =) k  
! j "   jj

* "  ~
 #

I

N

3

-6RI

N

7

f3 4

I .

@

- I

4 kN3 N

I

%I/2

4

-/.

4

;

N

I3 5'N

4

-I

76'3jNN

1.

4

5O76
N(- I

76N
4 72

3

Nm3

6N

76
N

2

7N

1.

6I

4

0m3jN

7.

@

N

f3 4 N

:<;1=>'>>?;A@
-/.102'3)4 516
798
2CBD3FEHGJI3LK$MON4L3

4

4

N

NN

4

7.

4 5

'3jN

N -/7%4 .
?E

1.

I

?E

E

H4 76

F3jNN

76
N

3 7

f3 )I-/N

N -/7%4 .

PRQSTUQSVWYX%Z'[\(]^W ]`_
W \La%Q
b
cedf[W%a
dZ'gWihjZ\kX%Z'[`TlZmdS%X nocp S/qmb S
\rb a%]Dn

=
76
N

-43

Q

Section 3.2. The processes in die casting

liquid
metal

air streaks

 4
/O P  & 
4 5

.

f3 N

AE



73rI

@W U


-N

.

4






4

N/7 I

'7.

76NU3

    Y  

EG 

   A    * #
  
:
E 


 . @
 uj"   ,$7   
- k
j9j #( j  U
 b
=
/  Y .
   k9j   I=jK* "(k / 
   * 
k
  "
' ' ~   
#
: S
e g 
 Q 2 .   "  y  F 
  F- 
@


9 *

  
  R 
(
#
E 4

       
 
  W* #"  * . =
   *
4
  
513rI

4 7 2CI

0f6
N
4

.

N

m4

4

@

I4L3iN

N7Nm3

4

N3

I

N

76
N

.

7N3 )I-N

-3jN I
7N
I4L3

N -/7

I4L3

.

N

0m3 .

I H-/.

N I

N

N

/.

.

5N .

3 7

4

N

@

NfE

;

N73 2(72f0m4 - I

2

I
7

@

N

@

I

@

N

4 N

N7Nm3D4

N

? A

Nm64

I

76N
@

7.

N

7

N

.

.

-4 7 2

/6.
I

6
N

N

- I 7%4

.

N7

N

  g 
( 61
C R* , "  * 
K
  
  4
HO P /1  H "%
    .  I1
.  < E  
4

 4

 
 ,

764 (-I

6
N

-Nm3 7 I4

.

0m3jN

7.




.

6N I

f0'0m.

I
7N

I
7No0I3jI

6I O7.

I4L3 5'I

-I

f

Z\[X]!^

4

NI
7O76N

76m4

E

.

N/7 I

.

N3

4

7E

-m6

73rI4 516
7

73jN I

N 4 5

H4 76

N

NUI

73jI

7`-3jN I
7N

-N

-Nm3

@

.7

6N I
7

73jI4

0m3j.10mN3

-I

73rI4

N Y6.

N3

.

7

N3 2

7E

?

N

7 2f0m4 - I

4

4 5

4

N

N

516
@

I

A

f3jN

AE

E

H64

76I
7

4 NU-I

7%4

H6N

4 7

N

76
N

.

Nm3FE

.

17.

-3jN I

76'3j.

4 7F7

@

NC4

7U4

N

N

.

7

N

64 516

73jN I

-
4 72 E

2

7i764 `4

76
N

;

5

H6N

7N

4

I

N /0mN
-
4 I

2

 j&   
  
 " 
  jvj#P 
 <" 'N 
$ j! 
  j #
# j
 U



5AE



&d lbo m<o7}e2fha blhgXm-oXktd&lbo he5q cf d<lbo {&wbfbfho{pm<jKm(d&ox cmWh{<o6m<m<wb{&c 7o7a gIfha d<lhod(jzbc}7gIi
{<wbfhfbo{€i o7f Id&lƒcm€c f e2{!aKo{€eI|‡FbˆA x $ˆ f\d&lhg5dW}7g2m<o2kc |‡qo†lhg Xo g ig2{ Xo 2o7i eK}~c d(j io~dsm<gj
A7F x 5m<o7} %ˆ lbo 2oieK}~c d(jaKwbo@d<e 2{!g 3c d(j†cm
bˆ x 5m<o7} %ˆ lbo
? fzwbxpn/o{ g2m&m<wbxyo7md<lbo
g2i wh;
o iGA7F  | e2{rqrlbc}!l X{&g zc d(jbigj g†i cxyc d&o7a {<eXi oXˆ


    



  


 ! "   # $

%





‰VŠKŒ

1
 
6 U4

 * Q 
K

H6N

N

5

4

76N

4

1.

Nm3j5

.

5

4

5

6
.

4

E

f3 4

%.   (--
 / 




( R %  Q  
   
^
  [  @

F*
  
/  Q  ,
 


-/.

NN3

N/7 I

3

.

N

N 4 5

I

76
N

N

-m6

7N

7Nm3 H76N

-7

I

76N(73jI

7 i7.C3 N
3

-/N

N3

2 7N

H4 76YIU72'04 -I

N -/.

;

7 I5N

.

4

3"I

N

/ 

 * 10 * .
Z\[X]!^‘_ 
2 4" 

   1
Q 
$ , 
*

64 -6O4

I

f0mNm3r-3)4 7%4 -I

.76
N3

4

5o0mNm3)4 .

.

.

1.

E

@

I
7`7 f3

4

.

.

.

3

N

N

-/N

N3



4 .

;

P
P

QS/T

QSVWYX%Z'[\

]^W ]`_
W \La%Q
b
cedf[W%a

dZgWDhjZ\AX%Z'[`TlZmdS%X nocp Sqb S
\jb aFWn

Nm3

-N

7

I

I

I

;

 *
4
 ?
@

.

4

Im3 2

2

kN/2

@

2

I

I

6I
7`I

N

N

4

1.

4

N
I

N

.

@

4

5'.

I
7N

Im3

-4 7 2

 *

 
1.

-7%4 .

2

Nm3

4 N

- I 7%4

-

76I
7

.

N(7.oIC0

;

76N

=>>'>?;A@

;

5

N -



 K


7.

76
N

7%4

N

/6.

3 7

f3)4

7%4

2oBD3FE

N'E

5o76
N




:<;
-.10/2f3)4 516
798

5

4 N

4

N

.

.

4 7E

I-7 I

.

 H  
B


I/2 Nm3D4

3*
A

I

I3

I

76
N

@

0m3j.

N

4

iI

5

() '"+ A6F-,/.
*
1.

2 7N

- I

I

>

7%4


=

7.3

N

.

.

76
N

H6N

4

@

4 N(-I



Nm3

  ^
( X  @ K *
>  
. *

(  
 .  @  

@ Q  :    * K 
,
 (
,

ß ƒ ; 
? H. 
'& A6F  S
~
 
6Z  4 



7 '3

I

4

eSg




K ,
 

4 7%4 .

76
N

GJI3LK$MON4L3

;

Chapter 3. Dimensional Analysis

pressure

 4
/O N    *  ^

4 5

f3 N

AE

.

4

3

  


;

 - 
  ß  '

"  %   P  ;E *

1

@

`6
N
76N

.

Im3 2

7%4

764 -

4
4

N

5

I2Nm3

76N
>

D.

4

7%4

76m4

=

E

- I

>

N(.

@

N`-I

>

E

*

N3

4

%  
- 

'3)4

5o03 N

f3)4
4

 

5o0m3j.

-/N

   f   $  
. (  ,
( 

4

6
! * S
  

NHN

N - "76
N

64 -6

#


6N

7%4

4

4 - I
7N

I
7N

-/.

76I
7

I

4 72

.

.

I

1. <4

3A7%4

NH.

(4

I

4

k76N
@

76N

3

7^0f6I

.

I3 2

Y  *


N'E

;

2'6.

I2N3

4 H.

76
N

Im3FE

‰‹ŠbŒ




,

 


 
 


Z\[2]'^

I



.

4

-

4 7%4 .

@

7 f3
4

.

4

I

N

@

N

       @
 

E   4


  
 
F*

N
4

N

-

4 .

4 .

-/N

0I
7F7Nm3

3rI

-m6

I

Y@

`4 76

I

kI

@

.

I

7

2Y0m.

.

76N(0m.

2 4

@

3rI

3

.

.

-m6m4

N 4 5

3

 <H
  
 
  

D764 OI 0mN -7
5e4

4

N 4 5

4

-m3 N
I

E^G

3rI

7 I

7 I

NU3jN 4 7 I

-m6m4

5

4

5  
 4
 <
 

( 
4

4 I3

N.

5
% 
 = * / *T *
$ , 
 (  


@
 

7.

73jNN7Nm3

7 Im3 7%4

-/NO4

3

76N

Nm3

5

1.

E

4

N

2 7N

0m3 N

-

H4 76

`4 7 -64

76
N

4

 *


7 I
7%4 .

.

.

4

N

4

N

5o0m3 .

4

5

7.

 
\

-N

-6If0 7N3

‰‹ŠbŒ


!*45%3&#1




 _ ;
   $ , 
 , ( ' ,
E . @   
 
Y , 
 O O ß
 


  
 
4
 K  ^*
 # * Q R  R

'  @ 

(  
* 2"  @f @
 
.     

E F * Y 
,
   

   
% !
 #T
N9j" % (k
ok 

4 - K Q ] 

 a 


R 
N9j"T
 j' “
  j   9k 






$
 &   T
N9j" >
   
   

  .  




4






X
1



*
4

- 
4   j   )
 W1 '   




 


 2 *

     K 5  4
 <O à(Q
?76N

4

Nm3)4 -I

@

7 f3

N

N '4 7N

-N

N/7 I

@

I

7.

@

N

0m3jI2U4

@

7%4

.

-N

I

N

76NY-I

E

3jN5

I

2

E

`6
N

- I

N

4

.

6I
7

4 N`- I 7%4

4 .

4 N

.o7

.

N

.

-/.

.

1.

.

7%4

5

N f0mN3 4

N

4 5

f3jN

@

2

?E

I

.

7`N -

76N

4

N -7%4 .

f4 DIf0f0m3j.10m3)4 I
7N

1.

f3rI
7%4 .

7

N

E

N

.

76
N3 No4 (-.

5(-/.

N N

5oI3 N

0'6I

4

K

64 NU76I
7

72'04 -I

7

.

4 7 2oI (I

0m3rI/2

7.

N

I
7%4 .

-.

J7 '3

4 N

@

4

I

7Nm3

NYI
7.

3"7 f3

4

.

N

I4 I

.

7

4

E

-/7 I

@

Nm3rI

E

`6
N

76NOI

76
.

N

2

O@

I

@

2

2CI

3

N

4

I

4 %-

.m7^I3jNO0m3jN

4 7(4 U03 N

4 7Nm3rI
7 f3 NYI

1. 9-I

3

.

;

N

AE AE

I
7.

.m76Nm3

@

Nm33 N

.

/6.

I

I

N

4 .

N

7N

2o5N.

76
N

.

1.

7H76
N

H6N

76N

N4 76
N3

76I
7

@

I

E

76I
7

7

4 N

H *
4

h1 ; U

H * * ,
   
 R  
; * 



5C76I
7`76N

4

m4

1.

`4

N/73)4 N

4

I

I

1.

.

4

Im3

7 f3

E

<¹C¶OÁ À¿;Ÿ\¯ ¶)¾³@®)µS—8¹ ±t¯ ¶m³@®)µ¸ÊŶO¶)µ)¸°À)°³µ)ºGȶ)¹ÖÁ Á ¯ ¶)¾¹

·>³@®)µBÃ&² Ú¯ ³\À
y¸ µ ³@®)µ ¹CÄĹ°=¯ ³¯ ¹C¶³¹9³@®¯ °D¸_µQ°µ ²)¸_Ã)®ݚÄOµ)¸*® ²OÄ)°¹C¶ µ ¹ ·³@®)µ9¸_µ<·\µ)¸_µQµ&°²)°Æ¯ ¶³@®)µmÛ3ÄOĵ ¶)¿C¯ Ô"Û
·\¹O¸³@® µ ²OÁ ÁCÃ)Á Å)µQ°BÕ0® ² Ú)µ¸_µQÃ&µ ¯ Ú µQ¿Î
Õ ˜Å)°³U±>¹C¶)¿Oµ)¸>±U®)¹±>µ
!

:<;1=>'>>?;A@
-/.102'3)4 516
798
2CBD3FEHGJI3LK$MON4L3

PRQSTUQSVWYX%Z'[\(]^W ]`_
W \La%Q
b
cedf[W%a
dZ'gWihjZ\kX%Z'[`TlZmdS%X nocp S/qmb S
\rb a%]Dn

-



Section 3.2. The processes in die casting

 +
 O \ ß V* , 2 * 
*
 W  -  . <  












$
$
K
  ,  + 
 4



 4 4

.


.


$
Y
 H   Q 4 %U
%
^* : F * 6
@
G
 * 
  #. 
Wc
( 4
 '    
 * 
  @

.
 . ,
# 

E.  >
E
/1 <    4


 S  *  (. ;  , 
(
 *
 
 )  ' 

 


K

  
( S 2 *  '  
0!
 K 0W
 ß%M(M Q Q f&('   



* " 4; 
  @  

 S*  


 N 3 K 5 
" 


.
%
ß
(
M
@
N

N
Q
] ,

 - *
  F1 t*  

'   







K
4  *

E % '   *



 
 
    F 
% .  
h*
%  Q
.     ^
   
  
,

 
/ / *  '
k"  &# "  P
 # 
  
&('    2 
 K  
   H 4F ß%M(d O Q *
4 -  +
 :    * 4





 B
 


 W *
!1  +B

 >   5 
*

 . 
'    S* ?  

.



?




  #*



@   
.    *
; *
  *
.

  
76
N

I

N
-7%4 .

2`.m76Nm3$0m3j.

7%4

N

- I

N

Nm3j.

@

I

.

7%4

.

5

3

I3 N(I
7.

7.

(4 I
7%4 .

4 N

764

-I

7%4

I

I

N

4

6I
7(4

N

0I
7F7Nm3

.





I4

If0
7

.



-/.

6I

N

0m3j.

-/N

@

I

N3 2

Z\[X]!^

d

.

@

3

2

;

4

N

.

76m4 D0f6I

`6
N

I4

.

7%4 .

E

0m3j.

-/N

@

4

4


I
7%4 .

.

7(76
N

.

7i76N

.

03 .

-/N

N

76N

-/N

N

4

N

Nm3

5

.

4 HI

/64L0
4

N f0mN3 4

@

N7

N N

7 `I

@

4

.

-

N

7

N

4

NU4

-/N

.

3

N

4

4 kN3 N
N

.

E

.

3

4 N

N

7 I

7 f6'3 N

.

4

I

N f0mN3 4

-7N

4

Nm33jN

0mNm3)4

76
N4L3

N3 2

-N'E

-
4 72

N

E

4

76I
7

I
7.

H64

N f0mN3 4

I
7%4 .

-I
7%4 .

N

7

4 (4 Im3)4 7 2

4 7N

E

N/7

H4 76

N '4 7E

5NfE

76N

H4 76

4

-4 7 2

>

2O-/.

/6.

3jI

4

7^I

4

4 N ^4

.

IU-/N3 7 I4

I

(4 I
7%4 .

)I-7

N

7

@

I4 I

4

f3 76Nm3

64 -6

N

.

I3 5'Nm3

-/.

4

N I

6I
7

'3jN

5

76
N

4 H76
N

1.


S 4   U
  
[ 


 * 
  : U
K 



.
 
4 A U

  A


.


 





K
Q


 %U




$   Q


1 
 *  *
  @
   ^
G  @

.

76N

1.

I

2

3

4

.

4

5

4

4

5

3 7

.

N

4

4

6
N
I
7

@

4 I

73jI

N

N3

.

4

4

4

`-

N I3

4

4

;

2

4

;

N

4

N

7 I
7N

H6

76N

.

4

I-m6m4 N

2

I

m4

N
-6I

NH7.

7N I

f3rI
7N'E

N/7 I

5

5

7%4

I
7%4 .

.m7HI--

-N

4 r2H76N

76
N(-.f.

m4

Im3jN

76
NC0m3 .

.

4 N(I

I

.

6N

N -/7

.

3

N

N
I-6

E


 @
 
  $
;

Nm3

 


.

@

7.

76N

76NH7 2f04 -I

I /0mN
-7 `.

f3jN

-.

4

-/.

'3 iI

76
N

4 NHI

4

7.C76
N

--

2U4

%  


7i764 `4

F3 .

-m6I3rI-7Nm3)4 7%4 -

% 
 



7F7Nm3jN

6I3 0

.

76N

3

.

.

N
-7N

=

LE

Nm3

0m.f.

1.

iN 4

I

0I3jN

3

76I
7H76
No0m3jN

76N

.

Nm3jN

F3 .

6N I
7

Nm3jN

-/N

76NY03 N

-m3 N
I
7%4 .
N

76
N

76N

.

.

76
N2

7

N

@

N

-/N

.

4

7

76N(4

N7

-/.

Nm3A.

 &*/

 

7.

03 .


^* 
.
 
'    4

.

;

Nm3

6
.

N

5kE

@

4 I

4

N

0I
7

)I 7

-I

7.e-.

.

7%4

4

6N

-7N

/03jI2

4

N 73jI-/7^6N I
7

H6NY6N I
7H73rI

Nm3 7 I

3 N

 "

7.

6
N
I
7^73rI

4 7N

.

4 5

N

Nm3)4 -I

I
7

iI

-I

516

Nm3 2

-
4 72 E

3jN 4 7 I

E

I3 5'Nm3A76I

.m76Nm3

N`4

N

1.

4

6N I
7"73rI

7 I4

iI `-.

I
7%4 .

4 N

-7N

.

2

0mNm3)4

3

7

N

@

76I
7i76N

N

N

-.

.

N

@

^.

Nm3$.

-/N

N

4 I
7%4 .

-7%4 .

H4 76YI

64 7N

N4

@

7 f3

NN

N

N

N

-m3 4 7%4 - I

4 7 I
7%4 .

6
NC3 N

I

4

J76N

4

4

@
I

-4 7 2

@

4

-

.

3?I
7.

5

NU4

0If0mNm3

76
N

I
7%4 .

7.YI

NfE

N

Nm33 N

.

.

N3 NY0m.f.

@

4

7 I
7N

76NU0m3 N

I

0Im3jN

N

-Nm3

N(0I3 7

2

N/7

.

`6
N

"%&*0"+,2 4&!/
"*/ !/

0m.

iI
7Nm3

7N
I

E
N

-/.

.

76
NH-/.

73jN I

@

7 '3

.5m2

Nm3

I

ND76
N

   '
@   [1 H   
 4,
 Q S1

%  0 * .
 2* 
+

 K
  








a 


 8

%   
,


2OI

4

-
4 72

.

I

.

I

0

.

N(- I

6I
7`4 D76
N



H6N

-.

@

.

.

N

-3)4 7%4 -I

I

1 
 
X*
 4


. .
 

.

1.

76N

-3)4 7%4 -I

76
N

7

N

;

N

76I
7i- I 7%4

Nm3 2

iI
7N3lEDG$N - I

A;

N

f3

)I-/7

3?N mI

I

-/.

6I

H64

;

0m3 .

.

/6.

3FE

.

iI
7Nm3

4

7

Im3

5

7.

6I

N/7

I

-/N

4

4L3 N

E

I

76I
7"76N^7%4

k;

NDI

4 N

1.

76
N

5U03 .

0mNm3)4

3

.

4 (4 7 I
7%4 .

3jN

1.

4
4

/6.

- I

'0mN3 4 .

/03jI2

7%4

N

N

7

2O-4 7N

I-N

7%4

7 I

/03jI2

5

.

5

NUIm3jN

I

(4

@

`4

4 I
7%4 .

N

I

4

-.

I

.

7.

0mNm3)4

I

4 7

4

E

iN

0I
7F7Nm3

-I

E

-/N

NU-/Nm3 7 I4

1.

4

AE

N

4 7 2
'3)4

;

I

5

7N

.

4

4


# 
 

0mNm3rI
7 '3jN'E
- I
7%4 .

E

N3 7H76N



Nm3)4

Nm3 7(76
Ne.m76Nm3

.

I
7%4 .




0If0mN3

N'E

‰VŠKŒ

=

 $F®)µ Ä ¸_¹CÑOÁ µ)ºB°F¯ ¶B³@®)µQ°µDµ=ÔCÄOµ)¸Ê¯ ºDµ ¶ ³°5±>µ)¸_µÈ8²ºB¹C¶)¾ ¹ ³@® µ)¸J³@®¯ ¶)¾°QÈ;³@®)µD¿C¯ ºDµ)¶)°=¯ ¹C¶ ²OÁ8¶OÅOºÑµ ¸y°¶ ¹ ³Ù°=¯ º ÅÁ ² ³µQ¿G°=Å)Ã)®
²)°)OÈ‚µQ¹CºBµ<³@¸yÀƵ<³ÃÎ>²O¶)¿m³@®)µ ¸yµQ·\¹O¸yµÆ¿C¯ Ü0µ)¸_µ)¶ ³5¿C¯ Ü+µ)¸_µ)¶ ³¯ ²OÁOµ!;Å ² ³¯ ¹C¶)°¶)¹ ³³ÊÀOÄO¯ Ã&²OÁ³¹m¿C¯ µUÃ&²)°³¯ ¶ ¾m±>µ)¸_µÍ»*°¹CÁ Ú µQ¿ÇÎ%$3®)µ
¸_µQ°µ ²)¸_Ã)®)µ)¸_° ²OÁ °¹ÞÁ ¹¹C´"² ³U±U® ² ³B¯ °m´ ¶)¹ ±U¶Í² °B² »ÄO¹¹O¸F¿OµQ°@¯ ¾C¶ Ç'¯ ¶9±F®O¯ Ã)®,¿C¯ °³@ÅO¸*Ñ ²O¶)Ã&µQ°m³¹@—;¹ ±×¿O¹ ±F¶ °³@¸_µ&²Oº ƒÊ³@®O¯ ° ¯ °
Á ¯ ´=µÄOÅ)³R³¯ ¶)¾"°Ã)¸_µQµ)¶9¯ ¶ ³@®)S
µ —8¹&± „<Î*+¹&±µ<Ú)µ ¸RÈ ²¾¹¹¿I¿OµQ°@¯ ¾C¶"¸_µ!;ů ¸_µQ°U°<ºD¹¹ ³@®Ã&¹C¶ ³¹CÅO¸_°&Î
"ËJµQ°@¯ ¿Oµ"¹ ³@®)µ ¸ÆÄ ¸_¹CÑOÁ µ)ºD°m°<Å)Ã)®S²)°m¿;¯ Ü0µ)¸_µ)¶)R
³ —;¹ ± Ú µ)Á ¹à ¯ ³\Àͯ ¶,¿C¯ Ü+µ)¸_µ)¶ ³ ¾O² ³µQ° ±F®¯ Ã)®Þ¶)µQÚ)µ)¸Æ¸_µ&²OÁ Á ÀSºDµ&²)°<ÅO¸_µQ¿ ȳ@®)µ
Ä ¸_µQ°°<ÅO¸_µ¯ ¶F³@®)µ3Ã&² ÚO¯ ³ÊÀU²O¶)¿#;Å ²OÁ ¯ ³\À¹ · ³@®)µÁ ¯ ;ů ¿ºBµ<³²OÁ&µ)¶ ³µ)¸Ê¯ ¶ ¾D³@®)µFÃ&² ÚO¯ ³ÊX
À ƒ¯ °>¯ ³¯ ¶F³\±>¹ ÄO®² °µ qÝ „¶ µ<Ú)µ ¸0ÑOµQµ)¶m¸_µQÃQ¹O¸_¿OµQ¿Î

à
P

QS/T

QSVWYX%Z'[\

]^W ]`_
W \La%Q
b
cedf[W%a

dZgWDhjZ\AX%Z'[`TlZmdS%X nocp Sqb S
\jb aFWn

:<;
-.10/2f3)4 516
798

=>>'>?;A@

2oBD3FE

GJI3LK$MON4L3

k" 5
 # 
  I jK X  1  
1
j"ok
k" zN9
j     1+ j 1

9  k " D  ~j #   4  #
 .
# 
   <&  
    &# j
$  
  )
 
 !
  ,-  .

Chapter 3. Dimensional Analysis




!   



 ,1&)(+*
/



!*+,&#"%$

#"

!,

- / -03*
&




"%&


(^KŠ ]+Š ^ ŠK^ ‡] ]  "!#Šz]

4#     

: * 

   : #  . ^
( 2 E  

 @ $ ,  
. )

   
(
     


 


  ; ^

F1 %   

'   %$  2] '  
.  
 *  ßEQ  f  . Q

    
O Q # 4 . c
 %  3     S 


(  '  
,  * $  

( 
 
 
=O d ' 


(   *     4
   ? * 


1

    
%'
   /eSg 
(
*
  

 
  
 

 h1
 W *


( 

1 $ 4
  %
a
 %U

 # *


 
   
* R  
 . 
 [1 $ 4
  



K "  *  
 *
Xeg 
(
[eSg 
( + 2 A Q C

  

 
 : *W
   @ E 

 . 
6   * . G  

 .  A aZ  4 
( R1


  
 G   %
  R"  *F

'
   '


.
 
 

E
    4
 #

/*
 S* ,   
  h1  * #  
   # 
 . R

K   , 
Q 

'
 


(  2 *  

Y 
> U4
  4

  ,
  ß 3 < 
21 2 ;"  *   #  $ H 

@ ; [ 4  
 4

 :U
  = *
' 

(  K  ' Q
 E
a

$ , 
 K   
  Q ,,
(  0   

  /* 
.





   ; 2 

 c * *
' 
#U

/ * 


  /  * ,
 . @

K


  4
;O MQ
A* . Q : , K , ( =- . @ Q 
K
Dh  8 * 



* . .



(    ' 1 ;eSg 
(

 
. 
K*
eSg 


)O Q 1
  
W* .

 F f  .

 @ Ž
 '   
i A6F 
Y % 

2* . '&)( X1 % 
    # 4"  h*
2"  *  
*
j jo ko k9 "j  ! ~ j7  6j # 
 2     
#

#
 .  2 *
  

      4
  

 

4

 * : 
 % f 4 6    * 

 
*  K ]   "  D   ßE0M à O Q
< *
Y
 *
   
R  f > * * = 

 eSg 

 . 
 S  K   ^*    



  Q 4
!  . @

; <. 
@ 2 * 0 
     



(   $ 
 R 
;  ,@-   * . F  ! 
F* . . @   /  . 
.







  
 uj"   ,$   

1

9k @
+c
"   


R
 <B

N9j"b V
 
  jVN  ,$ 
.





.




 @
K
 X&
 4   j   )2
  ,$
4 
Q 1 Seg

@

S ! 



4   j   )~ ~ ! uj    4 





.

i A6F,+ * 6 
‚
4

6

@
#
1 
 * 


7

-/.

.

f3rI
7%4 .

3 N0m3jN

N

1.

2I

.

7H76N

4

N

-
4L3r-

'3jN

f3jN

64 -6

@

N

.

I

.

.

.

'3jN

I
7%4

.

N

4

7 I

4

7 I

I

73jI

I

76N

7%4

N

0m3j.

-N

.

2

76
N

76
N3 N

.

.

.

76
N

3 N

.

- -

J76N

@

N

.

76N

4

.7N

5

4 7 I

64 -6

5

-4 7 2

.

-
4 72 E
N

.

76
N

N

4

76
N

76I
7
-/N

N I

N

mE

3 f0 7
7

iI

Nm3

F3j.
N

4

.

@

.

Nm3

I3 2

7

@

E

-/NC4

4

76N

1.

H4 76

N N

iI

4

76N

I2N3

7 I

6I

N

@

2

.

.

N

7.

N

4

5

N

4

5

5

I2Nm3J4 iI

.m7

N

N

@

NN

.

I

N

I

N

.10mN

4

5'N

76
N

7%4

5

.

3

I

2

4 7Nm3rI
7 f3 N
.

516

5U76N

4

4 `76N

5

1.

4

N

4

-m6

.

73jI

7 f3

N

.

7.

7

I

-4 7 2

@

N

.

4 i-/.

76I

76N

-7%4 .

.

4 H4

3 N

;

N

.

7

-4 7 2

-
4 72(I
N

N I

.

$7%4

IC3rI

76
N

N N

@

N

-N

N

N/7N3

76
N

6I

N

N

7

4

1. 97.O7 f3

@

`6
N3 N

N

.

E

76
N

0mNm3)4

7 2f04 -I

-3jN I

I

-m3 4 7%4 - I

N

.ON

7iI
7

4 I

E

I3

-
4 72

76
N

ND7.

N3lE

76N

76
N

.

N

1.

4

@

I

.

I3jN

04L0mN

)I 7Nm3

.m7.

.

4

6I
7^4

I

76I
7

4

I

N

76I
7^76
N

N

@

4 HI

I
7

I

7

N

7

N

7

I r7Nm3HN

iI

@

I

E

I r7Nm3

-

/N3 .

N

76Nm3jN

7 Im3 7%4

@

I3k7.O7 f3

@

f3

4 N(-I

f3 4

7

3176N

7

F3j.

f3

4 7

;

7

--

N

.

7%4

N 7%4 .

iI

N

.

5N

I

.

N

E

.

0m3 N

N .

-m6I

N(4 ^73rI

/6.m7

7%4

N

-N

I

76N

7

A;

f3 N

%-
4 N

f0mNm3r-3)4 7%4 -I

I

4 7%4 .

AE

7%4

N6m4

.

7 I

4

.

f3 N

E

N

1.

I

3 N
I

76N

@

-I

76I
7

4 5

7

- -

-N'E

f3

N f0mN
-7N

iI `-m3 N
I
7N
NO76
N

`6
ND72'04 -I

.

76N

N

4 kN3 N

N

I

@

7 I
7N

- -

1. <4

4 O0m.

(4

2

-/NO.

7.

`6
N

4 Y3jN

@

.m7

N3i4

3jNO4 7`4

N I

@

N

4

-/N

4

Nm3

.

N/7 I

N

N

N

7E

64 -6

7 f3

N

7N I

f3`0m3jN

E

N '4 7

NN

iI

3

@

6
.

E

.

@

N -.

76
N`73jI

@

N

5

N

4

-I

76N

I
7%4 .

4 7i4

-/N

@

>>'>

K

N7

;

-/N

7

H6N

^76I
7D76
N

@

N

N

7%4

4

4

7 f3

.

N

4

I
7

7.oI
.

@

1.

Nm3

2

76
N

4 $76
N

7.UI(7 f3

4 7%4 .

Nm3

N -/.

4

-N

4

.

"I

N

3iI

4 7%4 .

76NH764 E

.

73rI

76Nm3jN

)I-7

`6
N

@

7.e7 '3

E

N

.

N

;

-/N

6N I

='>>'>

5'N

0I

73jI

1.

I

4

76
N

H64

@

N

4 D7 f3

H6N`N 7%4

N I

r7N3

4 7%4 .

0I
7F7N3

N

N

7 '3

5

@

I

4

N

4

7 Im3 7%4

4 CN f0mN
-7N

I

76I
7

N

7.Y7 f3

7%4

I2

'3jN

N
-/.

E

AE

-4 7 2

.

73rI

76N

-I

7

;

76
N

.

N mI

@

1.

4 7%4 .

4 N

N

N .

@

N

N I

4

f3FE

E

73rI
7N

5'N

4 7%4 .

A76N

.

76NO3rI

6I

@

N

76
N

4 kN3 N

E

I

3jN I

76
N

76
N

3jNO73rI

4 7%4 .

N

7 f3

I
7N

.m7DN '4 7E

3rI

iI

F3j.

.

N

Im3jN(4

73jI

I

--

.

;

7N

-I

1.

7 I

7

76I
7

2

N

.7N

/76
N

N

6
.

N/73 2o4

4

N -.

If0f0mN I3 N

@

.

4fI

I

.7`.

5N3

-N

N

4

76N

4 ^4

@

H4

N

'3 (I
7

73rI

N3J.

(4

NU4

--

4 I3

>

4

0

76N

7

4

N

I

N

NN

I

f3

N I

I

73rI

.

4

4

@

0m3 .?0I5fI
7%4

76
N
7.

1.

N

.

4 7 2
E

I

7 I

7 f3

73rI
7N

@

N

5'N.

64 -6e76
NoN '4 7N

.

N6m4

R2
5

3

NN

6m4 -m6

4 7Nm3rI
7 '3jNYI

.

5N

3H4

3jNm0m3jN

7.

.

If0

.

2

3

I 4

513rIf0'6

N

H6N

@

I

.

.

Nm3

6Nm3jN4

-I

76I
7

1.

2K

N

I O76
N-3)4 7%4 -I

4

@

4

1.

N -/.

/6.m7
@

.

I

7

m4L3jN

f3 N

4 7%4 .

0m3 .

3 7

Io3jI

N

"76N

7 f3

6m4 -m6

6
.

7

/6.m7

N3

1.

/6.

N

4

4

76N

76N

$76N

1.

@

7%4

.

;

2

@

N

.

5

f3jI
7%4 .

'0

3jN

7.CN

N3lE

;

N/7

N

3

.

(4

.

N
I

;

N

76N

Im3jNON I

76
N

76N

4

NN

76I
7

I3 4 2

76N

.

No6I
@

E

N

5

/6.m7

N

I

@

7 D.

Nm3

N(7%4

76NU73rI

4 7N

4

H6N

.

Nm3 2

N

@

76I
7

4

N7%4

76N

N
Im3

kN/2

`4

'3jN

`.

E

;

N -N

I

I3 5'N(7%4

76
N

0
7%4 .

N

H6NO0m.

I

@

7 I3 7lK

m4 N7%4

E

4

.(I

Io7 '3

7 ^7%4

N
-/.

N3jI

0mN -/7N
Nm3 2

.

N I

f3

7

I

7

7.

N

4 7

2 7N

N

4 7%4 .

76I
7

4

I3 5'N

N

4

3

--

.

N

;

NOI

N3

4 7

3jNm0m3jN

N3jI

-/.

7.eIU7 f3

N

.

`6
N

3

-3)4 7%4 -I

I

4 7 I
7%4 .

4 7%4 .

3 N0m.

N

N .

2

-/N

4

3 No4 7O4

764 CI3 N
I

%I

@

7 '3

f3 76Nm3

4 .

73jI

73jI
7N

H76I
7

3iI3jN

76
N3 N

-4

N

-/N3 7 I4

/6.

3jN5

76N

@

.

76N

N

4 7

I

@

N

N I

@

H6N

7.O7 f3

5

;f=

N

.

6m4

4

4 72 E

73 -7 f3jN'E

NN

4

N

1.

A76
N`- I

-/N

/6.m7

?E

4 7%4 .

H64

.

N

N '4 7

Im3i0m4L0mNfE

73jI

76I
7(76
N

5

@

7 f3

-N`4

4 5

I

4

76
N

@

7 '3

N

?76N

1.

N

5'N

.

-I

}.-Õ ³U® ²)°5³¹IѵD°²¯ ¿³@®²&³3°=¯ ºm¯ Á ² ¸+°@¯ ³@Ų&³¯ ¹C¶)°² ¸_µ·Ê¹CÅO¶)¿I¯ ¶B³Ê±>¹IÄO® ²)°µQ°‹—8¹&±tÑÅ ³5³@®)µ<À ¿C¯ Ü0µ)¸_µ)¶ ³ÆÑQÀm³@® µD·Ê²)Ã<³Ù³@®)µ ;— ¹ ±
¯ ¶ ³Ê±>¹,ÄO® ²)°µ —;¹ ±t¯ °U²m°=¯ ¶OÅ)°¹¯ ¿²OÁ0¯ ¶°¹CºBµ ¸yµ&°=ÄOµQÃ<³°&Î
:<;1=>'>>?;A@
-/.102'3)4 516
798
2CBD3FEHGJI3LK$MON4L3

PRQSTUQSVWYX%Z'[\(]^W ]`_
W \La%Q
b
cedf[W%a
dZ'gWihjZ\kX%Z'[`TlZmdS%X nocp S/qmb S
\rb a%]Dn

-0/

Section 3.3. Special topics
@

  
(  , @
N

I

N

I HI

(,
H *L*

.

7DIY0

5

1.

 

'

`4 76(76
N(N -Nm0
7%4 .

S 

.

76
N

F3j.

7

3jN5



4 .

,-
%
N9j" T < j   
) 
 
 0  '&   j  

    
k "1 
~ 

  => j
 &#9 j,<.  

E

 ŠK]![+Š Š## [ I^ #^3]+Š

  
 = f ;
 
1 a @ 4;   @ 

 
#
 

.



.

 *
"^ 1   
   

$
 4
 

( 
ß 
4
  <
 @

 K = 
 Q
 

E  
 K   > U
K  Q  A '  @
O
  U
 4 * 2
. Q 


;    R  $   K   a    * Q
\

   
1 ;"  @     <
 % f*
%   

$









 ! 
*
4
 '
  V*
  
(
! ) 
 
E  
(  <Dh  X*
( ^  S*

6"  

 @ 
 4
 

  .
 * 

( $  
 *
- 
  

4





 '
U
%
 H)










.



Y


(
 





E    4


.



 
*

G  

   
(  


 
 % 
. *  .    , 
% X 
 . (
 , 
;
 ;- 
 @
 
4
  
 a @     = /  .
] 
  



(


. Y
  . 4
  F *  -
W  4 

'

. a R
 
 > U
   %.  @ 6 4





 U
  E
   W 
 

  4
   
(
.

4

 X"^   F 
    
  %  '   

     

 *
@


  $ H    

 
( 

 
  "   G 
Z\[X]!^ 
G @ F  $
% / G 
$





- 
a
  

=
H6N

.

76N

7

1.

4

E

4

=

-.

- I

N

EH-/.

7 I

ED76
N

4 72 E

3jN I

4 72

1.

7

;

@

N

2

4 7

4

.

-I

3

N

-6I

76
N

Nm3rI

5'N

;

3"5fI

)Im3

4 .

4 N

-I 7%4

I

5

4

73 2

.

3

4

I
7%4

5

0 7%4 .

.

.

;

"76NU0m3j.10mNm3 7%4 N

4 '4

5

.

;

76N(5'I

4

m4

I

.

4

6I
7

.

3jN I

N

/.

3

7

76N

NDN

3jN

5N

@

Nm3

N(4

N

N -/7 (.

0m3j.10mN3 7%4 N

-m6

4

N
Im3

.

4

@

7.o7 '3

N

73 .?0m4 -

7

- -

.5'N

.m7

N .

k;

N.

@

N

4

.

.m7

)I3

F3 .

"I3jN

)I3

F3 .

N

@

7 '3

.7

NN

@

.

N

Nm3 2

0mN -/7`76
N

.7iN

7

Nm3

76
N

-/NH4

N

4 J764 H4

I U3jN

6N/76Nm3

N

NU-I

E

N/7

^I3 N

N/7N3

.'5N

f3 3jN

E

O0 7%4 .

0m3j.10mNm3 7%4 N

4 72(6I

1.

0
7%4 .

- I

.

6
.

I3

6Nm3jN^I

N

5NU.

4

I

N

4

-/N

4 %-/.

I

73j.104 -H6.

`-6I

I

;

2

7.

76
N

-I

N

N

N

4 7%4 .

6Nm3jN

76I
7

7
E

N
-/.

76N

73jI

N

k;

0 7%4 .

-m6I

7.

N

- I

0mN -/7N

76NDI

N

3 .

7N

.

516

0mN3jI
7 f3 N

4

I

2

I

.2

NfE

.

H76
NC-.

3 N
I

6I

N

76N

.

- I

N.

;

4

76
N

F3j.

.

4 %-

N

7%4

4

4 7 2

I

4

7%4

.

76N

I3j5N

N

4 N

- I

F3jI-/7%4 .

I4L3 5fI `0f6I

4

4 72 E

.

N'E

4

I

N

4 %-

76N

N

I4L3^4

-6(-I

;

N

4i3jN I
0m3jN

76N

76N

4

4

.

4 .

2

m4

N

@

I

N7 I

73 .?0m4 -

No4

;

76
N

76N

?I

6
.

.5'N

6
.7

NN

1.

4 DI
7.

-/.

Nm3

N.

I

N

N

4 /N

2

.

N

0
7%4 .

E

N

.

@

@

76N

-.

4

7.

4 5

I

N

4

7

0
7%4 .

76I
7i76N

/.

.

I/2OI

.

;

3 N

NU7.

3 .?0 H4

76N

6
.

4

.

(4

4

N

N

;

-N

/6.

U-4 N

5N

0mN -/7N

@

I

3"I

-N `N3 3j.

.

/6
2

4

N/7 I

N3 2

76I
7

@

N

.

I

6I
7

N

0

3jN I

;

N6I

4 7

N

m4

4

;

Nm3jN

4

76
N

Nm3

@

4

.7

k0m3 .

76NoI

3

4

N

I

;

4

6m4 N

I

4

Im3j5NH-m6I

N 0mN -4 I

-/N

14

.

2

N

/6.

7.o6I

5N'E

N

7 f3

.

'3 76Nm3

4 -I
7%4 .

-6I

I

7

N'E

-N

0

N N

N

@

I

N

.

N .

.

.

7 '3

`6m4

4

4 ^-.

@

6I

N 7%4 .

-/.

N

76N

4

@

N

@

7 f3

A0m3j.10mNm3 7%4 N

4L0I
7%4 .

.

3jN I

I
7N3 4 I

3

I

4

H6N

.

.'5N

.

;

Nm3

N

E

6.

7

7%4

N

.

4 72U4

73j.104 -

AEH-/.

7 f3

.

76
N`I

-6.

4 -N

i76
N

N

7.

0 7%4 .

N

.

76N

N -7

Im3j5N

.

76Nm3

.

7 '3

J76N

N

.

@

I

.

@

N

-/N

4

4

.

N N

.

N

- I
7%4 .

Im3 2

3jN I

.

N

.

.m7

.

.

N

@

N

N

5'.f.

I
7F7Nm3

.

3"76
N(-I

-

Bi4

Nm3jN

LE

I

N f0mN3 4

I
7%4 .

7`0m3j.10mN3 7%4 N

N

7

E

4

4

Nm3jN

7

I2Nm3FE

‰VŠKŒ

 W* >"  *
 @

Z\[X]!^

*I*

N

6
.

.

N(-I



-

 

.

.7

NO7.



N 4 5

.m764



 >*
%  

5

76
NU0m3j.

3 N 5'I3
-/N

4

5

HI

6I
7

76N

 %  - #* R* 4


0Im3 7%4 -

N

4 /N

N



.

0m3jN

Nm33jN



7.

.

6I

;
N

5'I
7NfE

‰VŠKŒ
Z\[X]!^

 #U
%  *
6N

76
N

*
7

/ * 
 / * G  .

N 7%4 .

.e0'6I

N

1.

6N/76Nm3

76
N

1.

N kN
-7 (6I

N

4

7.

@

N

4 N

-I
-/.

. 

(  !  
 

 - 
4 7 2Y4 H7 '3

4

Nm3jN

@

-6

N

7H.

3

I
7.

I

(4

4 I
7%4 .

I3
;

4

< 
  
N -/.

I4L3 5fI DN

I3 2 E
73rI4

5 
 

N/7 -E

=

‰VŠKŒ

M
P

QS/T

QSVWYX%Z'[\

]^W ]`_
W \La%Q
b
cedf[W%a

dZgWDhjZ\AX%Z'[`TlZmdS%X nocp Sqb S
\jb aFWn

:<;
-.10/2f3)4 516
798

=>>'>?;A@

2oBD3FE

GJI3LK$MON4L3

4

-/N

N

7

Chapter 3. Dimensional Analysis

ŒhŒ  ]+Šb^
VŠK]![+ŠƒŠ## [ I^   ^3]+Š
 
 + R >
  < ,
 5

1 F 4,
 @  4  
 %U
 


.
  K R 4


*   *

@  *  6 
( 


.




$
ß
Q
O V1 W ,

@ 
+ *
*
@
@

 W ,
 


.
.

*
W *9

 < " * ! * 0 *
   % V *

.







 @

4

2B
(,
*
' %

X1



  % Wc!
  
    ,

   % 
E ^







.






 
(
 
   ^

 
 
)
W

)
 
  !   % h*

+ * +
 
B


EU4
 "



  R ,
  * A



4,
6 
f  ,










Y



 %
' @, '  (  



?* "
  &    K
"  a5  ßEM@+M à(Q <  +* " ; *  # +  . S* 
  - h1  
@ 2 * *    E*
  @
,
@ " 

( 
E




K
P
Q
(
> 4
3 #1

@ <* ^" ' (
. 
E O  
(  

  %


(
+*  F 
  ,







; *
1

   
 >
  %


(   
(  + *     '  

H6N

.

-I

N

E

7 '3

.

7

7 I

.

.

4

4 7%4 N

76N

I

I

I

@

.

E

N

7.Y76N

AB

.

[2[
'[
N

.

k76
N

.

--

-N

.

4

5'I4

N

GJI-

Nm3

4 -I

N

I

N

I

4

7

N

H6N

.

N

iI

4

7

H6NC0m3jN

N

7.

@

7 I

6
.

64 -6

7

4

2

4 7 2

0f6
N

.


.
, 
K  ' Q


$
 
* #;
 
 U4
4

B
, ;* ,
5(76
N

4 N

4 AN '4 7

4

4

7N -m6

4

-/N



!,, 

.

;

E

'3)4

I

.

H4

5

N

.

I

- I

I

N

Im3j5N

76
N
4

4

N

4

N/7%4 -

7

4

@

N

N f0mN3 4
NC4

If0'0mN
Im3

.

@

I

7
N

N

4

N


I
7%4 .





N3LK

@

7 I

3 N
I

/6.

I

.m7%4

4

I4

4 7%4 N

76I
.

NN

N

3 N
I

3

iI

7 I

N

76I
7`76N/2

0mNm30mN

76I

N

4 UI

N

5

I

N3

5

/6.m7

0

.

7.

3

@

@

4

I
7N

7

-/.

k4

4 -

@

7 I

I3

4

4 7%4 N

4 7 2
E

0m3jNm6N

;

.

.

@

`4

  $





W 
S
   q
 '    
E 
5  a"  *


^I

4 E NfEJ76N

7`4 DIU6.10mN

.f.

-/N

4

N0mNm3

.

.

?7N

.

4

^76N

.

3

 

76N

3

N

E



 

N

4

.

*/%& - /

&*02

7.

0I3 7%4 -

7

2

76Nm3

76m4

I

4

Im314

73jI

5'.

.

.

0m.

N

4

0mNm3)4

3jN

I
7F7 I4

I3j5NH0m.

4 7%4 .

.

76N

I

.

7 m-3)4 7Nm3)4 I

N

N

N

3 7%4 .

7

4

5

@

5NU-I

N

/
*

!, *

I3

N

0f6
N

2CI
7

.

76Ne3

N

.

Nm3

N7

.

76N.

.

I
7

,   
 R*
,

3jN/7%4 - I

76N

2

-I

- I

N

4

-3jN I

6
N3 N

I

N

A76
N

Nm3j5m2 E

K O à(Q
?E

 

(

N7 I

I

NO3jN I

;

-I
7%4 .

'E

&)(+*

4

0mNm3rI
7 f3 NfE

73rI

N I

4

4

1. R4
6N

76I
7

7N

D7.

76
N

$ 
N

4 7%4 .

 +&
"
.

-

Nm3 7



@

Nm3

K O (d Q
4 
?E



4

    $
R   

4L0I
7%4 .

N -7 `I3jN

0

(4

6 U4


76N

4

4

I/2 oI

4

I

4

-I



7o3j.

NRI

LE



N/7 I

4 5

1Im3jNO-.


4

3

4

- I
7%4 .

76N(0f6
.7.

N

Im3j5N3

%  

f *

* 
W 4
 

0m3j.

k;

] 6N    
 @ Nm3 4 . Nm3 2C Im3j5NR4 7A N I  Y76I
7 76N
-M   "   2


 
    Kj # -/. %. Nm3 N@ 2;* 6N    
( @ N3 4 2  I,76N 4  4L0I
7%4 .  NG
  4
 "  jXN 5   
      j
LP"
  j. . & "<
~# j9j  =j  
9N j"( L" “ <
    1.
 76NY0m3j.10mN3 7%4 N% `.
Z [2]'^
 j5k"< ~ 9 k 

  j
9N j"  \
6N
NGkN
-7H. 7N@
0mNm3rI
7
'3jNO.
 !  ( k 

 "
   =T
 


3rI
5N
. 76
NH;
 /6
2#-/.
NfE
j  )
1" 

  !
   1
j
9N j " K "  I h  L "   "“ h  
j3     1
: ‰‹ŠbŒ
,- 
 &
 6
 1 V V 
  ( k 

 "


  

1 

 1      &
 


k
jok  
"  'N .  ;
(
  
 "  " 
 !!  
:<;1=>'>>?;A@
-/.102'3)4 516
798
2CBD3FEHGJI3LK$MON4L3
   1 OP
  X



I

3

2^76
NH4

.m7DN '4 7`4

- I
7%4 .

4

.

7
E

76m4

/
"

4

2DN

764

4

4&!/
"* *  &

-
4 7%4 N

Nm3j5m2



1 EU4

`6m4

.

N/7 I

N

(

2

.

.  % @ a U4
  K 
( 
1 a
^
(  Q





? U
  @

61 : 



  R "

" 
   ^ 
  
H6N

@

73

4L3jN

.

.

1.

-/7%4 .

N

Nm3 7 I
7%4

NN

NOI3 N

73 .

3

f3 N

7%4 .

N J764

4

76
N

-6

4 5

.

N - I

Im3j5N3

1. <4

E

N N

N

- I

5U.

3

i76I
7

4 7%4 .


F  $


  
[*  3 
  
" * ,
4"

76N

0m3j.

7D0m3jN

3 7i7.

;

N

2

(


Y  
' 
  


4 7 2

-N

7H3jN

6
.?0mN



3jN

0m3j.

N

I

-I

4

-I
7%4 .

4 I3 4 72





7Nm3

764

76
N

.

@

76N
@

7%4 .

7

2(4 H3 N

6m4 -m6

0m.

O@

- I

I

Y4

;

3

4

7

I

2

4 7%4 N

/6.f.7%4

4

.

N

- Im3jN

-6

I

I

4

.

4

7 I

4

@

7 I

N3LK

I

7%4 .

Ne.

76I
7

4 .

E

;

N

.

7 I4

;

Nm3

5O4

7 `.

N

.

0

N

-
4

@

4 7%4 -

E

4

N3 4 - I
7

7 I

N mI

>

76N/2

?3jN

(3jN

4

7

76
N

N
-I

7

.

@

.

764 H6If0'0mN

73j.

- I
7%4 .

1.

- I

E

@

7 I

76N/2OI3 N(I

N

76I
7

4

7.

I

1.

.

N
I

4

-
4 72

N

I3jN

3jN I

N m-/N

.

iI

2

73

N

N

H6N(3 N
I

73)4

76N

F3j.

Nm3)4 -I

E

4 N

-/NUI

1.

5

N

6Nm3jNH76N

E

@

76
N

4

f3 DI

76
N

N

.7O0m3j.

I
7%4 .
E

;

7.UI

76I
7"76
N

N -I

i4

4

I2

  ]+Š  ] # !## [zŠK]  ]  ^ ŠK^  

76N

@

-

@

7.

N

4 4 7%4 N

7 Im3)4

1.

-6

-I

k76N

-
4 72

4 7 I
7%4 .

] (^KŠ

$
Y 


(

 + 4

 

6  
 

r7Nm3

;

3 N

2

2

4L3 N
-7%4 .

76
N3 N

7 '3

-I

.

3$-/N3 7 I4

6
.

I
7%4 .

4

@

N

N

5'N

-I

7 I

I
7 '3jN`.

7

- I

-

4 72 E

0I

0mN.?0

1.

4

.

3 7N N iI

I

4

H6N

N

.

7%4 .

-N

N3 .

I

7 I

9-/.

2

6I



 

4

N3 N

1.

- I

E
@

I
7%4 .

2H-6I

`4 76

73 .

2 /N

N

Nm3rI
7N

I
7%4 .

4

N

-6

N3 4 - I

76N

4

N

.

N

-

76I
7

4 7 2

7%4 .

E

I
7 f3jN

f3 N

3 N
I

7

H4 76

.

@

7.

N

lN/7

1.

76NO-I

.

.

`6
N

@

.

7

64 -6D76
N

4

.

4 ^76N

>

?E

7%4 .

Nm3rI

@

 
N

4

PRQSTUQSVWYX%Z'[\(]^W ]`_
W \La%Q
b
cedf[W%a
dZ'gWihjZ\kX%Z'[`TlZmdS%X nocp S/qmb S
\rb a%]Dn

76
N

.

Section 3.4. Estimates of the time scales in die casting

.
.
 
G 
 1
 H 
. G
1

H6Ne513rI

N

N

N

4 72 E

.

C@

.

]

(

I

N

I

.

@

E

N I3

7E

5?3jI

.

3r-/N

;

I

%I

N

.

4

N

IU.

2

7.

)I

4

H4 76

- I

@

3j-N
E
I4L3lE

4

;

H6

;

N3

4

 Y
1
 

.

5e4

76
N

4 72 E

N

6Nm3jN

.m76Nm3

lN -7

5Y76N

3 .

N

N

@

O0I3 N

4

I

I
7%4

3

1-/.

76N

.

Nm3

3jN

I

I

3r-/NY4

.

N

I3 5'N

N3 2

.

@

4

76
N

I
7N

3j-N

3j.

.

4 7 2Y4

4

.

4 7 2

4 72Y4

N

4 72

`6
N

I

4

.

3

Nm3

N - E

H6N
N7 I

76
NC3jI
7%4 .

% 

N/7N3 (4

N `4

76
N

I

N/7 I

N(.

@

N

.

.

3 N

76I
7

4

i76N

04

5

I
7N`N

- I

I

.

N

4

.

76N

I

76.

.

.

2

4

Im3

/6.

N N

1.

4

5

76N

6I `7.

7 I

76N

N

513rI

-I

-I
7%4 .
N

3 7

N

7 I

4

76
N

N

N

3r-/N'E

.

-
4 72

- I

.

N

E

516

-N'E

N

.

N f0mN3 4

76.

4

4 72

N kN
-7

N

5e7 2f0m4 - I

76
N



.m7HI iI3 N(.

4

4

76N

'3)4

1.

4

I

I

4

N
73jN

.

N(4

76
N



5m76

4

3

7.

N 4 7%4

5

N -/7

N /0mN
-
4 I

2 4

E

I(-I
N

N

;

N

3 7i7%4

N

4

.

Nm3

-6

/6.

764 -

7

I

f4

76N

. ; + '  (

ß N  

  . 


.



* @ '  
 S *

a 4 $
 G Q & &
  
 F   .  4

eSg 
(
 . 

/
 1 ;eSg 
(
$ 




.
'
  =c


 S  . / 
b
F *    . F 
 . ,
@

 2  * ,
 . @
Q


.




K

"

D
>

H6N

@

4

2

4

E

R 

ß 
   ' 

-6I3jI-/7Nm3)4 7%4 -

.

6I

I

4

>

N(.

76
N

;

5m76

N

N3$4

2

76N

4 ^76N

N

N -I

4 7 2

N

 X1

;

-
4 72

7%4

N

H6N`5?3jI

5?3jI

I4L3

76NO.m76Nm3

3 7 I

5

7%4 -

@

3jI
7N

I '4

3j.

.

'3)4

76
N

I3 5'N

1.

76
N

-/N(76N

. 




;

ß
   ' W1
 % K  * $ ? 

R U4
   


 @ /



"    @

q
E
   


 4  G

K
 % ,
     ; *

-m6Y-I

N`76I
7

76N

0m.

2

. ?
>
 . 
+
;   <

+ ,  
 . 6  , 4
*
> U4

4  /

. S1 

$ , 
. /
 >"  *   S 

 4 ^ 


 4


(
$ 

.

513rI

?E

4 ^76N

4


4

4



6N

K O M(Q

-6Im3rI-7N3 4

0I
7F7Nm3

Nm3rI
7N

2

@



  

  
(
KBi A7F,+ Q

R *
 %' ;
 . ,

.
1


 4


(
 ß D  ^
d(Q

H4 76



3r-/N i7.

4

  ?*



N -/7O.



-6I3jI-/7Nm3)4 7%4 -H0m.

*

7

.

(


N
-7N

7

?

6Nm3jN

5N

N 5

N

4 7 2ON kN
-7 HI3 N

$

5N

N

.

N

G


I3 5'NCN

-
4 72o3rI
-I

`6
N

76
N

513rI

6I UI

.

N -7

*  &,

 
 
  4
> 4  
(
 
  %



4 72

72'04 -I
I4L3

*

/45%3&#1



;

N3 4 r2

4 7(4

@

;

N

1.

@

I

3jN

4

.

76
N

E

.

Nm3"4

N3

76N

;

N

76N

3jN I

@

.7N

0

3 N
I-6

76N

E

N mI

7 H7.

N/7

H6N

4 .

3

N

I
7%4

N

7.

N

2

e@

N

2

-4 7 23jN I-6e4 7

f3 )I-N'E

76
N

/6.m7

.

N N

0

NO76
N

N

5N3

513rI

4

N

4 72Y4

.

-/N`76
N

7 2f0m4 - I

-
4 72(0mNm3)4 .

7.C-.

4

I

I3 N

N

4

.

76N

Nm3rI
7%4 .

$76
N

3jI

N N

5N

6If0
7Nm3

E



)

H6N

N

.

76I

3

=

I

N3

N

0m3j.

7%4

73jI

@

0m3j.

7%4 -

N

.

;
2

N

(@

-I

76
N

N3k76I

-/N

N

  !#"%$

&



  #    
 ) 


* "+, !/
" 0 "  
1 ,2!, /

2

/

/

%( 

  &*/ !,&

- I

.

4

3j.

N

N

4

N3"I

3jN I

0m3j.

76N

4

N/7Nm3

-I
7%4 .
4

4

N

4

5o0m3 .

-N

N

0m3j.

7.

.

@

4

-N

76'3jNN

4

76
NY-.
^4

N '4 7 2Y.

76N

4 N`-I

Nm0Im3rI
7NH-I

- I
7%4 .

4 N

0

4

^7.UN

4

5o4

^76N0m3j.

4 7 2O4

N

m4

@

I2

N

f3 N(IY0m3 .?0mNm3

.

N

4 N

4

5AE

N

-6

76N

4L0I
7%4 .

76I
7

@

H6N

4

N3 N

7.Y76
N
I

.

;

4 -



3^N mI

N

2

.

7%4

5O0m3j.

4

I

4 D76
N

5

4

@

-I
7%4 .

.

-N

7.

7i.m76Nm3



7%4 -

  $ , 

7%4

N

.

3

4

5UI



4 N

-I

.

4 72

4



 

N7Nm3

4

N

e@
2

i(

KO ß Q
?E

}y} Õ;±>¹CÅOÁ ¿ÍÁ ¯ ´=µD³¹IÁ µ ²)¸*¶G²OѹCÅ ³°=Å)Ã)®µ<ÔÄOµ)¸Ê¯ ºBµ)¶ ³°&ÎV~JÁ µ&²)°µB¿;¸_¹CÄ"ºDµB²9Á ¯ ¶ µ ¯ ·À&¹CÅ9´ ¶)¹ ±ÆÎ

P

N

-/N

*

H6N(-6Im3rI-7N3 4



4

Nm3D0m3 .

%I4

;

N

4

76N

`4 76

@

0

76
N

6N I
7D73rI

N(-I

*

'  ( 
$ ,  

$

,
%
*  4 $
Q
 
 
 S 4

E

Im3j5N3176I

N -6I

-/.

?

2

&

E

1




N

N3

76NO6N I
7i73jI

J.
@

6
N
I
7

76
N

 
 

,*2





    
4  ' @
 
  y
4 $


. 2;
R
  

   4"  
+
 % ßEQ 

    $
 O Q 
 K


  H $ ,  * ;* 4
  "

 

$ , 
$ ,  X1 S 
 


-6Im3rI-7N3 4

 2


Q
D E.  
S  *
  %

7%4







&!
#"%$

 

1





QS/T

QSVWYX%Z'[\

]^W ]`_
W \La%Q
b
cedf[W%a

dZgWDhjZ\AX%Z'[`TlZmdS%X nocp Sqb S
\jb aFWn

:<;
-.10/2f3)4 516
798

=>>'>?;A@

2oBD3FE

GJI3LK$MON4L3

>

;
E

Chapter 3. Dimensional Analysis

  %
  





   (
  ,

 c
 


]



6Nm3jN

N7Nm3

N

4



4

4

N

N
-/.

2

4&!/
"

u

 

*
1

7%4

 

*

4

H6N(-6Im3rI-7N3 4

N

.

7

   %
.
$ ,   . 

 P ß
  % 
,
$ ,  


$76N

4 N`I

0m3rI-7%4 - I

.m7i76N

I-7 I

- I

N

4

N

5

N

7%4 -

3

I
7.

I
7%4 -

7%4

4

N

.

@

N

@

7 I4

@

5e6I ^7.

N

@

N

7

4 I
7%4 .

.

3

I

@

.

76
N

I

Nm3rI5N

NH72'04 -I

3jN

K

N3

I
7N

4

2O4 D4

.

3

Nm3

5.

@

.e.

H4 76

Nm3

7 I4

I

N/7

4

3

F3j.

N7

-.

;

4 7 2

I
7.

4 ^76N

4 I
7%4 .

f0

.

.

f3 )I-N

3

7N

N N

I
7%4 .

-/.

. ( Q . 

I3j5N

4 %-/.

4 72

4

5

4

@

N

2

;

@

I

 
. 

"    @

4 ^76N

Nm3

4

5

4

@

N

764 -

N

^.

N

76N

N

N

I
7%4 .

7

.

I

G

Im3jN

N

76
NU6N I
7^73jI

7 I

J76N

5fI
7N'E

2

KO ß Q
  /
=

4



Nm3jN

7iI



76N


 4 -

I-7 I

I
7.

(4 I
7%4 .

7%4

7%4

N3

N

7 D76I
7

N

.

4

N/7N3 (4

N

4

4 N

E

3

N

4 N

3 N
I

4 .

N

I

N

N(.

N

76
NY5'.

.

76N

Nm3

4

-6Im3rI-7N3 4

5N

7%4 -

I
7%4 .

7%4

N

I

@

2

N/7

KO ß O Q
?E

% 
?


0m3 N

N

4 7^7.

7

4 7
4 72 E

76N

-/.

.

4

7%4 -

0I
76O.

5U-6I

"76NU6
N
I
7i73rI

Nm3

F3j.

76N

4 NO4

N3

K O ß\Q
?E

f3 )I-N

N

%-3)4L0 7

@

G

M

.

4

4

6m4 -m6

N I

N

.7N

5

7N

O0mNm3rI
7 '3jN(.

N/7 I

N

4

v i * p




4

4

94 76O76
N

c

K

>'>

N

7.

K )=k 

   "    & j
K 
-N9
j " 5 = j ,b
 j
 

"/ . 
 ~ 

.

;

-
4 72

?E

4 .

Im3j5N

 EU4

 * . ,


<76N

76N(-6Im3rI-7N3 4

@

.

?E

76NY-6I3jI-/7Nm3)4 7%4 -

513j.

N

5UN

N

7.C4 7E

 /ŠKŒ 5]+Š ]  [-Œ  [ #Œ
.   %U

  

1
  p
 
 p
 p
p   
p  p  8 
      

.   %U
 
1
 *     % 




.
*
4
 
^
,
@ @
 #
  $ 


!
!

'&
8!

p
"p
#


8 p
p
p



v  
    %$ )( '&
!



  
b

@





4


( 
4 


  

 4  : U4

 U
 _   


]
% $   %U
 K O ß O Q   
  


 p
 
 
$
v !+*  p  8-$ , p    $ ,  p   $ ,  p 

* 6 !   

 
H6N

5

K O ß0ßEQ

(

 

7 ^.

.m7N

76m4 i7%4

7%4

  6 * eSg 
(

4 -

.

u      
  4
1
 
( 



^* 
7%4

4

NO4

.






-I

576

*

7%4



4 i76N

H6N(3jN

N



. @   
b
 
#" @


 
4  f /eSg
(

*

6
N3 N

76m4

2

7%4 -

;

4 I513rI

;

&



H6N(-6Im3rI-7N3 4

-m6I3rI-7Nm3)4 7%4 -

0

.m7N

1




76
N

76N

FE

2


&/

.m7N

C@

7.UN

4 7%4 .

7%4

N

7%4

DN

I
7N

5

-/.

.

7N

I
7%4 .

.

76
N

4

5

4

4

0mN3jI
7 f3 N

AE

4 D73jI

-m6I3jI-/7Nm3)4 7%4 -

.

7%4

3

N

7.

?E

N(I



76N(-6Im3rI-7N3 4

K O ß%P(Q
K O ß%N(Q



?E

7%4 -



7%4

N

4



G

.7^N

N -/7N

:<;1=>'>>?;A@
-/.102'3)4 516
798
2CBD3FEHGJI3LK$MON4L3



e@

2O76
N

$ 
N

4 7%4 .

 
.

76
N

$p
E

PRQSTUQSVWYX%Z'[\(]^W ]`_
W \La%Q
b
cedf[W%a
dZ'gWihjZ\kX%Z'[`TlZmdS%X nocp S/qmb S
\rb a%]Dn

-

Section 3.4. Estimates of the time scales in die casting
/
"

-

 &!/
"

*

#"

&)( *

- 

!

2



*
&   , / !

.  
EU4
  ! 4  @ F U4
  W   %U
 K O %O Q
 


 a U4
 (   h1
 
.     
. 4
 


     




 &
8

,
 ,
 , 
KO Q
8 ,


v  
 
 

'

(
'&
 $







*
v
 R


%  
   % > 
@



.


   ^  *   
$
 
[]
%
 . 
1

H6Ni5'.

*

2

&

Nm3

4

H4 76O-m6I
Nm3)4

5

N

5(6N I
7JN

4

4

I
7%4 .

4

5o0m3 .?0mNm3 7%4 N D7.

4 I3

2OI

.

N

76N

4

.

4

4

0m3jN

0f6I

N7 I

4 .

@

2

Ni.

.

2U4

4

76
N

0'6I

73j.

4

4

-
4

NfE

N/7 I

H6N

5O76N

4 "76
N

I

NDI "N

-m6I3rI-7Nm3)4 7%4 -

4

N

4 .

I

7%4

N

0Im3rI

?E

I
7%4 .

.

3"-.

-7%4 .

4

N/7N3

?E


6
N3 N

76N

4

76N

6N I
7i-/.

-m6I3rI-7Nm3)4 7%4 -

-7%4 .

-6I3jI-/7Nm3)4 7%4 -

7%4

0m3 .

-N

NO4 H5

 
v i *

*
c

= 4 $
* 4 < 4 $
 #


  % 2*
@  $   


  
S

4

7%4

4 N

@

N

N

-I

.

3

-.

4 7 2 E

-7%4 .

4 76

76
N

0m3j.

N

-/N

N

k;

I

;

4 7%4 .

;

4

N

4 I3

.m7N H76N

2(I

I4

iI

.

0I
76U.

@

N

N

.

3 N

K O dQ




.7N(I5'I4

.m7N
6.

N

76
N

4 N

.

4

.

4

4

-6Im3rI-7N3 4

.m76Nm3D0m3j.
N

-/N

414

3jN 4

N

@

I

.

   [ †^


3$76N

. `4

5

-

4

N/7 I

0
7%4 .

@

N/7

76N

4

76N

.

4 N

. H4

s


}…

I

N I

NN

7N3 N 7E
4

N

.

;

I

-/.

4

7%4

N

NO4

N

.

76
N

.

4

76
N
I

^" ,
  

 Q
 ,

 & | 0
;

3

M

4

Nm3

I

I

0
7%4 .

0f6I

7.(-/.
.

N

4

-

E





.

.

N

4 YI

76
N

N^76I
7
N

7

I

N

N

.

7

'I

-I

N3

I5

3jN 4

-

M

6
N
I
7

4 7

7 I

N

Nm3

4

73jI

I

-ND7.

N`76I
7

o@
4

.

4

4

4

N

I

4

4

4

4

.

4

-3jN I

N

4

I

76
N



 
( E

 6
  ;1  
 

. 


7Nm3jN



-I
7%4 .

7%4

-I
7%4 .

F3j.

7

76
NU-I

4 i4
.

7%4

-

N

N'E

I

4

4 N

`6m4

76N`4

N DI--.

I

7Nm3 )I-/N

3

4

5

7.

K O MQ

   

?E

%  235.06(  74,   8:9

ƒ

$



$GIH JIK L

M

$

(* ( % '#; 0
 !<=9   > '!

%  23!N  28 O.0M(*N#& '*P  Q(*!$#;  8

!;(?#; 0
V_` ` a Tcb .O#&523!?% #$!d #&2,0
 '#$3V#$0

%  23V.0h( 7i,  8:9kj-%M#&l7m02 g#&<.10 2(3.10 

„ $

G RCH JIK L (''!=#; 8F@'!

b F2*  #1+N#&  !4W k0 .O(*!=#; 85@O  t7X'-0
F_ R R RCH #$0
 L
9

D#+-,  (' 2

?#$ 17i *De?+i#&i, % 8 .0M(*m#&i7X'(   i,  M#$!>#&  !&  '#>( (?#$1 !$#; (*!Q?#$(9

‚

7X'(   0

%  23u.0M(*n! 0
% ce 
%3!;!3gv0'@w!,0
!=023

 '#E !>#& 0 8- ( S
y

N

4 /6N

N

-m6I3rI-7Nm3)4 7%4 -

.

76N
.



N3

76N

76N

ZV0 2 "0 .)7X'8
 #&%  28 E#& B   E(* ( % '#; 0
V!?%8 8 3!$#$*

P

@

N 7 I

H6N

LE

#&  !"23!=* 2(<D0'@x74%( #h(*0 !$# T

O@O

E

-m3 N
I

5

(* ( % '#$3k#$0en N#&D8 <0 .>op p p/q r<s$9

'+ S

7

.

6
N3 N

I/2 Nm3^4

7 ^.

I

N'E

N

I

N

.

3 N

0f6I

N3 2

4

4 7 I
7%4 .

N3 2

3jI-4 .oI

-7%4 .

I4

-.

.

-/.

3

76
N

-NH76
N2



?y

3

4

4

5e76
NC- I


, M(M Q 
F 
 K 0


 
  
 R 4 $
H 

   
+ 4 $


,

F 4 $   2
64

76I
7H76N

G RIH J
KL =S
TVU 3( WF #X0
%'#4 D#&' ",  ,), 8 NYZ C[]\O^ U \

}†

.

4

76N

4 I3

5N ^I

76N

-

;

0m3j.

E

7%4 -

14
4

N

0mNm3rI
7 f3 N

-m6I

^76N(-6Im3rI-7N3 4

e 0
%#Xf RIH JIK L (''!=#; 8/g>05.0M(*@>  ]eDM

ƒ

76m4 -

4 7%4 .

`4 76

N/7 I

OI

E

76
N7N

     !"!$#&% '#)(* ( % '#$#&#+-,  (*/.10 2(33!42

7m02

4

-/N

;

I

N

4

03 .

2O76N

7)<!?0'@A '#$23!=#; 8B,0
7)0
C D@E  (F!?7) (*!=#; 8

ƒ

76N

76
N

4 7%4 I

N3

- I
7%4 .

.

5

Nm3 2

76
N

4

5C3jN I

'3)4

*

3 F*


@



Nm3 7

@

I

4

4

4

4

0m3j.10mNm3 7%4 N

5'N

.

I4

.

3

I/2 Nm3

N'E

3jN

3 5'.

2

&

764

N

.

-6I

76
NU4

-m3 N
I

Nm3j5.
.

;



 4, *  8& "
 & 

K  U
  
 



* 

 , *
.

4

N

b^ 




7%4 .

N3 2

N

7 I

;

.m7H.

6Nm3jN(7.

J/ ! 
  4&!/
"
Z

3

N

576

4

.

@

7.

N

N

N

-N'E

N

7%4 -C7%4

4 7N

7 I


"  
 @ H U4
    4  Y 
 
 


%  

E  
 6*





%  ,
"     F?K . H  , Q +1
.
   . =  ,
v  i F Y H 4 $ 
  %
  !0 * .
$
@


 , (   K 






5
Q

# 
  [ 
  # 






$
  
* 
%  W* ,  % 
  @   
  
 . #  ,

6I

4

4

-6I3jI-/7Nm3)4 7%4 -(7%4

76N

?E

76I
7

76I
7

76
N

2

QS/T

QSVWYX%Z'[\

]^W ]`_
W \La%Q
b
cedf[W%a

dZgWDhjZ\AX%Z'[`TlZmdS%X nocp Sqb S
\jb aFWn

:<;
-.10/2f3)4 516
798

=>>'>?;A@

2oBD3FE

GJI3LK$MON4L3

Chapter 3. Dimensional Analysis

]

  . 

6
N3 No6
N3 N

F3 .

7

N

.

-
4 72 E






H6N

6Nm3jN

-/.

N

0m3jN

.7

N

4

7%4 I

4 .

2

`3jN

0mNm3)4

N

HI

7 I

N

['[zŠK]W^
0

 

@

N I
7

I

I

76N

4

 
.



NY6N I
7H73rI

5

7%4

NO4 H5

4

Nm3
@

N



-/.



N U-4 N

EU4


2(76
N(N

I
7%4 .

 
$ ,  
  K


$
4
f 

: 4 $

" 


76I
7

76
N

7 I

2

4

7

@

I

4

4 N

E

.

4

N

5

7%4

I--.

7

.

.

4

-N

3

4

4

4

@

7.

N(4

5

@

O4 7

MU4

2

-/.

E

I3 2O-.

3 7%4 .

I

`6m4 C4

N

I

7.

3j.

0m3 .?0m.

N3

@

N

f0

`I

N I3

0m3j.

03 .

I-

E

4

7.

- I
7%4 .

-I
7%4 .

N

7 I

76I
7`I
7
4

76
N

.

4

4

`6
N

I

4

4

.

4

4

64 -6

4

.

6I (I

4

4

4

.

;

-N

0mN3jI
7 f3jN'E




-/N

76N

c
 i  
&
.7N

.

•

}

`6
N

76I
7

76N


I



76N
5

I

Q

=>

 .  

sC  
"   
 ,
E    , 
 
  Q h1 

 4

,  , 
.

N(- I

4 N`764 -

-/.

-

76N

4 I3`3jN


4

-/.

f3

N

;

N

F3 .

76m4

-/N

73rI

@

0m3j.

-.

N

4

4 .

7N )I

7
E

Im33)4

N

4 -/7 UI

E

MU4

"76
N

H6N

I

N3H6I

76
.

I

2m4 N

4 5

4


76N

2YI

- I

7

I

@

6I i7.

.2 `76
N

N

N -7

.

N

4 7 2

76N

.

4 5

@

4

NO-.

N

" 
 4   Y

 # 4 $




@ ? U4
   H]
  

@


[
%'  0 
#

7 I

-6I

4

I

N 5

N

5N

5e.

76N

f3 4

i76N

f3 76
N3

0I3 N

I
7

4

0'6I

5Y76N

4

.

4

I

N

7.C.76
N3

.

.

N

E

4

4

4

76I
7

NN

-I
7%4 .

F3j.

7N

N

N

7E

0mNm3rI
7 '3jN

;

-/N

76N

0mNN

7.o76Ne6
N
I
7

-6Im3rI-7N3 4

N

- I

N

73rI

4

.

Nm3

7%4 -(6N I
7

0mNm3rI
7 f3 N

7%4

4

Q


 '
U



@
0'0mN

4

4

m4 7N

N

.m7%4 -/N

5?3jI

4 N

.

7

76
N

73rI

Nm3jN

3J76
N

F3j.

-/N

F3j.

Nm3

@

4

7

@

a 4 K 4   U
Q  !
   )( & C  &%
; 
6   @



 


4 N

F3 .

<76N

NN

N(N

7.o76N

.

.

76N

7%4

4

- I
7%4 .

7%4

Q

==

?E

76N

N/7

- I

KO

N

4

I
7N

7%4

e@

5

-/.

0m3 .?0m.

7N

.

4

5

3 7%4 .

4

I

4

4 O4

76
N

7.

0mNm3rI
7 '3jN

mE

I

76
N

@

.

4

4

5

2

KO O Q



.

=

?E

?E

N

4

 3 =  VB

7`I

4

N I3

-/7%4 .

 @
.

76
N



"   

4 N(764 -

N

;



;J@


RB

7

I

=



-/7%4 .

E

\>'+*0
c 'PC +ud
,   *#; 0
 S

$



  !5(30
 4(' '# !D(30
7i7)0
 +c%!=3

#$0k2, 23!;'#)#&n23!& !$#=(3De?#1@3n#1@05!=0
  !'9

' #& Ne?#@63w!=0
  wx 

%  :g)0



b 00 #"#&  -W g0
, gt#& '#Q#&3+F2?.#& '#"#& !m(30- 4(' '#

2, M*!='#$!#&>23! !=#=  (3Ee ?#1@3 >#& 6#1@0O!;0
  !t!&  (3h #  !tO7X 0 -.l(?#$0 :  E0
3!0 #3#$l7X  #&h( (?#$1 !=#; (
#; 7)9

}–$

3!$#; 7)'#$(*DeN 74,20 P 3e?+N(*0
'P  #; 85#&n23!& !$#=(33!i0 .6#&<I 4#$0k2, 23!= '#$3
 n 8 #&D5#&

!;7m".10 ]#&X0 #& 23! !=#=  (34 #$0#&X(30
0
   8N 

} 

3

A76
N

KO

'3 )I-/N

I

s    

)( &
 p 
 
;  $





4

N

H6NO-6I3jI-/7Nm3)4 7%4 -(7N

7N

.

@

7N3 )I-N

;

7

N

7.

;

3jN 4 7 I

E

I

E

7Nm3 )I-/N

N

F3 .

I3

.m7NO76I
7(4

4 N

I4

4 N

2

4 -

;

76N

4

4

 

4 .

7%4

.

  



7%4 I

4

.

-

7.

7Nm3jN

.

6
.

H U4
 4  b
  s



I
7^76N

0mNm30mN

4 7%4 .

@

 
 4 &

NN



-/N

4

*

N/7


,

"    Y
4,



2 ^



Q
, L1


5
  K  6"  *  
 @ A *    
( 

764 -




(
 
F 





V




Y
D
,

, E




$


_*
 =
G
a . 
     C   i  p   C    B

 > U4
  C   i F [ 4  4




.
 ) U4
  
 
 s

i   )( ! &





 s
 s
   4

1 a   
# 4 0 
   

1
@

G  * 


f1
 S  
    
6Nm3jN



?E




*

@
7

KO

b^ 




I
7%4

%

-/.

.

.

I
7N D76
NU6I

N
Im3r-6

I iI3 N

 . .
$ ,  



N 4 5

73 -7%4 .

4 UN

s



  
 ^

   ,
. 4
 
 *
 

'   .

*



4 `76NU4

1



 





%$

(*<e 42, 23!= '#$3e?+

   
 !#"
&

% DM9 9

J

m9

(')$*

Q.10 d 74, m!;3m#&7)0 2m!& 7i,  /3<'!;!%74,'#; 0
n *!>#$0n,%-M

:<;1=>'>>?;A@
-/.102'3)4 516
798
2CBD3FEHGJI3LK$MON4L3


9

PRQSTUQSVWYX%Z'[\(]^W ]`_
W \La%Q
b
cedf[W%a
dZ'gWihjZ\kX%Z'[`TlZmdS%X nocp S/qmb S
\rb a%]Dn

3

Section 3.4. Estimates of the time scales in die casting




!,,2

4&!/
"

&('  ( % *



^*
@ ,  >
mI

4

73 .

%-
4



c

N

 .   / *  / 4




  3 ;   6 
  4


    '     
 @F 
 
 *   4

% 
4

4L0I
7%4 .

4 `5.

-m6I3jI-/7Nm3)4 7%4 -O7%4

-N7

I
7%4

*



6
.

4L0I
7%4 .

4

.

0

2

&

5

.

-

I

I

4 - I

.

g2x†hi o

4

NC4

"N mI

N/7N3"I

N3

7

0

7

N

;

.

5

76N

-/.

.

.

4

%3)4 5

4

1. <- I
2

7

4L0I
7%4 .

e@

.

3j.

N

.

4 N

03 .

@

2

Y@

4

@

@

I

I

N

3 N 5

Im3

E

516
7i7.

N

IY3 N 7

4

 
=

 

I

0m3j.

7

: 
5 

  * $ 

  *
 

2U4

4

@

I
7 f3 NfE

N

4

I(764

4

N -m6I

-2

4

N
I

4

4 -

5

-N
N

`4 76

76
N
3

7

76
N

Nm3FE





!" #$% #!&'()+*,-./#)0'21% #!3%4!5* m76 #8#)9:;:%=<>
#+

?@;A;CBD
)4E)F#G)42%?H1I<>"# 6IJ K#G4)
'(LM#N*,%4E ;O(*5
 6PJ Q;;)SR
42#2/#)TVU/W?;%!=XY
!B[ZY\W]4) H
42
^9X^
!B[Z[%REW_^`2!9X^
!B 65J #24E!#8#_:;@X^:!1?#G
42

#2 B[; HQ;42;4)+(*$:%F4) H
42
9X^
)B 6 a ;9XD%S:%F4) H
42
3% H#b3P4)2;S:;b4!. H
4G

9X^
!B 6

eXi wKd&c eXf
Gd

$ef



Dd

h d



c

ij^k lmn
F


g   
 
o

? H
1F3#pX(.
!Bq>r H:N9XY
!B 6



g2x†hi oHs

t:;
Ou
C?v  A2W4p1;

;;)w*,

">r H:x

(
b #,Y3;
)By
NF`G)
Y4! H
1)Z[z 6+{ :%] B[
b';(!1F #
',Y2BD:w3+#)3X 6 #8#)
)B|#2)4G;;?}1F<>~#]u€r)E0 #=4)!

Z‚4 6 WZ~%/#24!.
'(:;<>
#@x*,%4E ;*r
 6=ƒ 

„?:%3;  A_…
C?v 6

eXi wKd&c eXf

f d

d
  


 ) d



ij^k l†;n
F



J #24E!#8#:%42#G=*",X^
x9XY
!B[Z[;F:;=4G#29*r:;=4!:?34) #)
49X^
)B
‡@ˆE‰)Š8‰O‰2‹Œ;Ž% ‰!ŠFH

‘Šp’2“Œ’C‰O’2ˆ?Œ’+’2ˆ‰y”ˆEŒ“Œ?”G’C‰“3 ŠC’K ”S’KH_‰|•–—( ŠpŠ2HŽEŒ’K •^˜A”)Œ;˜š™‰qŒEŠpŠp‰!ŠpŠ8‰!— ™G›
œ f  % C "ž  , ,   ’2ˆ;‘ŠNŸ(  ‰˜¡™G›   C * k-¢0•’C‰S’2ˆ‰|Œ;˜?Œ; •Ÿ›I™‰)’.£¤‰!‰˜
Œ;˜E—
p¥/¦ ?§ –,•“@£_ˆ ”?ˆ  
Œ;Ž;Ž‰!Œ“ªŠ_H˜x™•’2ˆ•–0’2ˆ‰ § ’2ˆ‰]”ˆEŒ“Œ?”G’C‰“3 ŠC’K ” ‰˜EŸ’2ˆ §  § Œ;Ž;Ž‰!Œ“ªŠ$ŒEŠV’2ˆE‰’.›;Ž ”!Œ;;—( ‰=’2ˆ ”«˜‰!ŠpŠk
Z\[X]!^

 





$E¬
$ ¬

   8 



 $E ¬

 ­  $E ¬ 
¡


* ¬

  

 8 

 

  

 
$   $E ¬   ¯f ®

$ 

ij^k l°;n

± ˆ‰“ª‰ ®  ŠV’2ˆ‰—( ŠpŠ2HŽEŒ’K •^˜=–&‘;˜?”2’K •Y˜+ Š@—%‰G²‚˜E‰!—NŒEŠ
®
µ
j†







­
 




 



 8 
 

 "·






¸µ


 
  


­
 


¹qº)»G¼Nº)»2½)¾x¿KÀ%Á?ÂÃľ!Ã$ž!ÂHÆKºÇÉÈSÊ;Á)¾KÆ
ÊEÀË)¾VÌÀ?Â[¿KÀ%Á$¼€ÀÊ?»K¿!ÍFÈ?Î »)Ï?Ç »ÂÇ Æ&¾2Í





G´
 
  
 

 "· 



h

¶µ
 


 8 



 8

 





 






 ¤·


­









ij^k l n

”)•YŽG›;“3 ŸYˆ’šÐÑ § lÒÒ%Ò § ™G›FÓV“&k5Ô~Œ“HՂÖ‰?H“

k  (
k= j
9
k 
(   : & 
(k  

~=j 

k" 8¨ 0 
 © ( 9k 

  j
k" 6V j
5 9 k
   9k 


  j '# j
%  -L"
   j 

Chapter 3. Dimensional Analysis

 ' ! (k

 -    "  < 
:


‰‹ŠbŒ

 

/

( *


4&!/ ,


/

/

5 

!/ +
- ,1&

2

*-,  3*%,

¢0•E£ £¤‰]”!Œ;˜N •;•^«Œ’VŠp‰) ‰“Œ;;’KH_‰+“Œ’K •%Š!kr‡@ˆE‰+“Œ’K •N•–¯Š8•Y  —( ²^”)Œ’K •Y˜=’KH_‰’C•+²‚
 H˜EŸ’KH_‰


¥  !


¥  '( ! &




 




œ


g



(  ¬  
$ ?
 ¬


£9ˆ‰“ª‰
‰)›%˜E•Y —%Š_˜;‘;™‰
“  
g 
 
 ’C‰G–3Œ;˜x˜;‘%™‰


“       

ij^k l %n

0 ‰“‰£¤‰Œ;‘EŸY9‰˜’w’2ˆE‰—( Š8”‘Š8Š/ •^˜•^˜]’2ˆ‰HŽ•“}’pŒ;˜?”G‰•–0‰ ^‘EŒ’K •^˜xi.j[k l %nGkr‡$ˆ‰+“ Œ’K •x Š@‰G‹’2“‰9‰ ›
HŽ•“ª’pŒ;˜!’VŠ/H˜?”G‰ ’5Œ?”G’2‘EŒ;
 ›—%‰G²‚˜E‰=’2ˆ‰+“‰^‘H“‰!—N²‚
 H˜Ÿ’KH_‰%k


¥  !





ij^k l "%n



 !


 $ ? g 
 ¬


#"’’2ˆE‰$_•^_‰˜’
’§ 2ˆ‰  ”G•^˜Šp’pŒ;˜!’  §§  Š‘;˜%«˜•E£9˜wŒ;˜E— ’CŠ~ ?Œ;
‘‰@ˆ?ŒEŠ‚’C•_”)•Y_‰w•Y‘’[–&“•Y7‰G‹;Ž‰“,H9‰˜’CŠ!k
$‘%“ª’2ˆE‰“_•“ª‰
§ ’2ˆ‰  ”)•Y˜EŠC’pŒ;˜’   Š¤˜E•’w“ª‰Œ;
 ›@Œ@”)•Y˜EŠC’pŒ;˜’"Œ;˜E— Š0Œ5 ‰“}›]]H —$–&‘;˜E”G’K •Y˜5•–Y’2ˆE‰VŸ‰)•^_‰G’2“ª›!k
  "  3 b1 '&
)h 
ok  ¢0•’C‰+’2ˆEŒ’9’2ˆ Š=‰^‘?Œ’K •Y˜xŒ; Šp•O— %‰“‰˜’=–&“ª•^ Œ;
[’2ˆ‰SŽ“‰G  •Y‘EŠG ›OŽ“•YŽ•%Šp‰!—F²‚
 H˜EŸb’KH9‰+‰&Y‘?Œ’K •Y˜EŠ
 => (  ('  

§
Š/H˜?”G‰ ’V’pŒ;«/‰H˜’C•+Œ?”!”G•^‘%˜’ÄŠ8•Y  —( ²^”)Œ’K •Y˜]Œ;˜?—+²‚
 H˜ŸFŽ“•”)‰)Š8Š$H˜’C•NŒ?”)”)•Y‘;˜!’ & k
‡@ˆE‰“Œ’K •]•–¯  ^‘ —+_‰G’pŒ;?”G•^˜E—^‘E”G’K •Y˜_”ˆEŒ“Œ?”G’C‰“3 ŠC’K ”Ä’KH_‰5’C•”ˆEŒ“Œ?”G’C‰“3 ŠC’K ”V²‚
 H˜EŸ=’KH_‰9 ŠŸ  E‰˜
™G›
!
!
!






(

œ





*



(






* *

*









g

$ ?  




ij^k jÒ%n



‡$ˆ‰Š8•Y  —( ²^”)Œ’K •Y˜]”?! ˆ?Œ“Œ?”G’C‰“3 ŠC’K ”9’KH_‰=’C•N”G•Y˜?—^‘E”G’K •Y˜”?ˆ?Œ“ Œ?”2’C‰“, Šp’K ”9’KH_‰ Š@Ÿ  E‰˜N™G›








œ




¬





¥  ) ( &

* !¥



A





)

¥





 



 



+*

!



ij^k j  n


‡@ˆE‰+“Œ’K ••–0’2ˆE‰9²‚
 H˜EŸ’KH_‰Œ;˜E—NŒ’C•^ ,)Œ’K •^˜ Š

.-



   *  (


 


 
!0/

œ e +





A7F

,

ij^k jl%n

21

¢0•’C‰9’2ˆ?Œ’  § H˜]’2ˆ Š@”)ŒEŠ8‰ §  Š5’2ˆE‰=’2ˆ ”«˜‰!ŠpŠ5•–¯’2ˆ‰]Ÿ;Œ’C‰]Œ;˜E—S˜E•’V•–0’2ˆ‰]—( ‰”!Œ  ’›!k

.-



  




  

(

 











 




œ

ij^k jj%n

F43A5 6

£9ˆ ”ˆN_‰!Œ;˜EŠV’2ˆEŒ’_ –0Œ’C•^ ,)Œ’K •^˜•(”!”?‘;“ªŠ §  ’w£$H
^™‰ E‰“ª›–3ŒEŠC’5”G•^ŽEŒ“‰!—+’C•+’2ˆ‰²‚
 H˜EŸFŽ“ª•(”)‰)ŠpŠk
7


b

 'P #=WV#&c  eM#1+u#$0w(* #& !5

% '#; 0
98
( WM#;:=<  $4' ?> !F

d
, 1 7m'#=
@60 lWi!=0@)(*<+'0
%6  7)"#$04#& !O

”G•YŽ)›%“3 ŸYˆ’šÐÑ § lÒ%ÒÒ § ™G›bÓV“&k@Ô~Œ“HՂÖ‰?H“

% *#; 0
I9

b

@0
% 

  Wk#$0

 'PuC8 0
0-

% '#; 0
I9

¹Iº)»2¼º)»2½)¾x¿KÀ%Á?Â]Ãľ!Ã$ž!ÂHÆKºÇÉÈSÊ;Á)¾KÆ
ÊEÀ%Ë)¾wÌÀ?ÂD¿KÀ%Á$¼€ÀÊ?»K¿!ÍFÈ?Î »GÏÇ »Â Ç ÆKÃVÍ


Section 3.5. Similarity applied to Die cavity

‡@ˆE‰+“Œ’K ••–"’2ˆE‰— Š8Š/HŽ?Œ’K •Y˜’KH_‰=’C•Šp•Y  —( ²^”)Œ’K •^˜9’KH9‰ Š@Ÿ(  ‰˜N™G›
 


 !


p¥/¦
¥ )( ! &
¥
 

 œ
 
A7F
ij^k jmn





 œ



$ ? 
* ¬



 ¬ 



’2ˆ Š_‰ ^‘EŒ’K •^˜]› ‰ —Š@’›;Ž ”!Œ;% ?Œ;
‘‰!Š@–,•“w=Œ;˜!›+Š/ ’2‘?Œ’K •Y˜EŠ9H˜’2ˆ‰x“Œ;˜EŸ‰•–rA7F H˜?—( ”)Œ’KH˜EŸ’2ˆ?Œ’5’2ˆ‰
Šp•^  — ²^”!Œ’K •Y˜=Ž“•”)‰)Š8ŠÄ ŠrŒEŠr–3ŒEŠp’rŒEŠr’2ˆE‰$—( ŠpŠ/HŽ?Œ’K •Y˜(k ’Ä! ˆ?ŒEŠr’C•+™‰˜•’C‰!—’2ˆ?Œ’"£9 ˆ‰˜$’2ˆE‰@Šp•Y  —( ²^”)Œ’K •^˜
Ž“•Ÿ^“ª‰!ŠpŠ ’2ˆ‰=— ‰_’2ˆ ”«˜E‰)ŠpŠ¤—%‰!”“ª‰ŒEŠp‰!Š!kr‡@ˆE‰]“ Œ’K •  C “ª‰—Y‘?”G‰—ŒEŠw£¤‰
Hk #Š$“‰)Š)‘% ’CŠw’2ˆ‰] ŒEŠp’¤ŠC’pŒEŸ%‰
•–’2ˆE‰Šp•^§   — ²^”!Œ’K •Y˜w”)Œ;˜_™‰w”G•^˜Š2 —‰“ª‰—$ŒEŠ~Œ9Ž%‘;“ª‰Ä”G§ •Y˜?—^ ‘E”G§ ’K •Y˜@Ž“•Y™; ‰šŒEŠ‚£wŒEŠ~—%•Y˜E‰5™G›w’2ˆE‰  ‰˜Ÿ^  ŠGˆ 
ŸY“•Y‘;Ž(k


  # 



/054*/ " #"+$

*E





-



  
     

%&!/
"+,

‡@ˆE‰²‚
 H˜ŸF•–w’2ˆE‰S_•Y —O”!Œ  ’›b”)Œ;˜O™‰N—   —%‰!—yH˜!’C•F’£¤•AŽ‰“, •(—%Š!k}˜N’2ˆE‰²‚“ŠC’Ž‰“3 •—Pi.•Y˜; ›‚‘ —
_‰”?ˆ?Œ;˜ ”)Š  H˜H‘% ˆE‰!Œ’@’2“ Œ;˜EŠC–,‰“EŠ8•Y  —( ²^”)Œ’K •^˜?n5Œ;˜?—x’2ˆE‰+Šp‰!”)•Y˜?—|Ž‰“, •(—|H˜£9ˆ ”ˆ’2ˆE‰Š8•Y  —( ²
”)Œ’K •^˜Œ;˜E—N—( ŠpŠ2HŽEŒ’K •^˜•(”!”?‘;“€k¯±A‰]—( Š8”?‘EŠp‰!Š=ˆ•E£ ’C•+”)•Y˜?—Y‘?”2’ĉ2‹Ž‰“3H_‰˜’CŠ9H˜— ‰”)ŒEŠp’KH˜Ÿ &  k ’9ˆEŒEŠ
’C•+ŠC’2“‰)ŠpŠÄ’2ˆ?Œ’w’2ˆE‰=”)•Y˜?— ’K •^˜ŠV—•E£9˜)ÕŠC’2“‰!Œ; ˆ?Œ ‰=’C•F™‰‘;˜?—‰“ªŠp’C•;•(—bŽ“3 •“D’C•+‰2‹Ž‰“3H_‰˜!’Ä£@ ’2ˆ’2ˆ‰
—( ‰9²‚
 H˜EŸ[k0‡@ˆE‰+  Y‘ —S_‰)’pŒ; E‰ •(” ’›NŽ“•²‚ ‰Œ;˜E—Y•E£tŽEŒ’&’C‰“.˜Œ“‰=Šp’KH
^Ž••“ ›N‘%˜?—‰“ªŠp’C••—NŒ’Ä’2ˆ Š
ŠC’pŒEŸ%‰%k 0 •E£¤‰) ‰“ § H˜’2ˆ Š$—( Š8”‘Š8Š/ •Y˜]£¤‰£$H
;ŒEŠ8ŠG‘;_‰’2ˆEŒ’V’2ˆE‰G›+Œ“‰«˜•E£9˜•“¤‘;˜E—%‰“ŠC’C••(—+’C•NŠ8Œ;_‰
—%‰)ŸY“‰)‰ &
k
‡@ˆE‰wŸ%• E‰“˜H˜EŸ_&‰ Y‘?Œ’K •Y˜EŠ¯Œ“‰ÄŸ(  ‰˜_H˜5’2ˆE‰_Ž“ª‰”G‰!—(H˜EŸ9Š8‰!”2’K •^˜Š0Œ;˜E—˜E•E£A£¤‰V— ŠK”?‘EŠp‰)Š¯’2ˆE‰_™•^‘%˜?— k" T &"'N 
= #T1 4 
  1
Œ“}›”)•Y˜?— ’K •^˜Šk¯‡$ˆ‰™•Y‘;˜E—;Œ“}›”)•Y˜?— ’K •^˜Œ’¤’2ˆE‰Šp•^  —NH˜’C‰“ª–3Œ?”G‰=–,•“’2ˆE‰=Ÿ;ŒEŠŒH“‚Œ;˜?—–,•“‚’2ˆ‰+  ^‘ — LP"
  
_‰)’pŒ;;Œ“ª‰ŒEŠ8ŠG‘;_‰!—+’C•S™‰  ˜E•?ÕŠG HŽ  ”)•Y˜?— ’K •^˜9£9ˆ ”ˆN“ª‰Œ?—Š
  %
"-#
%

1 ~
 "'N 

   "   
ij^k j†;n

 ­   ¬


­ ¬
F
£9ˆ‰“ª‰9£¤‰‘Š8‰9’2ˆE‰=ŠG‘;™ŠK”?“3HŽ!’  H˜?— ”!Œ’C‰)ŠÄ’2ˆ‰=Ÿ%ŒEŠ9Ž;ˆEŒEŠ8‰%k ’9˜•’C‰G£¤•“ª’2ˆ!›=’C•F_‰˜’K •Y˜’2ˆ?Œ’w’2ˆ ŠVŒ; Š8•
Œ;Ž;Ž%  ‰—]’C•]’2ˆE‰_”)ŒEŠ8‰$£9ˆ‰“ª‰]  ^‘ —N_‰)’pŒ; Š_ ‹?‰!—]£$ ’2ˆ=ŒH“EŸ;ŒEŠwŒ;˜E—x™•’2ˆ]Œ“‰@’C•^‘E”ˆH˜EŸ’2ˆ‰9ŠG‘;“}–3Œ?”)‰%k
#¯’Ä’2ˆE‰H˜!’C‰“}–3Œ?”)‰™‰G’£¤‰)‰˜’2ˆE‰  Y‘ —S_‰)’pŒ;;Œ;˜?—Ÿ%ŒEŠŒH“Ž“‰)ŠpŠ)‘%“‰  ‘;Ž Š5‰2‹Ž“‰)Š8Šp‰!—NŒEŠ
?!





? 

  "

ij^k j°;n

£_ˆE‰“‰ ? Œ;˜?— ?  Œ“ª‰’2ˆE‰OŽ“3H˜E”EHŽEŒ;0“Œ?—(
~•–5’2ˆ‰–&“‰)‰bŠG‘;“}–3Œ?”)‰b”?‘;“} ?Œ’2‘;“ª‰ Œ;˜?—   Š’2ˆ‰xŠ)‘%“ª–3Œ?”G‰
’C‰˜EŠ/ •^˜x™‰G’£¤‰)‰˜’2ˆE‰Ÿ%ŒEŠ9Œ;˜E—x’2ˆ‰N  ^‘ —|_‰)’pŒ;Hk@‡@ˆE‰ŠG‘;“}–3Œ?”)‰Ÿ‰!•Y_‰)’2“}›x §Š_—%‰G’C‰§ “§ H˜E‰!—A™G›Š8‰G E‰“ Œ;
–3Œ?”2’C•“ŠV£_ˆ ”?ˆ+H˜?”?
‘?—‰=’2ˆE‰+  Y‘ —S_• E‰9‰˜’ ( H˜EŠC’pŒ;™H  ’K ‰)ŠV‰G’p”%k
¢0•E£¡’C•]’2ˆE‰_—  ”?‘; ’5ŽEŒ“ª’CŠ ’2ˆE‰$ E‰ •(”E ’.›Œ’rŸ;Œ’C‰]ˆ?ŒEŠ’C•N™‰9—%‰G’C‰“.]H˜‰—]–&“•Y ’2ˆE‰]Ž  —( ŒEŸY“ Œ;
•“$Ž“‰G  •Y‘EŠ]ŠC’2‘?—( ‰)Š]•Y˜F’2ˆ‰O“‘;§ ˜%˜E‰“@Œ;˜E—yŠGˆE•’ŠG ‰)‰) ‰;kF‡$ˆ‰x—(  ”?‘; ’K ‰)ŠŒ“, Š8‰x—Y‘E‰N’C•O–3Œ?”2’’2ˆ?Œ’£¤‰
”)Œ;˜;˜E•’ŒEŠpŠ/ Ÿ^˜=Œ=ŠGŽ‰” ²^”$”)•Y˜EŠC’pŒ;˜’¯ E‰ •(”E ’.›Œ;˜E—ŒEŠpŠG‘;_‰$•^˜% ›  Y‘ —#Y•E£š•^‘!’)k$ ’@ˆ?ŒEŠ’C•N™‰“ª‰Œ;  ,G‰!—
’2ˆ?Œ’V—^‘‰9’C•’2ˆE‰+ ‹%H˜ŸFŽ“•”)‰)Š8Šp‰)Š$H˜’2ˆ‰Š)ˆ•’wŠG ‰!‰G E‰=Œ;˜?—’2ˆ‰+“‘%˜;˜‰“¤i3‰!ŠGŽ‰!”E Œ;
 ›+H˜ŒNŽ••“~—‰!Š/ ŸY˜


b #&  !"'-
 #; 0


"

\68  i#&XI )(*!$#; 8D, 20-(33!;!" !O,   e0
  (, 20-(33!;!*9

7

&%

b  N0
 +4#; 7mm#$0NI !=( %!=!X0'@

'

#$0N(*0
I%(?#"d
, 1 7m'#$!me 0
%#O#&

.%#&%2 g 0 #& 30
*!E<
 2'#m, 20-(3*!=!=*!E@O  :e )
 !=(% !=!=* 9
7

(-

[]0 #$E#&X 

&

v   80 .6#&i
 9

b 4#&

%  4!%M.1(3"(*0 #Oe Q!$#&  8
'#?g
.0]%!=#$* +X!$#='#$ g e 3(' % !=) #h23!?% #$!O i0, 23!=!?%2"8

 '#

#&2?.10 2<0n7m0 P 7m#39

j


¹qº)»G¼Nº)»2½)¾x¿KÀ%Á?ÂÃľ!Ã$ž!ÂHÆKºÇÉÈSÊ;Á)¾KÆ
ÊEÀË)¾VÌÀ?Â[¿KÀ%Á$¼€ÀÊ?»K¿!ÍFÈ?Î »)Ï?Ç »ÂÇ Æ&¾2Í

”)•YŽG›;“3 ŸYˆ’šÐÑ § lÒÒ%Ò § ™G›FÓV“&k5Ô~Œ“HՂÖ‰?H“

Chapter 3. Dimensional Analysis


I ~ 5k


N  Kk
 
 -1  

* " < 1 - 
4 

1  4
 "
   9 k 
 ' ,X '1 $ 
# "     
 


Ž“•”)‰)Š8ŠwŒ;˜E—x“.‘;˜;˜‰“[ŠC›EŠC’C‰ ˜•E£7”)•Y_•^˜% ›‘Š8‰!—H˜9’2ˆ‰=H˜?—^‘Šp’2“}›nrŠp•^_‰]Ž•“ª’K •Y˜9Œ’r’2ˆE‰]™‰)Ÿ(H˜%˜H˜EŸ
§ ”)•Y˜’pŒH˜ŠwŒH“EŸ;ŒEŠ!k0‡@ˆE‰“‰_Œ“ª‰9Šp‰G E‰“ Œ;(Ž•Š8Š/H™H  ’K ‰)Šr’2ˆ?Œ’’2ˆ‰9”G•Y˜?—( ’K •Y˜EŠ
ˆEŒEŠVŒŠ/ Ÿ^˜ ²^”!Œ;˜!’VŽEŒ“ª’0£9ˆ ”ˆ=
”)Œ;˜q™‰OŽ“ª‰!Š8”“,H™‰—[kS‡@ˆE‰²‚“ªŠp’Ž•%ŠpŠ2H™H  ’›S Š]’C•y—%‰)Š8”“,H™‰’2ˆE‰OŽ“‰)Š8ŠG‘;“ª‰N ?Œ“, Œ’K •^˜FŒ’9’2ˆE‰N‰˜’2“ Œ;˜E”)‰%k
‡@ˆE‰$Šp‰”G•^˜E—xŽ•ŠpŠ2H™H  ’› Š’C•—‰!Š8”?“3H™‰$’2ˆE‰@ E‰ •(” ’›_ ?Œ“, Œ’K •^˜i.ŒEŠVŒ9–&‘%˜?”2’K •^˜9•–‚’KH9‰nGkr‡$ˆ‰@ E‰ •(”E ’.›
 Š_“‰!—^‘?”G‰!——^‘%“3H˜EŸ’2ˆE‰_²‚
 H˜EŸ•–~’2ˆ‰”)Œ  ’›]Œ;˜?—x ŠVŒ]–&‘%˜?”2’K •^˜•–~’2ˆE‰=”!Œ  ’›]Ÿ‰)•^_‰G’2“ª›!kr‡@ˆE‰9”ˆEŒ;˜EŸ‰
H˜’2ˆ‰_ ‰ •”E ’.› Š5ŒŠGˆ?Œ“ŽH˜’2ˆE‰H˜ ’K Œ;(ŽEŒ“ª’¤•–~’2ˆE‰$²‚
 H˜EŸ—^‘‰9’C•’2ˆE‰9”ˆEŒ;˜EŸ‰_–&“ª•^tŒ=–&“‰)‰  ‰)’’C•Œ;˜
H_‰“ªŠ8‰!—  ‰G’)k‡@ˆE‰+Ž“‰)ŠpŠ)‘%“‰= EŒ“3 ‰)Š@Œ; Šp•NŒ’w’2ˆE‰]‰˜’2“ Œ;˜E”)‰ ˆE•E£¤‰G E‰“ ’2ˆ‰= ?Œ“3 Œ’K •Y˜EŠ@Œ“‰_•“‰]H —[k
‡@ˆ;‘Š  ’= Š™‰G’&’C‰“5Ž•ŠpŠ2H™H  ’› & ’C•F”G•^˜Š2 —‰“"’2ˆE‰xŽ“‰)Š8ŠG‘;“ª‰b§ Ž“‰)Š8”“,HŽ’K§  •Y˜(k=‡@ˆE‰Š/HŽ; ‰)Šp’_ŒEŠpŠ)‘%Ž’K •Y˜
 Š$”G•^˜§ Šp’pŒ;˜!’$Ž“ª‰!ŠpŠG‘;“‰
"

$

A


(



ij^k j n




±A‰Œ; Šp•ŒEŠpŠ)‘%9‰9’2ˆ?Œ’V’2ˆ‰]ŒH“EŸ%ŒEŠ5•^™‰G›EŠÄ’2ˆE‰ —‰Œ;;Ÿ;ŒEŠ_9•—%‰Hk
"
ij^k j %n
g 
£_ˆE‰“‰ g  Š"’2ˆ‰5ŒH“EŸ%ŒEŠ¯”G•Y˜EŠC’pŒ;˜’"Œ;˜?—   Š¯Ÿ%ŒEŠ ?ŒH“;’C‰Ž‰“Œ’2‘;“ª‰;k 0 ‰“ª‰Ä£¤‰$‘EŠC’0H˜EŠp‰“}’"’2ˆ‰_Ž“ª‰)  •^‘Š
ŒEŠpŠ)‘%Ž’K •Y˜]•–¤˜‰!ŸY  Ÿ(H™% ‰ˆ‰Œ’¤’2“Œ;˜EŠC–,‰“"Œ;˜E—+–&‘;“ª’2ˆ‰“"ŒEŠpŠG‘;_‰9’2ˆEŒ’Ä’2ˆ‰Ž“•(”G‰)Š8Š@ Š9Ž•Y ›’2“•YŽ ”  k¯±A‰
—‰)²‚˜‰=’2ˆE‰—H9‰˜EŠ/ •Y˜; ‰)Š8ŠwŸ;ŒEŠ5—%‰˜EŠ/ ’›ŒEŠ


,



 0 - " N 
 kT % )   <
 



"



ij^k j "%n
" 
‡$ˆ‰Š)‘%™EŠ8”“,HŽ ’‡F—%‰˜E•’C‰)ŠV’2ˆE‰]Œ’2_•Š)Ž%ˆE‰“3 ””G•Y˜?—( ’K •Y˜(k
‡@ˆE‰VŒH“EŸ;ŒEŠ Y•E£ “Œ’C‰V•Y‘’~’2ˆE‰5”!Œ  ’›9 Š0ŒEŠ8ŠG‘;_‰!—9’C•™‰ˆ?Œ ‰5Œ?”)”)•“—(H˜EŸ$’C•9’2ˆ‰9_•(—‰EH˜ ˆ?Œ;Ž’C‰“
"^kr‡@ˆ;‘EŠ
’2ˆ‰«˜E•E£_ ‰—Ÿ%‰$•–~’2ˆE‰9 ‰˜!’$“‰ Œ’K  E‰Œ“‰!ŒŒ;˜?— + # Œ“‰HŽ•“}’pŒ;˜’@ŽEŒ“ Œ;_‰G’C‰“ªŠk $?•“~”!ŒEŠp‰)Š
£_ˆE‰“‰’2ˆE§ ‰ ‰˜!’ Š9£¤‰
^—%‰)Š2 ŸY˜Oi, E‰˜’9Œ“ª‰ŒF Š˜E‰!Œ“r’2ˆ‰”?“3 ’K ”)Œ;[Œ“‰!Œ•“¤Œ;™• E‰’2ˆE‰—‰˜Š2 ’.› §  ”)Œ;˜
™‰—‰)’C‰“H˜E‰ŒEŠ5£wŒEŠ@—%•Y˜E‰™)›bipÔ~Œ“ 2Ö‰EH“  " "%†(™npn)k
‡•xŠC’2‘?—›’2ˆE‰”G•^˜!’2“•Y
 H˜EŸOŽ?Œ“ Œ;_‰G’C‰“ªŠ_’2ˆ‰‰ ^‘EŒ’K •^˜Š$Œ“‰—(H_‰˜EŠ/ •^˜% ‰!ŠpŠp‰—[k5‡$ˆ‰b9ŒEŠpŠ_”)•Y˜EŠp‰“ 
 EŒ’K •^˜]–,•“~’2ˆE‰  ^‘ —S_‰G’pŒ;D™‰!”)•Y_‰!Š










¬


, 



,
¬
 8  , ¬






,

¬
 
, ¬




,

¬
  ­ , ¬



ij^k m%Ò%n
F

 ,
 C   ,
 C  §  ,  C ( §
,
C ( § , C ( Œ;˜E—’2ˆ‰9—H_‰˜Š2 •Y˜; ‰)Š8Š
£ ˆE‰“‰ 8 ,
_
 §

§

­
­
’KH_‰ Š@—‰)²‚˜‰—NŒEŠ
,   § £_ˆE‰“‰ (


$ C k

Y‘?Œ’K •Y˜yij^k m%Ò;n9”!Œ;˜y™‰N’2ˆE‰NŠ8Œ;_‰NŠ2HŽ;  ²Y‰!—I‘;˜E—%‰“¤’2ˆE‰bŒEŠ8ŠG‘;Ž!’K •^˜N•–$”G•^˜Šp’pŒ;˜!’—‰˜Š2 ’.›x’C•


“ª‰Œ?—





 , ¬

-, 

 8




 

,

¬,






,

­  ¬,



ij^k m  n
F

(7 \t#h#&  !E!$#=8  g/@474%!$#Q23!;MP3<0
%-M!; .6#$0<  '#$   8  '#E8
%3!;!& 8:9
( ( 2i M)!;?P  v, 0 !;!& e   #; 3!*g b  'P )(0 !;)#&  !Q0
)0
 +i#$00
e'#=  4#& 7)




”G•YŽ)›%“3 ŸYˆ’šÐÑ § lÒ%ÒÒ § ™G›bÓV“&k@Ô~Œ“HՂÖ‰?H“

 i(30
#&M0
   8D, 7m3#$2!*9

¹Iº)»2¼º)»2½)¾x¿KÀ%Á?Â]Ãľ!Ã$ž!ÂHÆKºÇÉÈSÊ;Á)¾KÆ
ÊEÀ%Ë)¾wÌÀ?ÂD¿KÀ%Á$¼€ÀÊ?»K¿!ÍFÈ?Î »GÏÇ »Â Ç ÆKÃVÍ

/

Section 3.5. Similarity applied to Die cavity

" ‰ŒEŠp‰˜E•’C‰5’2ˆ?Œ’r£¤‰$”)Œ;˜;˜•’Ä‘EŠp‰@’2ˆ ŠŠ/HŽ%  ²^”!Œ’K •Y˜@–,•“^’2ˆE‰$Ÿ;ŒEŠ5Ž%ˆ?ŒEŠp‰;k¯‡$ˆ‰_•^_‰˜’2‘; &‰ Y‘?Œ’K •Y˜
–,•“~’2ˆE‰+  Y‘ —S_‰G’pŒ;YH˜’2ˆE‰_‹!&”G••“—(H˜?Œ’C‰=ŒEŠ8ŠG‘;H˜ŸN”)•Y˜EŠC’pŒ;˜’Ä—‰˜Š2 ’.›Œ;˜?—O˜E•S™•—›]–,•“ ”G‰)Š“‰!Œ?—%Š

,
,

¬

 , ¬
  , ¬
8  , ¬



,  ¬  ,¬
,  ¬  ,¬
  ,
 ,

 ­
š
 " ,
  ,
A
¬,  g
¬

8
 8 , 















)









,

,

, 

,  ,



, 

 8

,
 ,





, 

 

,  , 






,

,  , 



,
 

-, 

 8



  8

, š­

 



,

 ,


*¬  A
,  *  g
¬



,  , 
 

)

 ,



  

-, 

,

,
­ 

 

,    , 

 8 











 ,
 , ­ ,  ¬,

¬,
­ ¬,
F
‡@ˆE‰=Š)‘%“ª–3Œ?”G‰+™‰)’.£¤‰!‰˜]’2ˆE‰  ^‘ —S_‰G’pŒ;(Œ;˜E—+’2ˆE‰]ŒH“"Š8Œ’K Šp– ›
A
" ,  ? ,  ? , 

£_ˆE‰“‰9’2ˆE‰ " , § ? , § Œ;˜?— ? , Œ“‰—%‰G²‚˜E‰!—NŒEŠ ? , ?
‡@ˆE‰Šp•^
‘!’K •^˜9’C•N‰&Y‘?Œ’K •Y˜EŠ_ˆ?ŒEŠV’2ˆ‰–&“•Y • –



,


­



,
" ,

(
j "



8









b i@E1 #; 8#&  !Q



8
































C  ? ,


 


+ #

+  #

 


+  #









C

¬



k
ij^k m%†;n
ij^k m%°;n

+  #








, , ,g
,  ,  , g




, , ,g
8






,  ,  , g
8




ij^k m%l;n



¢¯•’C‰=’2ˆEŒ’$H˜]’2ˆ Š@‰&Y‘?Œ’K •Y˜Œ?—;— ’K •^˜EŒ;’C‰“.9Š5£¤‰“‰Œ?—;—% ‰!— §  * C * 


‡@ˆE‰  ˜E•€ŠG HŽ  ”)•Y˜?— ’K •^˜ŠVŒ“‰”G•^˜! E‰“ª’C‰!—+’C
•



*

ij^k mmn
*



 ,



ij^k m%j;n
F



,  , 

" ,

¬


,

 Š5’2“ Œ;˜EŠC–,•“_‰!—bH˜’C•





,


 ,


‡@ˆE‰=Ÿ;ŒEŠŒH“09•Y_‰˜!’2‘;t‰&Y‘?Œ’K •Y˜

, ­  ,

 

   , ­

¬


£_ˆE‰“‰ g  (  C * Œ;˜E— " , " C $ k
‡@ˆE‰Ÿ%ŒEŠ9 Ž%ˆ?ŒE Šp‰]”)¬•Y
˜’KH˜%‘ ’.›‰& Y‘?Œ’K •Y ˜“‰!Œ?—%Š


,



 





 
 

?  C 


¬





¬

¬


¬






*
 * ¬
*
 * ¬
*





*

















ij^k m n

% '#; 0
N #E !E!;!%7)3#& '#>P  !=(30 ! #1+40 .]#&i    ,#"0 ., 23!=!?%24#$74,  2'#&%29

¹qº)»G¼Nº)»2½)¾x¿KÀ%Á?ÂÃľ!Ã$ž!ÂHÆKºÇÉÈSÊ;Á)¾KÆ
ÊEÀË)¾VÌÀ?Â[¿KÀ%Á$¼€ÀÊ?»K¿!ÍFÈ?Î »)Ï?Ç »ÂÇ Æ&¾2Í

”)•YŽG›;“3 ŸYˆ’šÐÑ § lÒÒ%Ò § ™G›FÓV“&k5Ô~Œ“HՂÖ‰?H“

Chapter 3. Dimensional Analysis

–w ’Ä£$H
^™‰=–,•Y‘;˜E—N’2ˆEŒ’V‰^‘EŒ’K •^˜ij^k mmnĔ!Œ;˜x™‰]Œ;Ž%Ž“ª•‹%H9Œ’C‰!—
  ,
,   ,
,   ,
,   ,   " ,


, 
 8 , 
  , š­
 ,
  8 ,
’2ˆE‰˜]’2ˆE‰]Šp•^
‘!’K •^˜ Š9“‰!—^‘?”G‰!—N’C•


 ,











, , ,g
8



,

,   ,   ,  g
8



,


­

















+ #







+ 4






,  ,   ,  g
8















+ 4









ij^k m %n






™G›






ij^k m"%n
" ,  8 ,   ,   ,  g       + 4   
 
#"’’2ˆ ŠwŠp’pŒEŸ‰@£¤‰9—•N˜E•’5«˜E•E£
 –0 ’’2ˆE‰_”)ŒEŠ8‰9Œ;˜?—+ ’@ˆ?ŒEŠ¤’C•”)•Y_‰GÕ;•^‘!’0–&“ª•^ ’2ˆE‰_‰2‹Ž‰“3H_‰˜!’CŠk0‡$ˆ‰
—‰˜Š2 ’.›S“ Œ’K •F”)Œ;˜SŽ; ŒG›NŒO“•Y ‰x™‰”)Œ;‘EŠp‰’.£¤•|Ž;ˆ?ŒEŠp‰ Y•E£ ”ˆEŒ“ Œ?”2’C‰“3 ŠC’K ”H˜F=Œ  •“VŽEŒ“}’$•–¤’2ˆE‰²‚
 H˜EŸ
Ž“•”)‰)Š8Š!k




*4, 3$"

 ˜?—‰“  Y• ˜EŠC’2“‘E”G’K •Y˜

/








   0
* /  2

* "%&,







  

 #
  
 






H˜9’2ˆ ŠŠ8‰!”G’K •Y˜$£¤‰@Š)‘%=Œ“3 ,G‰$Œ;
’2ˆ‰]=Œ  •“[—(H_‰˜EŠ/ •^˜% ‰!ŠpŠVŽ?Œ“ Œ;_‰G’C‰“ªŠr£9ˆEŒ’‰ D% ‰”2’0’2ˆ‰_—( ‰$”)ŒEŠp’KH˜Ÿ
Ž“•”)‰)Š8Š!k
[zŠ#Œ

# !+[
Š

(

H˜E‰“ª’pŒH $?•“ ”G‰!Š
   Š8”G•^‘Š8‰_–,•“ ”G‰!Š
‰G›;˜•^ —Šb˜%‘;™‰““‰Ž“‰)Š8‰˜’’2ˆE‰y“ Œ’K •q•–$’2ˆ‰A_•Y9‰˜’2‘%
–,•“ ”G‰!Š’C•A’2ˆ‰F  Š8”G•^‘Š–,•“”)‰)Šk }˜y— ‰
”)ŒEŠp’KH˜Ÿ
‰)›%˜E•Y —%Š@˜;‘%™‰“0Ž% Œ)›ŒŠ2 ŸY˜ ²^”)Œ;˜’5“ª•^ ‰$£_ˆ ”?ˆ—‰)’C‰“H˜E‰$’2ˆE‰ Y•E£ Ž?Œ’&’C‰“˜H˜9’2ˆE‰“‘%˜;˜E‰“
Œ;˜E—+’2ˆE‰= ‰˜!’ÄŠC›EŠC’C‰+k‡@ˆE‰=—( Š8”ˆEŒ“ªŸ%‰=”)•‰  ” ‰˜’ §  §  Š9‘Š8‰!—xH˜]’2ˆ‰+Ž  —( ŒEŸY“ Œ;  Š@—%‰G’C‰“H˜E‰!—
 Œ“Ÿ‰ ›N™G›’2ˆE‰ g  ˜%‘;™‰“"’2ˆ%“•Y‘EŸYˆ]’2ˆE‰= EŒ;
‘E‰]•–¯–&“, ”G’K •Y˜”)•;‰  ”E ‰˜’ § – § H˜Š/ —%‰=’2ˆ‰+“‘%˜;˜E‰“&k
‰ 6 [ $] Š# !+[
H˜E‰“ª’K Œ;%‰˜‰“ªŸ›
A5C
( 
 
AC
   ’C‰“9Œ;‰˜E‰“Ÿ›
(”?«2‰“ª’$˜;‘%™‰“"—%‰G’C‰“H˜E‰)Š$ –"’2ˆE‰“•Y ‰•–~’2ˆ‰+_•^_‰˜’2‘; ‰˜E‰“Ÿ›’2“ Œ;˜Šp–,‰“‰!—+’C•’2ˆ‰“.=Œ;%‰˜E‰“Ÿ›+ Š
Š/ Ÿ^˜ ²^”!Œ;˜!’)k
g





*(

 C 
C  





•

(




  !O#$0
,  (4 !O(30
'#&20 P 2!&  v i#&X 2*i0 .#@0n, '!;

( –3!;3).0

—

0*@m9

#; 7mie' 808I(W  #(> !X, ,

”G•YŽ)›%“3 ŸYˆ’šÐÑ § lÒ%ÒÒ § ™G›bÓV“&k@Ô~Œ“HՂÖ‰?H“

¹Iº)»2¼º)»2½)¾x¿KÀ%Á?Â]Ãľ!Ã$ž!ÂHÆKºÇÉÈSÊ;Á)¾KÆ
ÊEÀ%Ë)¾wÌÀ?ÂD¿KÀ%Á$¼€ÀÊ?»K¿!ÍFÈ?Î »GÏÇ »Â Ç ÆKÃVÍ
3 

Section 3.6. Summary of dimensionless numbers

 Š 


# !+[

^bŠ Š

f (

ˆE‰!Œ’9Ž“•—^‘?”2’K •Y˜N™)›]  ŠK”G•Y‘EŠp‰]—( ŠpŠKŒ;Ž‰G’K •Y˜
ˆE‰!Œ’Ä’2“Œ;˜EŠp‰“~’2“ Œ;˜Š)Ž•“}’=™G›”G•^˜E—^‘?”2’K •Y˜
 
Ôr“3H˜%«=Œ;˜˜%‘;™‰“ Š¤Œ9‰!ŒEŠG‘;“‰V•–[’2ˆE‰9HŽ•“ª’pŒ;˜E”)‰5•–D’2ˆ‰5  Š8”)•Y‘EŠÄˆE‰!Œ’KH˜EŸ+“ª‰ Œ’K  ‰5’2ˆE‰$”G•^˜E—^‘?”2’K  E‰
ˆE‰!Œ’0’2“Œ;˜EŠC–,‰“€kr‡@ˆ ŠV˜%‘;™‰“‚ ŠÄHŽ•“ª’pŒ;˜!’¤H˜9”)ŒEŠ8‰)Šr£9ˆ‰“ª‰ Œ“ªŸ%‰V ‰ •”E ’.›=”?ˆ?Œ;˜Ÿ%‰)Šr•(”)”?‘;“Š• E‰“[Š)ˆ•“ª’
—( ŠC’pŒ;˜?”G‰)Š]Š)‘E”ˆFŒEŠ
‘;™“, ”!Œ;˜!’ Y•E£ iCŽ‰“.ˆ?Œ;ŽŠ Y•E£ H˜b’2ˆ‰xŸ;Œ’C‰n)k }˜F—( ‰b”)ŒEŠp’KH˜ŸS’2ˆ Š˜%‘;™‰“9ˆEŒEŠ
ŠG=Œ;
 ?Œ;
‘‰!Š$H˜?—( ”)Œ’KH˜EŸ’2ˆ?Œ’9Ž“Œ?”G’K ”)Œ;
 ›]’2ˆE‰9§   Š8”)•Y‘EŠ=ˆ‰Œ’KH˜Ÿb Š=˜•’@HŽ•“ª’pŒ;˜’)k
 ?


Zƒ^

 C  
 C  

\Š# !+[

/

(




 


?•“0 —%‰!Œ;%Ÿ;ŒEŠi3Ÿ••(—NŒEŠpŠ)‘%Ž!’K •^˜=–,•“"’2ˆ‰+ ‹E’2‘%“‰]•–0’2ˆE‰=Ÿ;ŒEŠ= ‰!Œ H˜Ÿ+’2ˆE‰”!Œ  ’›nGk ’_™‰”G•Y9‰)Š
$



œ
/




(
g

”ˆEŒ“‰!”2’C‰“, Šp’K ”9 ‰ •”E ’.›
Ÿ;ŒEŠ5Šp•Y‘;˜?—+ ‰ •”E ’.›




Ö+Œ?”?ˆ]˜;‘%™‰“[—%‰G’C‰“H˜E‰5’2ˆ‰@”ˆEŒ“Œ?”G’C‰“3 ŠC’K ”V•– Y•E£7H˜$’2ˆ‰V E‰˜’0Šp›Šp’C‰ £_ˆE‰“‰V’2ˆ‰$ŒH“EŸ;ŒEŠ" E‰ •(”E ’.›
 Š=“ª‰Œ?”?ˆH˜Ÿ’C•’2ˆ‰ŠGŽ‰!‰!—•–¯Šp•^‘%˜?—Dk¯‡$ˆ‰]ŒH“0 Š5”?ˆE•”«2‰!—Œ’w’2ˆE‰_ E‰˜’ĉG‹ ’5Œ;˜E—bH˜Š8•Y_‰”)ŒEŠ8‰)ŠV•’2ˆE‰“
 •(”)Œ’K •^˜Š5ŒEŠ5£¤‰
%–,•“~ EŒ?”‘%‘;t ‰˜!’KH˜EŸ[k}˜Œ’2_•%ŠGŽ;ˆ‰“, ”9 E‰˜’KH˜Ÿ+’2ˆE‰Y•E£  Š=˜E•’V”ˆ•(”«/‰—+–,•“¤ Œ“ªŸ%‰
Ž•“ª’K •Y˜x•–5’2ˆE‰OŽ“•”)‰)Š8Š!kyÖ•“ª‰!• E‰“ § ’2ˆE‰ Y•E£ § H˜b£¤‰
D—%‰)Š2 ŸY˜x E‰˜’ŠC›EŠC’C‰ §  Š˜E•’]”?ˆE•”«2‰!—Dk ‰)’
’2ˆE‰FŒH“V ‰ •”E ’.›A Šx Œ“Ÿ‰b‰˜•^‘Ÿ^ˆFŠ8•|
’2ˆEŒ’]’2ˆE‰PÖŒ?”ˆA˜;‘%™‰“ˆEŒEŠ’C•¡™‰b’pŒ;«2‰˜|H˜’C•qŒ?”)”)•Y‘;˜!’–,•“
“‰!ŒEŠp•^˜EŒ;™; ‰]”)Œ; ”‘% Œ’K •^˜•–"’2ˆE‰ Dk




#!+[



[ EŠ











 

 















-





 $







‰ % ‰!”G’K  ‰ŠC’pŒ’K ”+Ž“ª‰!ŠpŠG‘;“‰=‰˜‰!Ÿ‰“}›
Œ ?Œ“Ÿ‰+«2‰˜H9Œ’K ”9‰˜E‰“Ÿ›

˜E‰•–~’2ˆE‰‘Šp’@HŽ•“ª’$˜;‘%™‰“0H˜’2ˆ‰+Ž  — ŒEŸ^“Œ;-”)Œ; ”?‘; Œ’K •Y˜ Š
“‰Ž“‰)Š8‰˜’w’2ˆE‰ˆ•E£ Ÿ••(—+’2ˆ‰“‘;˜%˜E‰“0 Š$—%‰)Š2 ŸY˜E‰!—Dk


G‰“˜;‘;™‰“&k‡@ˆ Š_˜;‘;™‰“
,

 KŒh[ Š # !+[


(

H˜‰“}’K Œ;%–,•“”)‰)Š
YŸ “ Œ  ’.›]–,•“ ”G‰!Š
$ ? ˜%‘;™‰“^“‰Ž“‰)Š8‰˜’[’2ˆE‰@“ Œ’K •$•–;’2ˆ‰wŸY“ Œ  ’›w–,•“ ”G‰!Š’C•@’2ˆ‰$_•Y_‰˜!’2‘;P–,•“”)‰)Šk ’¯ Š‚ E‰“ª›_HŽ•“}’pŒ;˜’
H˜—%‰G’C‰“H˜H˜Ÿ’2ˆE‰”“, ’K ”!Œ;%Š) •E£ Ž;
‘%˜EŸ‰“ ‰ •”E ’.›k‡@ˆ Š_˜;‘%™‰“r Š@—%‰G’C‰“H˜E‰™)›’2ˆ‰+ˆ ŸYˆ’w•–¯’2ˆ‰
  ^‘ —9‰G’pŒ;H˜$’2ˆ‰_ŠGˆE•’rŠG ‰)‰) ‰;k¯‡$ˆ‰ $“•Y‘?—%‰˜%‘;™‰“—•‰!Š5˜•’ÄŽ; ŒG›=Œ9Š2 ŸY˜ ²^”)Œ;˜’¤“•Y ‰=H˜$’2ˆE‰5²‚
 H˜EŸ
•–0’2ˆE‰”!Œ  ’›!k
m

$



?

¹qº)»G¼Nº)»2½)¾x¿KÀ%Á?ÂÃľ!Ã$ž!ÂHÆKºÇÉÈSÊ;Á)¾KÆ
ÊEÀË)¾VÌÀ?Â[¿KÀ%Á$¼€ÀÊ?»K¿!ÍFÈ?Î »)Ï?Ç »ÂÇ Æ&¾2Í



 C 



”)•YŽG›;“3 ŸYˆ’šÐÑ § lÒÒ%Ò § ™G›FÓV“&k5Ô~Œ“HՂÖ‰?H“

Chapter 3. Dimensional Analysis

 ^
#  ^  #Š !+[


(

H˜‰“}’K Œ;;–,•“ ”G‰)Š
^Ÿ “Œ  ’.›–,•“”)‰)Š
”)Œ;ŽH
 Œ“ª›x˜;‘%™‰“Äi Œn$—‰)’C‰“H˜‰£9ˆ‰˜’2ˆE‰ Y•E£ —Y‘;“,H˜EŸ’2ˆE‰]²‚
 H˜Ÿ+’2ˆE‰”)Œ  ’.›x Š$Œ’C•Y ,)‰!—N•“
 Š$”G•^˜!’KH˜;‘•^‘Š Y•E£ i,–,•““‰ Œ’K  E‰ ›x •E£ g  ˜;‘%™‰“ n)k





0/

 C 





! ## !+[
[ +[ €Š

(

H˜‰“}’K Œ;%–,•“”)‰)Š
Š
)
‘%“ª–3Œ?”G‰–,•“ ”G‰!Š


˜;‘%™‰“5 Š=’2ˆ‰N•’2ˆ‰“@ŽEŒ“ Œ;_‰G’C‰“’2ˆEŒ’Ÿ• ‰“.˜N’2ˆE‰Y•E£ Ž?Œ’&’C‰“˜OH˜N’2ˆE‰—( ‰%k‡$ˆ‰Y•E£ H˜F— ‰
 £@ ’2ˆ”G•^™H˜EŒ’K •^˜ŠÄ•–0’2ˆ‰Ÿ%Œ’C‰]—%‰)Š2 ŸY˜Œ; Šp•—%‰G’C‰“H˜H˜Ÿ
”)ŒEŠp’KH˜Ÿb Š@Œ’C•Y ,)‰!—NŒ;˜?— ’2ˆE‰“‰G–,•“‰
’2ˆ‰—^“•YŽEŠVŠ2 ,G‰)Š@Œ;˜?—N— Šp’2“,§ H™;‘’K •Y˜(k §




AC
AC



C 



  ]I^ 2[KŠz]s^ $[3^

F




‡@ˆE‰]”?“3 ’K ”)Œ;(Œ“‰!Œ ŠÄ’2ˆE‰Œ“ª‰Œ]–,•“~£9ˆ ”ˆ]’2ˆ‰]ŒH“EŸ%ŒEŠ_  ŠV£¤‰ 
% ‰˜!’C‰—[k




















-



-








‡@ˆE‰—H9‰˜EŠ/ •Y˜?Œ;;Œ;˜?Œ; ›EŠ/ Š$—%‰_•^˜Šp’2“Œ’C‰!Š5’2ˆEŒ’5’2ˆE‰#‚‘ —O9‰!”?ˆ?Œ;˜ ”GŠŽ“•(”G‰)Š8Š § Š)‘E”ˆŒEŠ@²‚
 H˜EŸ•–0’2ˆ‰
”)Œ  ’.›=£@ ’2ˆ  Y‘ —_‰)’pŒ;Œ;˜E—‰G ?Œ?”?‘?Œ’K •Y˜ E‰2‹E’2“ Œ?”2’K •Y˜9•–’2ˆ‰9ŒH“[–&“•Y ’2ˆE‰]_•^ — ”)Œ;˜™‰9—%‰!Œ; ’r£_ˆE‰˜
’2ˆ‰=ˆE‰!Œ’¯’2“Œ;˜EŠC–,‰“D ŠÄ˜E‰)Ÿ^  ŸH™; ‰%k~‡$ˆ ŠÄŽ“• E‰!—]Œ;˜$‰G‹?”)‰
 ‰˜’"•^Ž%Ž•“ª’2‘%˜ ’›V–,•“YŠ2HŽ;§ ‰__•(—%‰ Š¯’C•+Ž“ª‰— ”G’
9Œ;˜›]ŽEŒ“Œ;9‰G’C‰“ŠwH˜@’2ˆ‰@—( ‰V”!ŒEŠC’KH˜EŸŽ“ª•(”G‰!ŠpŠ0£_ˆ ”?ˆ$Œ“ª‰@—( Š8”‘Š8Šp‰!—H˜@’2ˆ Šw™••^«%k ’ ŠV“‰!”G•^_‰˜E—%‰!—
–,•“DH˜!’C‰“ª‰!ŠC’C‰—“‰!Œ?—%‰“Š¯’C•“‰!Œ?— (”«/‰“}’  Š¤™••^«  #5˜?Œ; ›Š2 Š¯•– 0 ‰!Œ’¯Œ;˜?—ÖŒEŠ8Š"’2“ Œ;˜EŠC–,‰“  ’C•ˆ?Œ E‰_™‰)’&’C‰“
kN"'0
. #- 5 7
  G¨ 0 
 ©  Œ;˜E—|_•“ª‰Ÿ%‰˜E‰“ Œ;^‘;˜E—%‰“ŠC’pŒ;˜?—H˜EŸ+•–0’2ˆ ŠV’C•YŽ ”k






H‚



 





 Œ; ”?‘; Œ’C‰9’2ˆE‰  ^‘ —F_‰)’pŒ;% E‰ •(” ’›+H˜]’2“ Œ;˜Š2 ’K •Y˜]–,•“~’›%Ž ”)Œ;;ŠGˆE•’wŠ) ‰)‰) ‰ § “.‘;˜;˜‰“€k


H‚7± ˆEŒ’= Š@’2ˆE‰”“, ’K ”!Œ;; E‰ •(”E ’.›–,•“ÄŽHŽ‰]£@ ’2ˆ— Œ;9‰G’C‰“0•–¤Ò^k   
 Š$lj%ÒÒ H



£_ˆE‰˜”?“3 ’K ”)Œ; g



˜;‘%™‰“

 ˜?—‰“¯”G•^˜Šp’2“.‘?”2’K •^˜

”G•YŽ)›%“3 ŸYˆ’šÐÑ § lÒ%ÒÒ § ™G›bÓV“&k@Ô~Œ“HՂÖ‰?H“

¹Iº)»2¼º)»2½)¾x¿KÀ%Á?Â]Ãľ!Ã$ž!ÂHÆKºÇÉÈSÊ;Á)¾KÆ
ÊEÀ%Ë)¾wÌÀ?ÂD¿KÀ%Á$¼€ÀÊ?»K¿!ÍFÈ?Î »GÏÇ »Â Ç ÆKÃVÍ

3


Section 3.8. Questions



e

 Ÿ^‘%“‰]j^k r ‡D›;Ž ”!Œ; Y•E£tŽEŒ’&’C‰“.˜H˜—( ‰”)ŒEŠp’KH˜Ÿ §  G‰ ’5‰˜’C‰“3H˜EŸxH˜’C•‰Ž’›”)Œ  ’.›
$

m%j

¹qº)»G¼Nº)»2½)¾x¿KÀ%Á?ÂÃľ!Ã$ž!ÂHÆKºÇÉÈSÊ;Á)¾KÆ
ÊEÀË)¾VÌÀ?Â[¿KÀ%Á$¼€ÀÊ?»K¿!ÍFÈ?Î »)Ï?Ç »ÂÇ Æ&¾2Í

”)•YŽG›;“3 ŸYˆ’šÐÑ § lÒÒ%Ò § ™G›FÓV“&k5Ô~Œ“HՂÖ‰?H“

Chapter 3. Dimensional Analysis

12.00
11.00



10.00

Re10^3

9.00




8.00
7.00
6.00
5.00



4.00





3.00
2.00
0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

Time [sec]
$ Ÿ^‘%“‰9j[k ¯‡0“ Œ;˜Š2 ’K •Y˜9’C•]’2‘%“™;‘% ‰˜!’Y•E£ H˜]”H“ ”?‘; Œ“0ŽHŽ‰$–,•“"H˜Šp’pŒ;˜!’pŒ;˜E‰)•^‘Š Y•E£
Œ– ’C‰“[±I›EŸY˜?Œ;˜Š)«E
Œ;˜E—x•’2ˆE‰“Š9™)›+H˜!’C‰“.Ž•^ Œ’K •Y˜

almost
still
flow

thin
boundary
layer
plus
solidification

Transition
zone

 ŸY‘;“‰j[k " $Y •E£-ŽEŒ’&’C‰“.˜+H˜’2ˆ‰ŠGˆE•’VŠG ‰!‰G E‰
$

U1
U2

U1
U2

( ŸY‘;“ª‰j[k  Ò 0 ‡£¤•ŠC’2“‰!Œ;9ŠV•– ‚‘ —%Š@H˜’C•NŒx_‰—H‘;
$

”G•YŽ)›%“3 ŸYˆ’šÐÑ § lÒ%ÒÒ § ™G›bÓV“&k@Ô~Œ“HՂÖ‰?H“

¹Iº)»2¼º)»2½)¾x¿KÀ%Á?Â]Ãľ!Ã$ž!ÂHÆKºÇÉÈSÊ;Á)¾KÆ
ÊEÀ%Ë)¾wÌÀ?ÂD¿KÀ%Á$¼€ÀÊ?»K¿!ÍFÈ?Î »GÏÇ »Â Ç ÆKÃVÍ

3#3

Section 3.8. Questions

L

cooling
liquid

 ŸY‘;“‰j^k v
$




”ˆ‰9Œ’K ”=•–Vˆ‰Œ’w’2“ Œ;˜Šp–,‰“wŽ“ª•(”G‰!ŠpŠ8‰)Š$H˜’2ˆ‰]—( ‰
D

H
equilibrioum
level

H

K

M



e

 Ÿ^‘%“‰j^k  l ¯ ‡$ˆ‰•ŠK”H
 Œ’KH˜EŸb=Œ;˜•^_‰G’C‰“‚–,•“‚’2ˆ‰]‰G‹?Œ;Ž; ‰]j^k m[k 
$

m%†

¹qº)»G¼Nº)»2½)¾x¿KÀ%Á?ÂÃľ!Ã$ž!ÂHÆKºÇÉÈSÊ;Á)¾KÆ
ÊEÀË)¾VÌÀ?Â[¿KÀ%Á$¼€ÀÊ?»K¿!ÍFÈ?Î »)Ï?Ç »ÂÇ Æ&¾2Í

”)•YŽG›;“3 ŸYˆ’šÐÑ § lÒÒ%Ò § ™G›FÓV“&k5Ô~Œ“HՂÖ‰?H“

Chapter 3. Dimensional Analysis

D

t

( ŸY‘;“ª‰j[k  j
$




”G•YŽ)›%“3 ŸYˆ’šÐÑ § lÒ%ÒÒ § ™G›bÓV“&k@Ô~Œ“HՂÖ‰?H“

 Ÿ —S™•(—›b™“ª•^‘Ÿ^ˆ!’@H˜!’C•S“‰)ŠC’)k

¹Iº)»2¼º)»2½)¾x¿KÀ%Á?Â]Ãľ!Ã$ž!ÂHÆKºÇÉÈSÊ;Á)¾KÆ
ÊEÀ%Ë)¾wÌÀ?ÂD¿KÀ%Á$¼€ÀÊ?»K¿!ÍFÈ?Î »GÏÇ »Â Ç ÆKÃVÍ
3



     





      ! 
"$#
 ˆEŒ;Ž’C‰“&%w˜E—%‰“"”)•Y˜EŠC’2“‘E”G’K •Y˜

' )( *  
,+ 



‡@ˆE‰b—( ‰x”)ŒEŠp’KH˜Ÿ|‰˜Ÿ(H˜‰!‰“ĉ˜E”)•Y‘;˜!’C‰“ªŠ=Œ;˜!›OŒEŠGŽ‰!”G’CŠ•–˜E‰G’£¤•“.«Y•E£=k $?•“ĉG‹?Œ;Ž% ‰ § ’2ˆE‰|  ^‘ —
_‰)’pŒ; Y•E£VŠ¤H˜_’2ˆ‰]“‘;˜%˜E‰“~ Š¤Œ˜E‰G’£¤•“.«Y•E£=k¯‡@ˆE‰Y•E£¡•–’2ˆ‰$ŒH“Œ;˜E—•’2ˆE‰“^Ÿ;ŒEŠp‰)Š•^‘!’r•–D’2ˆE‰]_•Y —
’2ˆ;“ª•^‘Ÿ^ˆ_’2ˆE‰@ ‰˜!’¤Šp›Šp’C‰- ŠÄŒ; Šp•Œ;˜E•’2ˆE‰“D‰2‹Œ;Ž% ‰˜‰)’.£¤•“«Y•E£=k0‡@ˆE‰]Ž ¡—( ŒEŸY“ Œ; Œ; Šp•N“‰ ^‘H“‰)Š
H˜’KH9Œ’C‰N«˜E•E£_ ‰—Ÿ%‰=•–r’2ˆ‰b˜‰)’.£¤•“«Y•E£k 0•E£¤‰G E‰“ § _•%ŠC’@— ‰+”)ŒEŠC’KH˜EŸN‰˜EŸH˜E‰)‰“ªŠ ;“‰)Š8‰!Œ“”ˆ‰“ªŠ$Œ“ª‰
‘;˜!–3Œ;H  Œ“"£$ ’2ˆ ‚‘ —|9‰!”?ˆ?Œ;˜ ”GŠ_Œ;˜?—x–&‘;“ª’2ˆ‰“._•“‰xˆ?Œ E‰ŒS H ’C‰—|«˜E•E£_ ‰—Ÿ%‰Œ;˜E—y‘%˜?—‰“ªŠp’pŒ;˜E—(H˜EŸ
•–r’2ˆE‰x˜E‰G’£¤•“.« Y•E£=k5‡$ˆ‰“ª‰)–,•“ª‰ § ’2ˆ Š_”?ˆ?Œ;Ž’C‰“ Š=—‰— ”!Œ’C‰!—’C•F—‰!Š8”?“3H™‰ŒF™“3 ‰G–VH˜’2“•—^‘?”2’K •Y˜’C•bŒ
Y•E£-H˜xŒS˜E‰G’£¤•“.«%k ’] Š=ŒEŠ8ŠG‘;_‰!—b’2ˆEŒ’@’2ˆE‰F“ª‰Œ?—‰“—%•‰)Š˜•’]ˆEŒ E‰‰G‹’C‰˜Š2  ‰b™EŒ?”«)ŸY“•Y‘;˜?—SH˜ ‚‘ —
_‰”?ˆ?Œ;˜ ”)Š!k 0•E£¤‰) ‰“ §  ’_ Š_ŒEŠ8ŠG‘;_‰!—+’2ˆ?Œ’5’2ˆ‰“‰!Œ?—%‰“¤ Š@–3Œ;H  Œ“~£@ ’2ˆ’2ˆE‰N™?ŒEŠ/ ”]”)•Y˜?”G‰Ž’CŠ5ŠG‘?”?ˆŒEŠ
Ž“‰)Š8ŠG‘;“ª‰VŒ;˜E—_–,•“”)‰ £¤•“« Ž•E£¤‰“&k¤Ö•“ª‰V”G•YŽ“ª‰ˆ‰˜Š2  ‰Ä”G• E‰“ ŒEŸ‰V”)Œ;˜=™‰w–,•^‘%˜?—]H˜9™••Y«!Š¯—%‰!—( ”)Œ’C‰!—
’C•‚‘ —F_‰”?ˆ?Œ;˜ ”)Š@§ Œ;˜E—SŽ§ HŽ‰ Y•E£tip˜‰)’.£¤•“«_–,•“ŽHŽ‰n)
k $H“ŠC’@Œ—( Š8”?‘EŠpŠ2 •Y˜]•Y˜]’2ˆE‰+“ª‰ ‰G ?Œ;˜E”G›•–¯’2ˆ‰
—;Œ’pŒO–,•Y‘;˜E—A–,•“@•’2ˆE‰“  ^‘ —%Š’C•A’2ˆ‰O— ‰O”)ŒEŠp’KH˜ŸšŽ“ª•(”)‰)ŠpŠx ŠxŽ“ª‰!Šp‰˜’C‰!—Dk Œ’C‰“$ŒOŠ2HŽ% ‰ Y•E£ H˜
ŒSŠC’2“ Œ ŸYˆ’ŽHŽ‰ ?”G•^˜E—^‘ ’ ŠŒ;˜?Œ; › ,G‰!—Dk¡Ów %D‰“ª‰˜!’”)•YŽ•^˜‰˜!’CŠ£9ˆ ”ˆS”)Œ;˜OŒ;Ž%Ž‰Œ“$H˜q˜E‰G’£¤•“«Œ“ª‰
—( Š8”?‘EŠpŠ8‰!—Dk ŒEŠC’2 › § ”)•Y˜;˜‰”2’K •Y˜]•–¯’2ˆE‰]”G•YŽ•Y˜E‰˜’CŠ@H˜Š8‰“3 ‰)Š@Œ;˜?—OŽEŒ“ Œ;
 ‰%Œ“ª‰Ž“ª‰!Šp‰˜’C‰!—Dk

.-0/

21

01

43

53

76 58:9 ;>=<?>A@X:< XCB>D<FE:A@G>A;GHI<HQ;4)B]*7;GHKJL<FM:B)HIB)>NE&9?< OQPG<?JSR

( ŸY‘;“ª‰m[k
$



' UT V
XW#GY"Z2[

2
\ ^ ]_W`[
aY"Yb+$
cWed`+
fW "Y

)g

Ów ‰@”)ŒEŠp’KH˜Ÿ9‰˜EŸH˜E‰)‰“Š¯£_ˆE•Œ“‰_˜E•’¯–3Œ;H  Œ“£$ ’2ˆ ‚‘ —_‰”?ˆ?Œ;˜ ”)Š0ŒEŠ)«w£_ˆE‰G’2ˆE‰“(’2ˆE‰9 •ŠpŠr”G•‰ ”E ‰˜’CŠ
•Y™’pŒH˜E‰!—–,•“0•’2ˆE‰“¤  ^‘ —%Š@ŠGˆE•Y‘; —?”G•^‘% —S™‰x‘Š8‰!—–,•“¯’2ˆ‰N  ^‘ —O_‰G’pŒ;HkV‡•xŒ;˜EŠC£¤‰“¯’2ˆ Š ^‘E‰)ŠC’K •^˜ §

Lh
m

Chapter 4. Fundamentals of Pipe Flow

0.01
0.001

0.50

1.00

0.12

0.25

0.06

0.02

0.03

0.00

0.01

1e−07

0.00

1e−06

8.00

1e−05

4.00

Air
Crude Oil
Hydrogen
Mercury
Water

0.0001

2.00

Head Loss [meter]

1
0.1

B_HIB R P.9FE R7;GH E BG; <?>c@]X:< XCBD<FE ;GHI<HQ
)B
Velocity[m/sec]

( ŸY‘;“ª‰]mDk l

{


$

9Œ;˜›=‰G‹;Ž‰“,H_‰˜!’CŠ_ˆEŒ E‰™‰!‰˜]”)Œ“.“3 ‰!—•Y‘’r–,•“—( %D‰“ª‰˜!’@  ^‘ —ŠY•E£$H˜ŸH˜— %‰“‰˜’w”G•^Ž•Y˜E‰˜’CŠÄH˜
’2ˆ‰+ ŒEŠp’ÄjÒ%Ò›)‰Œ“Š!k #5˜‰G‹?Œ;Ž; ‰•–0ŠG‘?”?ˆ]‰2‹Ž‰“3H_‰˜’CŠ_ Š@Œ#Y•E£ •–0—( %D‰“ª‰˜!’9  Y‘ —%Š@H˜ŒNŽHŽ‰=£@ ’2ˆ
Œ;˜+•“3 ²^”G‰Ni.Šp‰!‰ $ Ÿ^‘%“‰mDk EnGkÓw %‰“‰˜’]  Y‘ —%Š_”?“‰!Œ’C‰Š2 ŸY˜ ²^”)Œ;˜’9ˆE‰!Œ?—y •Š8Š@–,•“¯’2ˆE‰ŠKŒ;_‰ E‰ •(” ’›!k
Ö•“‰)• ‰“ ’2ˆE‰9—( %D‰“ª‰˜E”)‰)Š–,•“D’2ˆ‰=— %‰“‰˜’@  ^‘ —%ŠwŒ“ª‰$Š8•Š/ Ÿ^˜ ²^”!Œ;˜!’0’2ˆ?Œ’’2ˆ‰$Š2HH Œ“, ’›] Š_‘%˜?”? ‰Œ“
ŒEŠ9Š)ˆ•E£9˜N§ H˜ $ Ÿ^‘%“‰mDk l[k #Š_’2ˆ‰F“‰)ŠG‘; ’CŠ_•–¤’2ˆE‰xŽ?ŒEŠC’$Ÿ‰˜H‘EŠp‰!Š$£¤•“« §  ’_”)Œ;˜S™‰Š)ˆ•E£9˜’2ˆ?Œ’$£_ˆE‰˜
“ª‰!ŠG‘; ’CŠŒ“‰=˜•“9Œ;  ,G‰—™)›
‰)›%˜E•Y —%ŠÄ˜%‘;™‰“~i g  nH˜EŠC’pŒ’C‰—•–^’2ˆE‰V ‰ •(” ’›@Œ;˜?—=£_ˆE‰˜@’2ˆE‰=ˆ‰Œ?— •ŠpŠ
 Šw“‰Ž; Œ?”G‰—™G›5’2ˆ‰9 •Š8Š¯”G•‰ ”E ‰˜’ §   •Y˜E‰w•Y™’pŒH˜EŠ~’2ˆ?Œ’¯Œ;
G’2ˆE‰_ H˜E‰)Š0Œ“‰V”)•Y
 Œ;ŽEŠp‰—_•^˜V’C•=Œ@Š/H˜EŸY ‰
“ ‰)ŠG‘; ’H˜?— ”!Œ’C‰)Š_’2ˆEŒ’$’2ˆE‰+‰2‹Ž‰“3H_‰˜’pŒ;~“‰)ŠG‘; ’CŠ_•^™!’pŒH˜E‰!—b–,•“
˜ $( ŸY‘;“ª‰+m[k j^k ‡@ˆ Š
   k  !#()*((   +! #"%$ & &#(9!k  '  H˜‰ŒEŠ=ŠGˆE•E£_˜NH9
, &-(9k#$ 
$    "   $ /$ &   1  .
0 

F6

)g

1.2
Loss Coefficient

1.0
0.8
0.6
0.4
0.2
0.0

100

1000

10000

B_HIB R P.9FE R7;GH E BG; <?>c@32:< 2CBD<FE ;GHI<4
)B
Reynolds Number

( ŸY‘;“ª‰]mDk j
$



{

•Y˜E‰  Y‘ —”!Œ;˜™‰]‘EŠp‰—–,•“DŒ;˜E•’2ˆE‰“~  ^‘ —_‰G’pŒ;;Ž“•  —‰—]’2ˆE‰@•’2ˆE‰“¯  Y‘ — Š¤Œ¢0‰G£w’C•^˜ Œ;˜]  ^‘ —5!k
‰)Šp‰Œ“ ”?ˆE‰“Š+ŠGˆE•E£_˜O’2ˆEŒ’’2ˆ‰q  ^‘ — _‰)’pŒ;¤™‰ˆ?Œ E‰)ŠNŒEŠ|¢¯‰)£w’C•^˜ Œ;˜I  Y‘ —š –_’2ˆE‰S’C‰Ž‰“Œ’2‘;“ª‰q Š
Œ;™• E‰$’2ˆE‰‘EŠGˆ0
› ,G•Y˜E‰$’C‰Ž‰“ Œ’2‘%“‰%kr‡$ˆ Š¤‰G‹?Œ;Ž% ‰] Š$˜E•’w”G•““‰!”2’•^˜% ›=–,•“[’2ˆ ŠwŠ)Ž‰)Š2 ²^”@Ÿ‰!•Y_‰)’2“}›
™%‘’Đ Šw”G•““‰!”2’r–,•“Œ;
’2ˆE‰_”!ŒEŠp‰)Šr£9ˆ‰“ª‰$’2ˆ‰]“‰)Š)‘% ’CŠÄŒ“‰_”G•^
 Œ;ŽŠ8‰!—H˜’C•Œ=Š/H˜EŸY ‰ H˜E‰%k0‡@ˆE‰]Ž?Œ“ Œ;_‰G’C‰“ªŠ
£_ˆ ”?ˆ”G•^˜!’2“•Y’2ˆ‰Ž“•Y™; ‰tŒ“‰9–,•^‘%˜?—£_ˆE‰˜’2ˆE‰“‰)Š)‘% ’CŠ@Œ“ª7
‰ 6&”)•Y
 Œ;ŽEŠp‰!
— 8H˜’C•+ŒŠ/H˜EŸY ‰ H˜‰;k$ ’w£wŒEŠ
–,•Y‘;˜E—A’2ˆ?Œ’]’2ˆ‰A“ª‰!Š/ ŠC’pŒ;˜?”G‰x’C•|’2ˆ‰ Y•E£ –,•“=9Œ;˜!›|”G•^Ž•Y˜E‰˜’CŠ”)Œ;˜I™‰F”!Œ; ”?‘; Œ’C‰!:
— 93•“5‰2‹E’2“Œ?”G’C‰!—
–&“ª•^ ‰2‹Ž‰“3H_‰˜!’pŒ;^—;Œ’pŒn™G›F«˜E•E£@H˜EŸ’2ˆ<
‰ ;  ˜;‘%™‰“rŒ;˜?—N’2ˆE‰Ÿ%‰)•^_‰G’2“ª›•–’2ˆ‰”)•YŽ•^˜‰˜!>’ =#}˜
Œ£wŒ)›]›)•^‘”)Œ;˜]’2ˆH˜%«]Œ;™•Y‘’@ ’@ŒEŠ@ŒxŽ“•–0•–0’2ˆ‰]—(H_‰˜EŠ/ •^˜EŒ;;Œ;˜EŒ; ›EŠ/ ?
Š 9CŽ“ª‰!Šp‰˜’C‰!—bH˜ ˆ?Œ;Ž!’C‰A“ @B@
C>=



DEGFIHKJ/LNM ONLQP M RTSNM UVJ/WXEGYZ[H]\E ^)J/P P J_F.M L`aZbH]c#E_ZbZdP OGFfehgjilk>m
kon
7

pXqsr>tBubv wsxTy{|~
z }s€B€€‚}1ƒ tf„…u =V†.‡ uˆ[‰‹ŠŒvu

Ž>N‘’Ž>N“>”–•—B˜Œ™3š›”/šhœT”/™ŽTž#Ÿ¡ 
˜>”
 %—B¢>”¤£!—Œ™I•—B˜h‘*—¥ Œ•/¦jŸŒ§ X¨¥ž T™ž š…¦

©%ª

'

Y a[ W

`Z YGZ ]b+ 

Section 4.3. A simple flow in a straight conduit


 



v w"!Bu!Š# = #%$&

B)> B)H @G9QR <('Q2:9?B ; > JQPG<FEDJ B RX )HI< 2 EI< ;Q>

)+* v-,r/. Š ‡/021 , q * yVpXq3,4, q 0 p>q3,r¥q 0 Š 0 y v * ‡5* yNu ‡ v wsxTyVp>q 021 !v y ‡6** x%q67 0 v 0 v w3!
u)Š4# = # =98 x%Š
* v-,‹r:. Š * y3pXq 021 !¥v y‹v *‡ pTvup2!/. ‡ uQr¥vr¥Š7Qx¥v p¥x 7 q3!/. 1 ƒ Š * y;! 1 v Š 1 x%Š¥u!Š<[u * y ==8 x%Š Š 0 yNu ‡/0 pXŠ7r¥u)q ƒ . Š>,
‡/021 yNxTŠ?! 06* y Š ‡21 t ‡6* r¥Š/pXy * 7Vv-.(. ƒ Š 1 v * p2! *@* Š 1 . ‡ y Š¥u =A8 x%Š?r ‡ u ‡ , ŠXy Šu * yNx ‡ ydyNxTŠ 1 v Šhp ‡6* yv 0 w3Š 0 wv 0 Š/Š¥u *
v 0 y Š¥u!Š * y Š 1 ‡ u!Š yNx%ŠB. v C3!v 1 ,QŠXy ‡ .ED%ŠF. qpTv y]t } yNxTŠ r¥q67 Š¥u?y q 1 ubv DTŠ yNxv * D%ŠF. qpTv y]t } ‡/061 yNx%Š:r¥u!Š ** !
u)Š
1 v IG Šu)Š 0 p>Š qp/p2
! uIKH quhyNx%Š u!ŠJC"!vu)Š 1LKF1 Š * vu!Š 1 D%ŠF. qpTv y]t =NM x ‡ y 1 Š>y Š¥u,?v 0 Š yNx%Š * Šr ‡ u ‡ ,QŠXy Š¥u *PO
8 x%Š
D%ŠF. qpTv y]t’v *1 ŠXy Š¥u,?v 0 Š 1 ƒ tyNx%Š r¥u!Š *@* !Bu!Š 1 v GIŠu)Š 0 p>Š ‡ rBr/. v Š 1 q 0 yNx%Š r¥vr¥Š ‡/021 yNx%Š’u!Š * v * y ‡/0 p>Š?y q’yNxTŠ
Q q67 =R8 xTŠ<u!ŠF. ‡ yv q 0S* x¥vr ƒ Š>y7 Š/Š 0 yNx%Š’r¥u)Š *@* B! u!Š 1 v G Š¥u!Š 0 pXŠ } yNx%Š Q q67 u ‡ y Š ‡/061 yNxTŠ’u!Š * v * y ‡/0 pXŠ?y q<yNxTŠ
Q q67 v * wv D%Š 0 ƒ tQyNx%ŠŠ;Tr¥Š¥ubv-, Š 0 y ‡ .¥ŠJC"! ‡ yv q <0 9 # = TC>=U8 x¥v * ŠJC"! ‡ yv q 0 v * ! * Š 1 ƒ Š/p ‡ ! * Š3v yR7 quV * =R8 x%Š
r¥u!Š **
! u)Š 1 v 
G Š¥u!Š 0 pXŠ 1 Š>y Š¥u?, v 0 Š 1 ƒ tyNx%Š wŠ/q3, Š>yNuKv p ‡ B. r ‡ u ‡ , Š>y Š¥u ›* ‡/021 yNx%Š ŠWT
r¥ŠuKv-, Š 0 y ‡ . 1
‡ y ‡ 7 xv pŒx
ƒ

*
*
1
Š;Tr¥u!Š Š
tYX[ZI7Qx¥v p¥x‹p ‡/0 ƒ Š3q ƒ y ‡ v 0 Š 1 HGu!q3, ‰‹qq 1 t]\ *^1 v ‡ wsu ‡ , =

/

76

v w3!
u!Š# = _ V
$ ‰‹qq 1 Lt \ *I1 v ‡ w‚u ‡

,

`5acb X df e g hj i `Yklb X4f e ghm 
n q¥y Š } xTŠ ‡21 v * Š 0 Š¥u!w¥t r¥Š¥u^! 0 v y7 Š%v wsxTyVqFH Q ! v 1 9 v = Š =Y qu!p>Š?T Š 0 wyNx K6M Š%v w‚x/y &
oqp%r H]SOXP P Y¤H]\Ec#E›OcEds JXcE›c#EoOoZ J/LZAWXSH[H]\EGY…OcE J/SoH.J^H]\E Z r JJtNE¤J^sH]\NM ZdWNJ/JJu
vqp H H]\NM Z ZbHbO`NE;Bw F1EVSZ EaU/M x Ec#ELoH UXEzy LNM H M J/LVH]\NONL J/LE SZ E UM L|{s\OWtoHKEcA}~E€.\E›UTM xEcEL r E
ƒ…„ ELoH M OXP P Y›F‚EdF.M P PTOU>OWot H.J/LE ZKYZKHKEPs ^)JNcH]\E…WXJ>JJu…~

3

#:†

 >Ž X‘ Ž>N“>”–•—B˜Œ™?š›”/šhœT”/™ŽTž#Ÿ¡ 
˜>”
 %—¢>”…£!—Œ™1•—B˜h‘*—¥ Œ•/¦jŸŒ§ >¨Œž T™!ž G”N¦

76

9 # = TC

3 Š 0 w¥yNx Ch‡/021

vy

M Z¤W Y O…^)O r KH JXcIJ^‚2~

p>qsrXt
ubv wsxTy{|~
z }€€B€‚}1ƒ tj„…u =a†.‡ uˆ[‰‹ŠŒvu

Chapter 4. Fundamentals of Pipe Flow

1

x ‡6*

! 0 v y * q>H . Š 0 wyNx =A8 x/! * } yNx%Š’u)Š>. ‡ yv q 06* xvr ƒ Š>y7 Š/Š 0 yNx%Š Š ‡21 9 . q *@*C…‡/021 yNx%Šru)Š *@* !
u!Š 9 . q **C v *
`Yacb `Yk m
9 # = C
d
8 xTŠ<u!Š * v * y ‡/0 pXŠ3pXqŠ pTv Š 0 y HKqu pTvup2!/. ‡ ulp>q 021 !v y…p ‡/0 ƒ Š 1 Š…< 0 Š 1 ‡6*
9 # = BC
 b X f e
8 x¥v * ŠJC"! ‡ yv q 0 v * 7 ubv yGy Š 0 HKqu ‡ p>q 06* y ‡/0 y 1 Š 06* v y]t Q q67 ‡/021 ‡ pXq 0S* y ‡/0 ypŒu!q *@** Š/pNyv q 0=58 x%Š Q q67
‡u y Šv * ŠW
T r¥u!Š ** Š –
1 ‡6*
 b g
9 # =# C
8 xTŠVpŒu!q **U* Š/pXyv q Œ0 ‡ . ‡ u!Š ‡ qFIH p%vu!pF!:. ‡ uIv *  b 
 b  f 
 } ! * v 0 wŠJC"! ‡ yv q 0?9 # = # C ‡/061* ! ƒ * yv y;!Tyv 0 w
v yhv 0 y q’ŠJC"! ‡ yv q 0 9 # = TC tv ŠF. 1:*
`Yacb Xd    fe  3 
9 # = _BC
8 x%Š<ŠSC3! ‡ yv q 7
0 9 # = B_ C* xTq67 * yNx ‡ yyNxTŠ u!ŠJC"¥! vu!Š 1 r¥u)Š *@* B! u!Š 1 v G Š¥u!Š 0 pXŠ }`Ya } v *‡ Hz! 0 pXyv q 0 q>H
f 
1
6
0
*
7 xv pŒx Š>, q yNu ‡ y Š * yNx%ŠyNu!ŠF, Š 061 q3! * ŠWG Š/pXyVyNxTŠ 1 v ‡ , Š>y Š¥u›x ‡6* q 0 yNx%Š Q q67 u ‡ y Š =I8 xTŠ. Š 0 wyN x } q 0
yNxTŠ3qyNxTŠu x ‡/021 } x ‡6* ,?! * x. Š *@*^* v w 0 v ‚< p ‡/0 y›ŠWG Š/pNyaq 0 yNx%Š Q q67 u ‡ y Š =
8 x%Š<r¥q67 Š¥u‚7 xv pŒx u!ŠJC"! vu)Š * y q 1 uKv %D Š?yNxv * Q q67 v * wv %D Š ƒ t
9 # = B C
 b 

g

76

8 x%Š * Š ŠJC"! ‡ yv q 0S*‹‡ !u ŠDTŠut v-,r¥qu)y ‡/0 yv 0 yNxTŠ ! 021 Šu * y ‡/061 v 0 w Ny xTŠ–ŠTpXq 0 q",htjq>Hu!
‡/061 7Vv-.(. ƒ Š * y;! 1 v Š 1 v 0 x ‡ r/y Šu @B@ v 0 , qu)Š 1 ŠXy ‡ v-. *T=
8 x%Š<r¥q67 Š¥uAv 0 y Š¥u, * >q HlyNx%Š3wŠ>q", ŠXyNubv p ‡ .‚r ‡ u ‡ ,QŠXy Š¥u *V‡/061 Ny xTŠ Q 6q 7 u ‡ y Šv * wv D%Š 0

0:0 Š¥u 1 Š * v w 0

b !
 
d & #"
%('$ )  )

h

9 # = BC

*,+.-/+10 2436587:98;=<6>@?&ACBEDF<GH5F;IGKJ&;=5KBMLI?(NO>
P8QSRUTVSW=XZY6[I\

<2
^]

`_¡ 7 ]

/ j2 2 j
ba dc e
' >'
'
/a  gf FhMikj'ml > onh ‹2 2 dc Fiqp rsj '4nt] gu ' >'
gf
b<_ 
>'
vrUj'?'wnxhMikj'?'wn hrUj'?'wn
yEz W={}|~ zq€

aON@GP <?9 @G>Q9?PPG<FE9 @ EIH 9?B <P.OQ> E PG> <?BJB)H QH DBB RE <F@GRE P.9:HI@ JB E < @ 9 ; B RU9 RB ; EIBI<FJHDE <F;M:; B)HIB)> )B Q7R;GB HX@ 7;G)<?HDH @@GPG>L9 J@ < HCB2)H 9?; B RU> R "ER B ; EI< ;Q> < CB 7I;G9?<H0SB_J H @ < <?> =B)J @G<FP 9FP
76
@G9 PG9 @ EIB E Bh2:; B)HKHIB)ONPG<?H B Jf7;GH&E B_@Mƒ ;„a B,B†….@>'Q2:9?B

8 xv * v * ŠWT ‡ ,‹r:. Š# = ‚ =
P8QSRUTVSW=XZY6[‚
yEz W={}|~ zq€

pXqsr>tBubv wsxTy{|~
z }s€B€€‚}1ƒ tf„…u =V†.‡ uˆ[‰‹ŠŒvu

Ž>N‘’Ž>N“>”–•—B˜Œ™3š›”/šhœT”/™ŽTž#Ÿ¡ 
˜>”
 %—B¢>”¤£!—Œ™I•—B˜h‘*—¥ Œ•/¦jŸŒ§ X¨¥ž T™ž š…¦

‡ˆ

}

 ?f+ Z [ Y _W"Y   ],W 44,W ?Z  W 
 Y W

' '

Section 4.4. Typical Components in the Runner andVent Systems

Y

0

yNx%Š–p ‡ . p2!/. ‡ yv q 06* qFHayNx%Š u! 0:0 Š¥u›yNxTŠ 1 v Š–p ‡6* yv 0 w¡Š 0 wv 0 Š/Š¥u¤Š 0 p>q3! 0 y Šu ƒ Š * v 1 Š–yNxTŠ * yNu ‡ v w‚x/y<r¥vr¥Š
xv pŒx 7 ‡6*1 Š ‡ . y’v 0 yNxTŠr¥u!ŠWDv q3! *Y* Š/pXyv q 0 ƒ !Ty‹qyNxTŠuV%v 061 q>HQpXq",r¥q 0 Š 0 y */= 8 xTŠ * Š¡pXq3,‹r¥q 0 Š 0 y *
v 0 2p .(! 1 Š…yNx%Š ƒ Š 061 }
ˆpXq 0/0 Š/pNyv q 0a‡/021 y ‡/0 wŠ 0 yv ‡ .>w ‡ y Š } 6 u)Š/w3!/. ‡ usw ‡ y Š 8 } yNx%ŠaŠ;T%y Š 021 Š 1 p>q 0/0 ŠTpNyv q 0
‡/021 WŠ T
r /‡ 0S* v q 0>K p>q 0 yNu ‡ pXyv q 0{9 v 0 p2.(! 1 v 0 w yNx%Š ‡ ƒ u!
r/y–ŠWT
r ‡/0S* v q 0>K p>q 0 yNu ‡ pXyv q 0¥CX= -0 yNxv * * ŠTpNyv q 0 ‡
wŠ 0 Šu ‡ . 1 v * Fp ! ** v q 0 q 0 yNx%Šfwqq 1 1 Š * v w 0 r¥u ‡ pNyv p>Š HKqu…yNxTŠ 1 v GŠ¥u!Š 0 yp>q3,r¥q 0 Š 0 yv * ru)Š * Š 0 y Š 1I= )
* Šr ‡ u ‡ y Š?p¥x ‡ rTy Š¥u v *^1 Š 1 v p ‡ y Š 1 y q<yNxTŠy ‡/0 wŠ 0 yv ‡ .‚u! 0:0 Š¥u 1 !%ŠQy qfv y * pXq",r/. v p ‡ yv q 0=

7

*,+ *,+10

 <&N

021 v * pŒu!Š ‡ y Š 1 ƒ ŠTp ‡ ! * Š ‡ pŒx ‡/0 wBŠQv 0 yNxTŠ?, q3, Š 0 y;!/, ‡/061 yNxTŠ Q q67 r ‡ yGy Š¥u 0=
yNx%Š ƒ Š 061 y q ŠSC3!v D ‡ . Š 0 ypXq 021 !¥v y?. Š 0 wyNx =58 xv * p>q 0 DTŠu * v q 0 r¥u!q 1 !ŒpXŠ *
‡21 ŠJC"! ‡ y Šfu)Š * !/. y * v 0*o‡ , Š<p ‡6* Š * 7 xv-. Š’v 0 q¥yNx%Š¥u›v y,?v wsxTyv 0 yNu)q 1 !%p>Š . ‡ u)wBŠ¥u Š¥u]u)qu =8 x%Š V 0 q67. Š 1 wBŠ
qFH…yNxv *?‡ p/p2!
u ‡ pXtfqFH›yNx¥v * p>q 0 TD Šu * v q 0 v * %D Š¥u)t . v-,?v y Š 1 ƒ ŠTp ‡ ! * Š=. v-,?v y Š 1 * y;! 1 t7x ‡ D%Š ƒ Š>Š 0 p ‡ u]u)tjq3!Ty
HKqudyNxTŠ’pŒx ‡ u ‡ pXy Š¥ubv * yv pqFH Q q67 * v 0 1 v Š’p ‡6* yv 0 w = u)q", yNx%Š. v-,3v y Š 1 v 0 HKqu, ‡ yv q 0 yNx%Š ‡ !TyNx%quAq>H yNx¥v *
ƒ qq3Vhw ‡21 Šu)Š 1 v y * Š>ŠF,~yNx ‡ y…v y…v * u)Š ‡6* q Œ0 ‡ ƒ . Šhy qp ‡ u]u)tQyNxv * p>q 0 TD Šu * v q 0 KH qu1yNx%ŠQp ‡ . p2!/. ‡ yv q 06* qFHE. v C"!¥v 1
, Š>y ‡ . Q q67 u)Š * v * y ‡/0 p>Š 7 xv-. Š v 0 yNx%Š ‡ vu K . v C"!¥v 1 , ŠXy ‡ .R,?v T%y;!
u)Š7v yH ‡ u^HGu!q3, ‡21 ŠSC3! ‡ y Š = ‰‹qu!Š>q>DTŠu }
6 x%q3. Š 8 q>H¤q3!
uIV 0 q67. Š 1 wŠ‹qFH yNx%Š’w ‡6* Q q67 v 0 TD Š 0 y * t * y Š>, ‡ u)ŠYH ‡ uI, qu)Š . ‡ u)wBŠ = n ŠW%D Š¥u)yNx%ŠF. Š ** } KH qu ( / !   & 0 &( N $zk  (  
yNx%ŠhŠ 0 wv 0 Š>ŠuKv 0 w’r:!
u]r¥q * Š ‡ yAyNxv *E* y ‡ wŠQv y * Š/ŠF, yNx ‡ y * q3, Š qFHyNxTŠ Š¥u]u)qu * 7Vv-.(.¥p ‡/0 p>ŠF.%Š ‡ pŒxq¥yNx%Š¥u ‡/061
yNx%ŠŠ 061 u)Š * !/. y V
7 v-.(. ƒ Š,?Œ! pŒx ƒ ŠXyGy Šu =
x%Š?u!Š * v * y ‡/0 p>ŠQv 0 yNx%Š ƒ Š

0 wv 0 Š>Š¥u *50 qu, ‡ (. . t–pXq 0 D%Š¥u)y

cross section

v w3!
u)Š# = 

R

θ

8

) * NV Š>y_pŒx3qFHAyNxTŠ
$N

ƒ Š

061 v 041

v Šp 6‡ * y v 0 w

8

x%Š * ¥p xTŠ>, ‡ yv p q>H ‡ ƒ Š 061 pXq3,4, q 0 . t! * Š 1 v 091 v Š¤p ‡6* yv 0 w?v ** x%q67 0 v 0 v w"!Bu!ŠE# = ‚=8 x%ŠVu)Š * v * y ‡/0 p>Š
qFH¤yNxTŠ ƒ Š 021 v *Q‡ Hz! 0 pXyv q 0 qFH * ŠWD%Š¥u ‡ ..r ‡ u ‡ , Š>y Š¥u * $ ‡/0 w3. Š }1} u ‡21 v-! * } ; ‡/061 yNx%Š‹wBŠ>q3,QŠXyNu)t ƒ Š…HKqu)Š
‡/021j‡ Hy Šu yNx%Š ƒ Š 061I=  q3,?,Qq 0 . t } yNx%Š–u! 0:0 Š¥u¤v * , ‡21 Š?7hv yNxyNx%Š *‡ , Š‹wBŠ>q3,QŠXyNu)t ƒ Š…HKqu)Š ‡/061j‡ Hy Š¥u
yNx%Š ƒ Š 0211= ‰‹qu!Š>>q DTŠu } 7 
Š 7V-v .(. ‡6*@* !:, Š’v 0 yNxv *1 v * p2! *@* v q 0 yNx ‡ y 1 q67 0S* yNu)Š ‡ , ‡/021 !
r * yNu!Š ‡ , 1 q 0 q¥y
0v Q !TŠ 0 p>ŠQyNx ‡ y Q 6q 7 v 0 yNxTŠ Q 6q 7 E= 8 x¥v *V6‡ *@* !:,‹r/yv q 0 v * D ‡ . v 1 7 x%Š 0 yNx%Š¥u!Š<v *0 q q¥yNx%Š¥u ƒ Š 061 qulq¥yNx%Š¥u
= 0 p 6‡ * Š * yNx ‡ y * !%p¥x ‡ pŒx ‡/0 wŠ 9*C ŠWTv * y * , qu!Š‹pXq",r/. v p ‡ y Š 1f‡/0%‡ . t * v * v *
pŒx /‡ 0 wŠ<v 0 yNxTŠ Q 6q 7 0 Š ‡ u ƒ t 
I
1
=
u!JŠ C"!¥vu!Š
0 yNxTŠ . v wsxTyQFq HayNx%Š HKqu¤wBqv 0 w 1 v * Fp ! ** v q 0 } 7 Š . WŠ Hy 7Vv yNxfy 7 qr ‡ u ‡ , ŠXy Šu * yNx ‡ ypXq 0 yNu!q3.‚yNx%Š u!Š
* v * y /‡ 0 p>Š } yNxTŠ /‡ 0 3w . Š } ‚} /‡ 021 yNx%Š u 2‡ 1 -v ! * } ; )R* . ‡ u)wBŠ¥u¤yNx%Š /‡ 0 3w . Šjv * . ‡ u)wBŠ¥u yNx%Š u!Š * v * y ‡/0 p>Š7Vv-.(. ƒ Š =
0 yNx%Šfru ‡ pXyv pXŠ3y q 1
‡ t } r¥u!q ƒ ‡ ƒ . t ƒ ŠTp ‡ ! * ŠyNx%?Š 7 ‡ t‹yNx%Š n qu)yNx ) ,QŠ¥ubv p /‡ 0 „¤v Š l6‡ * yv 0 w )R*@* qpTv ‡ yv q 0
y Š ‡ p¥x¥v 0 w } WŠ TŒp>Š ** v D%Š /‡ 0 3w . Šap /‡ 0 ƒ 9
Š HK3q ! 021 yNx
u!3q !%wsxayNxTŠhv 021 ! * yNu)t = y v * u!Š/p>3q ,?,QŠ 021 Š 140 WŠ D%Š¥uy q;Š T¥pXŠ/Š 1
= v "w !Bu!Y
‡ 1B‡ y ‡ y ‡ VNŠ 0 HGu!3q , * WŠ D%Š¥u ‡ . * "q !BupXŠ */5
= u)"q , yNxTŠ
yNx%Š * yNu ‡ v wsxTy /‡ 0 3w . Š "9 !$#$%/CXY
Š # = , 2‡ 1 4
Š HGu!3q , 
$ & 0 &)$  '  ( " $   $ &
  '  
v "w !Bu!Š‹v yhv * Fp . Š ‡ u.yNx ‡ y…qsrTy-v ,?!/, u 2‡ 1 -v ! *^* x%3q !/. 1 ƒ Š ‡ u!3q ! 061C
   & 

_

h

6

 >Ž X‘ Ž>N“>”–•—B˜Œ™?š›”/šhœT”/™ŽTž#Ÿ¡ 
˜>”
 %—¢>”…£!—Œ™1•—B˜h‘*—¥ Œ•/¦jŸŒ§ >¨Œž T™!ž G”N¦

p>qsrXt
ubv wsxTy{|~
z }€€B€‚}1ƒ tj„…u =a†.‡ uˆ[‰‹ŠŒvu

v w"!Bu!Š# =

k  0 $ '   &" 0 &! 0 $  &!

*,+ *,+



8

x%Š



Chapter 4. Fundamentals of Pipe Flow

h$)

wŠ>q", ŠXyNubv p ‡

GH?(N ON <KG BMLI?(N
0:0 Š/pXyv q 0 u!Š¥r¥u * Š 0 y ?‡ * r:. v yhv 0


ˆpXq

. 1 Š * pŒubvrTyv q 0 Fq H

yNxTŠ<u!

yNxTŠ’u!Š * v * y /‡ 0 Xp Š‹v 0‹‡ ƒ Š

0/0 Š¥u * t * y ŠF, R= 8

021

xTŠ<u!Š * v * y Š 0 Xp Š

*,+ *,+.- 243&9O58NO> LI?(N ?(NKB 5OG BMLI?(N
0 Š3qFHAyNxTŠY! 061 v * vu ‡ ƒ . Š?Š>. ŠF, Š 0 yhv * yNxTŠ<u! 0/0 Šu * t * y Š>, v *I* ! 1:1 Š 0 p¥x ‡/0 wŠv 0 yNx%ŠpXq 021 !¥v pXy ‡ u!Š ‡= 0
* q", Šjv 0S* y ‡/0 p>Š’yNxTŠ>t ‡ u)Šjv 0 ŠWD%q 1 Š ƒ . Š =M Š 7Vv-.(. 1 v ** p2! *@* x%q67 y q 1 Š * v w 0f‡/061 7 x ‡ y ‡ u)Š’yNx%Š ƒ Š>yGy Š¥u
1 Š * v w 0 qsrTyv q 06* 7Qx¥v p¥x ‡ D ‡ v-. ƒ . ŠHKqu.yNxTŠ?Š 0 wv 0 Š/Š¥u =







'

Z [ [

aW ^]_W

‚   [  ^ 
8 x%Š¥u!Š ‡ u)Š y7 q+, ‡ v 0 V%v 021:* qFHpXq 0:0 Š/pXyv q 06* ^* ŠuKv Š *f‡/021 r ‡ u ‡ .(. ŠF. = 8 x%Š u)Š * v * y ‡/0 pXŠ v 0 yNxTŠ * Š¥ubv Š *
pXq 0:0 Š/pXyv q 0 x ‡6* y q ƒ Š ‡21/1 Š 1 v 0 ‡ H ‡6* xv q 0 * v-,?v-. ‡ u¤y q Š>. Š/pXyNuKv p ‡ .Au!Š * v * y ‡/0 pXŠ¡v = Š = ŠWD%Š¥u)t u)Š * v * y ‡/0 pXŠ
x ‡6* y q ƒ Š ‡21/1 Š 1 r:. ‡ v 0 . t y qyNxTŠ¡y qy ‡ .¤u!Š * v * y ‡/0 p>Š =+8 x%Š¥u!Š ‡ u)Š , ‡/0 t7yNxv 0 w * yNx ‡ y<p>q 0 yNuKv ƒ !Ty Šjy q
yNxTŠ u!Š * v * y ‡/0 pXŠ ƒ Š * v 1 Š * yNx%Š u)Š/w3!/. ‡ u. Š 0 wyNx } v = Š = ƒ Š 061:* } Š;Tr ‡/06* v q 0S* } pXq 0 yNu ‡ pNyv q 0S* Š>y_p =) .(.yNx%Š * Š
pXq 0:0 Š/pXyv q 06*…‡ u)Š3q>H * Š¥ubv Š * y t
r¥Š =






*,+ /+10 /< LI<6> ?(N NO<KG BMLI?(N
8 x%Š Q q67 u ‡ y Šv 0 1 v GŠ¥u!Š 0 y . qp ‡ yv q 0S* v * ‡ Hz! 0 pNyv q 0 qFHyNxTŠ y Š>,r¥Š¥u ‡ y;!
u)Š =  p2VNŠ¥u)y 9  p2VNŠuy † >† C
1 Š>, q 06* yNu ‡ y Š 1 yNx ‡ yayNx%Š x%Š ‡ yayNu ‡/06* HKŠu v * v 06* v w 0 v <‚p ‡/0 y v 0 yNx%Š 1 !Bu ‡ yv q 0 qFHdyNxTŠ?<‚.(. v 0 w q>HAyNx%Š‹p ‡ D¥v y]t }
‡/061 yNxTŠu)Š…HKqu)Š?yNx%Š?y ŠF,r¥Šu ‡ y;!
u!Š3qFHAyNxTŠ. v C"!¥v 1 ,QŠXy ‡ .p ‡/0 ƒ Š ‡6** !/, Š 1 ‡ .(, q * yapXq 06* y ‡/0 y 1 !
uKv 0 w<yNxTŠ
<‚.(. v 0 w r¥Š¥ubv q 1 9 7 xv pŒxjv 0 , q * yQp ‡6* Š * v * ,4!%p¥x=. Š *@* €€ ,?v-.(. v * ŠTpXq 061:*C>=)R*|* !%p¥x } yNx%Š * q3. v 1 v <‚p ‡ yv q 0
v * v 06* v w 0 v <‚p ‡/0 y 9 yNx%Š . v C"!¥v 1 , ŠXy ‡ . 1 Š 06* v y]t<p¥x ‡/0 wŠ * . Š ** yNx ‡/0 € =
v 0 yNx%Š–u! 0:0 Š¥u C yNx%Š¥u!ŠWHKqu!Š } yNxTŠ
ƒ
Q
‡
/
‡
0
6
‡

*
*
1
S
0
*
/
‡
0
DTq".(!:Q, ŠXyNubv p q67 u y Š3p Š !/, Š pXq y y…$
 b   b   b 
9# = C






6



6



76











 . Š ‡ u. t } yNx%Š<r¥u!Š *@* !Bu!Š‹v 0 yNx%Šr¥qv 0 y * v *I1 v GIŠu)Š 0 y ‡/061
a bja  b a  b
9 # =† C
" " "
q67 Š…TD Šu[yNxTŠy q¥y ‡ .1r¥u!Š *@* !Bu!ŠY. q ** v * p>q3,r¥q * Š 1 q>HHGu!q3, ‡ .(.yNx%Š * , ‡ .(.‚r¥u!Š ** !
u)ŠY. q **
a a b a a   a  a   kd
9# = € C
 D%Š¥u)t * v 0 w". Šru)Š *@*
! u!Š5. q *@* p ‡/0 ƒ ŠQ7 uKv yGy Š ‹0 ‡6*
a
b  gh
9 # = TC
8 xTŠu)Š–v * ‡ . * q7u!Š * v * y ‡/0 pXŠ 1 %! Š‹y q r ‡ u ‡ .(. ŠF1. p>q 0/0 ŠTpNyv q 0 v = Š = tfpXq 0:0 Š/pXyv q 06* } t * r/. v y *Q‡/021 , ‡/0 v HKq". 1>*
ŠXy_p =^ vu * y } . Š>y * . qq"V ‡ y›yNxTŠ * Š¥ubv Š * pXq 0:0 Š/pXyv q 0 9 * Š>Š v w"B! u!Š# = C>= 7QxTŠu)Š/$

1





!

#"
$%

*)+



'&

!

(

&

76

(

76G6





pXqsr>tBubv wsxTy{|~
z }s€B€€‚}1ƒ tf„…u =V†.‡ uˆ[‰‹ŠŒvu

Ž>N‘’Ž>N“>”–•—B˜Œ™3š›”/šhœT”/™ŽTž#Ÿ¡ 
˜>”
 %—B¢>”¤£!—Œ™I•—B˜h‘*—¥ Œ•/¦jŸŒ§ X¨¥ž T™ž š…¦

‡

-,

Section 4.5. Putting it all to Together

y q ‡21:1f‡ s< w3!
u!Š ‡/021 pŒx ‡/0 wŠ‹v y



v w"!Bu!Š# = "$

; > > B> EI< ;Q> <?> R B H <?B R

yNxTŠ<u!Š * v * y /‡ 0 p>Š‹v 0 yNxTŠ ƒ Š 061
. Š 0 w¥yNx3qFHAyNxTŠ 1 !%pXy 9 DTŠ 0 y C }
HGuKv pXyv q 0 H ‡ pNy qu } ‡/021

" $%

eX

,* + /+ m5 5F; ;=<O; ?(N NO<KG BMLI?(N
)^0 ŠWT ‡ ,r/. Š?qFHAyNxTŠ<u!Š * v * y ‡/0 pXŠ?qFH…r ‡ u ‡ .(. ŠF.
p>q 0/0 ŠTpNyv q ’0 9* Š/Š v w3!
u)Š @
@BCX=
8 x%Š r¥u!Š ** !
u)Š ‡ y r¥qv 0 y v * yNx%Š *o‡ , ŠHKqu›y7 q ƒ u ‡/0 p¥xTŠ * x%q67 ŠWD%Š¥u¤yNx%Š
pXq", ƒ v %0 ‡ yv q 0
  
b   









6



y qy ‡

. Q 6q 7

u ‡ y Š v * yNxTŠ

0 y7 q ƒ u ‡/0 p¥xTŠ *a‡/021 yNx%ŠY. q *@* v 0 yNx%Š! 0 pXyv q 0 v * p ‡ . pF!:. ‡ y Š 1’‡6*
8 q ‡21:1 ‡ <sw3
! u!Š ‡/021 pŒx%Š/pFVv HAyNx%Šq". 1 q 0 Š‹v * wBqq 1
v w"B! u!Š# = †"$ ) r ‡ u ‡ .(. ŠF.
p>q 0/0 ŠTpNyv q 0
ƒ ŠXy7 Š>Š

_M

 >Ž X‘ Ž>N“>”–•—B˜Œ™?š›”/šhœT”/™ŽTž#Ÿ¡ 
˜>”
 %—¢>”…£!—Œ™1•—B˜h‘*—¥ Œ•/¦jŸŒ§ >¨Œž T™!ž G”N¦

76

9# =  C

p>qsrXt
ubv wsxTy{|~
z }€€B€‚}1ƒ tj„…u =a†.‡ uˆ[‰‹ŠŒvu

Chapter 4. Fundamentals of Pipe Flow

pXqsr>tBubv wsxTy{|~
z }s€B€€‚}1ƒ tf„…u =V†.‡ uˆ[‰‹ŠŒvu

Ž>N‘’Ž>N“>”–•—B˜Œ™3š›”/šhœT”/™ŽTž#Ÿ¡ 
˜>”
 %—B¢>”¤£!—Œ™I•—B˜h‘*—¥ Œ•/¦jŸŒ§ X¨¥ž T™ž š…¦

‡/©

     



"$#   !   



( *W> ,+E 

0 Š7qFH?yNx%Š ƒ u ‡/0 p¥xTŠ * qFH?yNx%Š Q !v 1 , Š/p¥x ‡/0 v p * 1 v * pF! ** Š 1 v 0  x ‡ rTy
v *@* !TŠ|Hz!
uyNx%Š¥u ƒ ŠTp ‡ ! * Šv yVv * wv D%ŠQyNxTŠ ƒ ‡6* v p4! 021 Šu * y ‡/061 v 0 w‹y qyNxTŠ 6 7 ‡
0 !:, Šu)q"! * ƒ q
q"V * yNx ‡ y 1 Š ‡ . v 0 w 7hv yNx¡q‚r¥Š 0 pŒx ‡/0:0 ŠF. Q q67 ‡/021 yNx%Š v 0
xv * K x%Š¥9
u V 0 6q 7. Š 1 wBŠ ƒ t¡u)Š ‡21 v 0 w ƒ qq"V * !ŒpŒx ‡6* r¥Š 0   x ‡/0/0 ŠF. t 1 u ‡
qu V:$ ‰<p ¤u ‡ 7  v-.(. † qq3V  q3,r ‡/0 t } 0 p = † _ † CX= Š¥u!Š ‡ ƒ ‡6* v p
‰Š/pŒx /‡ 0 v p *0 wv 0 Š/Š¥u *a‡ u!Šwv DTŠ 0=



1

6

1

1

1

Š¥u  = Š¥u!Š 7 Š ŠWT
r ‡/061 yNx¥v *
TD Š 8 r
xTŠ 0 q", Š 0 q 0=8 x%Š¥u!Š ‡ u)Š
y Š¥u!Š * y Š 1 u!Š ‡21 Š¥uhp ‡/0 ƒ u!q ‡21 Š¥u
!:. v p * ƒ t dŠ 0 8 Š  xTq67 9n ŠW7
pXq 0 pXŠr/y * HKquQyNx%Š 0 q 0  .(!¥v 1



$7
8 x%Š Q q67 v 0 qsr¥Š 0 pŒx ‡/0:0 ŠF. Q q67 v 0* y Š ‡21 t * y ‡ y Šv * ƒ ‡ . ‡/0 pXŠ 1 ƒ t ƒ Š>y7 Š/Š 0 yNx%Š w‚u ‡ Dv y]tHKqupXŠ *›‡/061
, q * y;. t ƒ t yNx%ŠYHGuKv pXyv q 0f‡ yyNxTŠ pŒx ‡/0/0 Š>. ƒ Š 1I=Y)R* q 0 Š ,3v wsxTyQŠ;Tr¥Š/pXy } yNx%ŠYHGuKv pXyv q 0 H ‡ pNy quRHKqu q‚r¥Š 0
pŒx ‡/0/0 Š>. Q q67 x ‡6*|* v-,?v-. ‡ u ƒ Š¥x ‡ DTŠuAy qjy qfq 0 ŠqFH yNx%Šfrvr¥Š Q q67 7Vv yNx<yNu ‡/06* v yv q 0 HGu!q3, . ‡ ,?v 0%‡ u Q q67
y q’yNx%Š?y;B! u ƒ !/. Š 0 y ‡ y ‡ ƒ q"!/y ;
 #  =n ŠWD%Š¥u)yNxTŠ>. Š ** } yNx%Š3qsr¥Š 0 pŒx ‡/0:0 ŠF. Q q67 x ‡6*I* ŠWD%Š¥u ‡ .1u!Š * r¥Š/pNy *
yNx%Š‹pŒu!q **I* Š/pXyv q 0‡ u!ŠD ‡ ubv ‡ ƒ . Š } yNx%Š * !
u H ‡ p>Š’v * ‡ y ‡ .(, q * yVpXq 0S* y ‡/0 yr¥u!Š *@* !Bu!Š ‡/021 yNx%Šwsu ‡ D¥v y]t4HKqupXŠ
‡ u)Šv-
$ &  &)$ '
, r¥qu)y ‡/0 y =
8 x%Š Q q677qFH ‡ . v C"!¥v 1 v …0 ‡ pŒx ‡/0:0 ŠF.Xp ‡/0 ƒ Š¤p¥x ‡ u ‡ pXy Š¥ubv XŠ 1 ƒ t¤yNx%Š * r¥Š/pTv <‚p Š 0 Š¥u!w¥t¤yNx ‡ y v *l‡6*@* qpTv ‡ y Š 1 0  
7Vv yNx‹v y =A8 xv * * r¥Š/pTv ‚< phŠ 0 Š¥u!w¥t‹v * p>q3, r¥ubv * Š 1 q>[H y7 q‹p>q3, r¥q 0 Š 0 y * $.yNx%ŠxTt 1 u!q * y ‡ yv p3r¥u!Š ** !
u)Š ‡/061 yNxTŠ
. v C"!¥v 1 D%ŠF. qpTv y]t 5>=
8 x%Š?Š 0 Š¥u!w¥t ‡ y ‡/0 t r¥qv 0 y…qF…H xTŠŒv wsxTyVv ‹0 ‡ u)ŠTpNy ‡/0 w3!/. ‡ u.p¥x ‡/0/0 Š>. v *
b ghm   a d 
9_‚= TC

76

 €.\E „ EP J r M HY…M ZlOXL…O „ EcO`NE „ EP J r M H)Y
_>_

 &+   k) ( 

Chapter 5. Flow in Open Channels

Fl

ow

∆x

y

d

g

76 $ P {S~=W=~~={ST

v w"!Bu!Š ‚_ =
‡/061 } * v 0 pXŠ 




7QxTŠu)Š/$


b  g h6m





b HKqu /‡ 0 tfr¥qv 0 yVv 0

z Sz 
dX
/~ € R € z VHX €
„R €S€ XdW
yNx%ŠpŒu!q

*@*^* Š/pNyv q 0 9 GH u!Š>Š * !Bu H ‡ pXŠ C }
9_‚=  C

* r¥ŠTpTv <‚pŠ 0 Š¥u!w¥t–r¥ŠuE! 0 v y
xTŠŒv wsxTy›q>H yNx%ŠY. v C3!v 1 v 0 yNxTŠp¥x ‡/0/0 ŠF.
‡ p>p>ŠF. Š¥u ‡ yv q 0 q>H w‚u ‡ D v y t
m
‡ TD Šu ‡ wBŠTD Š>. qpTv y]tqFA
g
H yNxTŠY. v C"!¥v 1
HlyNxTŠ|DTŠ>. qpTv y]tq>.H yNxTŠ5. v C"¥! v 1 v * v 0 pŒu!Š ‡6* Š 1 } yNx%ŠxTŠŒv wsxTy }[} x ‡6* y q<p¥x ‡/0 wŠhy qVNŠ>ŠrQyNx%Š *‡ , Š Q q67
b  g = qu ‡4* r¥Š/p%v ‚< p Q q67 u ‡ y Š ‡/021 pŒu!q **I* ŠTpNyv q 0 } yNx%Š¥u!Š ‡ u)Š, ‡/0 tp>q3, ƒ v 0Œ‡ yv q 06*
‡u y Š  b
/
‡
2
0
0 ‡1 v ‡ wsu ‡ , } 7hv yNx yNx%Š  ˆp>q
qu 1 v 0%‡ y Š ‡6* yNx%Š3xTŠŒv wsxTy
qFH[D%ŠF. qpTv y]t 1 x%Š%v w‚x/y = . qyGyv 0 w?yNx%Š * Š3r¥qv 0 y * q Q
‡/061 yNx%Šsˆp>q
qu 1 v %0 ‡ y Š ‡6* yNx%Š * r¥Š/pTv ‚< p¤Š 0 Š¥u!w¥t } } p¥u)Š ‡ y Š d
* ‡ r ‡ u ‡ ƒ q3. ‡ q 0a‡ w‚u ‡ r
x =U8 x¥v * . v 0 ŠVv * V 0 q67 0
‡6* yNxTŠ 6z* r¥Š/p%v ‚< p Š 0 Šu)wt‹p2
! u %D Š 81=  ŠW%D Š¥u ‡ . pXq 0 p2.(! * v q 0S* p ‡/0 ƒ Š 1 u ‡ 7 0 HGu!q3, v w"!Bu!Š _‚=  =9 vu * y } yNxTŠu)Š
* ‡ ?, v 0 v-,4!:, Š 0 Šu)wt ‡ y ‡* r¥ŠTpTv ‚< p–xTŠŒv wsxTyV 0 q67 ’0 ‡6* yNx%Š 6 pŒubv yv p ‡ [. x%Š%v wsxTy 8‚=! ŠTpXq 021 } yNxTŠŠ 0 Š¥u!w¥t
v
v 0 p¥u)Š ‡6* Š * V
7 v yNx ‡1 Š/pŒu!Š ‡6* Š’v 0 yNx%Š–x%Š%v wsxTy^7 x%Š 0 yNxTŠ. v C3! v 1 xTŠŒv wsxTy v * ƒ ŠF. q67 yNxTŠ<pŒubv yv p ‡ .[x%Š%v wsxTy = 0
}
*
6
‡
*
yNx¥v p Š yNxTŠ, ‡ v 0 pXq 0 yNubv ƒ T! yv q 0 y q’yNx%Š3Š 0 Š¥u!w¥t v *1 %! Š?y q<yNxTŠv 0 pŒu!Š ‡6* Šv 0 yNxTŠ%D ŠF. qp%v y t = 8 xv * Q q67
0 ‡6* yNxTŠ 6 * B! r¥Šu!p¥uKv yv p ‡ . Q q67 8‚=8 xvu 1 } 7 x%Š 0 yNx%Šfx%Š%v w‚x/yv ?* ‡ ƒ qF%D ŠyNx%Š<p¥uKv yv p ‡ .. x%Š%v wsxTy } yNxTŠ
v * V 0 q67 <
0Š Š¥u!w¥tjv 0 pŒu!Š ‡6* Š Q* ‡ w ‡ v 0 =|8 xv * Q q67 v * V 0 q67 <0 ‡6* yNxTŠ 6 * ! ƒ pŒubv yv p ‡ . Q q67 8 } ‡/061 yNxTŠŠ 0 Š¥u!w¥tjv 0 pŒu!Š ‡6* Š
v *1 %! Šy q<yNxTŠ’xTt 1 u!q * y ‡ yv pr¥u!Š **
! u)Š3p>q3
, r¥q 0 Š 0 y =
8 x%ŠY?, v 0 v-,4!:, r¥qv 0 y›q>H Š 0 Š¥u!w¥t<p2
! u %D Š’x ‡ r
r¥Š 06* y q ƒ Š ‡ y
b " m $#
9‚_ = B C
g 


pXqsr>tBubv wsxTy{|~
z }s€B€€‚}1ƒ tf„…u =V†.‡ uˆ[‰‹ŠŒvu

Ž>N‘’Ž>N“>”–•—B˜Œ™3š›”/šhœT”/™ŽTž#Ÿ¡ 
˜>”
 %—B¢>”¤£!—Œ™I•—B˜h‘*—¥ Œ•/¦jŸŒ§ X¨¥ž T™ž š…¦

‡&%

Section 5.1. Introduction

Y

EL
specific
energy line

Y2

2
specific
thrust line

Y3

3

YC
Y1

1

v w3!
u)Š 1_ = 

7

$ y V X&
~
P € X  R € T z TX € |{ST 4{  qX


x%Š¥u!ŠQyNx%ŠpŒubv yv p ‡ 1. xTŠŒv wsxTyav *1 ŠW< 0 Š

#



b



1









e, f




ƒt



9_‚= # C

m

8 x
u! * yhv *^1 ŠW< 0 Š 1 ‡6*

g 
9_‚= _BC
X b h   m
8 x%Š 3, v 0 v-,?!/, yNxBu! * y ‡ . * q x ‡ r
r¥Š 06* y q ƒ Š ‡ yQyNxTŠ *‡ , Š¡r¥qv 0 y g b " m  =8 xTŠu)Š…HKqu)Š } q 0 Š p ‡/0
1 ŠW< 0 ŠQyNx%Š 1 v-Q, Š 06* v q 0 . Š **0 !/, ƒ Š¥u ‡6* $

b m  
9_‚= BC
g
„¤v ¥D v 1 v 0 w yNxTŠ TD Š>. qp%v y t ƒ t " m  r¥u!qFDv 1 Š * q 0 Š7hv yNxfyNx%Š ‡ ƒ v-. v y]tfy q pŒx%Š/p2Vjv HVyNx%Š Q q67 v *‹‡ ƒ qFD%Š–qu
ƒ ŠF. q6:
7 p¥uKv yv p ‡ .J%D ŠF. qp%v y t =A8 x¥v * C"! ‡/0 yv y tv * DTŠut‹v-,r¥qu)y ‡/0 y } ‡/061 v y *R* v w 0 v <‚p ‡/0 p>Šap ‡/0 ƒ Š * y;! 1 v Š 1 HGu)q",
, ‡/0 t ƒ qq3V * q 0 Q ! v 1 , ŠTpŒx ‡/0 v p */= 8 x%Š wsu ‡ Dv y t¡ŠWGŠ/pNy *‡ u!Š 6 ,QŠ ‡6* !
u!Š 1
8 ƒ tfyNx%Š u!q3! 1 Š 0 !/, ƒ Š¥u
7 xv pŒx<v *I1 ŠW< 0 Š 1 ƒ tŠSC3! ‡ yv q –0 9‚_ = B C>=




Gh
_

 >Ž X‘ Ž>N“>”–•—B˜Œ™?š›”/šhœT”/™ŽTž#Ÿ¡ 
˜>”
 %—¢>”…£!—Œ™1•—B˜h‘*—¥ Œ•/¦jŸŒ§ >¨Œž T™!ž G”N¦

p>qsrXt
ubv wsxTy{|~
z }€€B€‚}1ƒ tj„…u =a†.‡ uˆ[‰‹ŠŒvu

T




 ?f+



Z [ 5fZ|GZ4 Y
 GZ4 [ f+ 4






Chapter 5. Flow in Open Channels

x%Š Q q67 p ‡/0 p¥x ‡/0 wŠ<q 0 . tHGu)q", ‡* !Br¥Šu!p¥uKv yv p ‡ . Q q67 y q ‡* ! ƒ pŒubv yv p ‡ . Q q67 } v 0 7Qx¥v p¥x’yNxTŠjxTŠŒv wsxTy
0v p¥u)Š ‡6* Š *?‡/021 yNxTŠYD%ŠF. qpTv y]t 1 ŠTpŒu!Š ‡6* Š */=58 x%Š¥u!Š v *Y0 q r¥q *@* v ƒ v-. v y]tHKquAyNx%Š Q q67~y q wq v 0 yNxTŠ¡u!ŠWD%Š¥u * Š
1 vu!Š/pXyv q 0 ƒ Š/p ‡ ! * Š›q>HsyNx%Š  ŠTpXq 061 ¥‡ 7 qFH 8 x%Š¥u, q 1 t 0Œ‡ ,?v p *›9 yNx%Š›ŠWT
r/. ‡/0%‡ yv q 0 qFH37Qx¥v p¥xhv * q3!TylqFH‚yNxTŠ
* p>qsr¥Š3qFHAyNxv *^1 v * pF! ** v q 0ŒC>= HAyNxTŠu)Šv *0 q Š 0 Š¥u!w¥t. q *@* } yNxTŠ Q q67 , q>DTŠ * HGu)q", r¥qv 0 y y q¡r¥qv 0 y  v 0
0 ‡ pXy;! ‡ . v y]t } Š 0 Š¥u!w¥t. q ** qp>pF!Bu * v 03‡/0 t * v y;! ‡ yv q 0 }‚ƒ !Ty * q3, Š>yv-, Š * v y›p ‡/0 ƒ Š 0 Š/w3. ŠTpNy Š 1
v w"B! u!Š ‚_ =  = -‹
0v yNxTŠ?p ‡ . pF!:. ‡ yv q 0ST* = 0 p ‡6* Š * 7QxTŠu)ŠQyNxTŠ Q q67 p¥x ‡/0 wŠ * u ‡ r¥v 1 . t 9 * !%p¥x ‡6* 7Vv yNxyNx%Š‹xTt 1 u ‡ !:. v p !/,r C }
* 
ƒ Šy ‡ NV Š 0 v 0 y q ‡ p>p>q3! 0 y = 0 yNxTŠ * Š’p ‡6* Š * } yNx%Š Q q67 , q>DTŠ * HGu!q3, r¥qv 0 y y q
yNxTŠ<Š 0 Š¥u!w¥t . q *@
0

‹
/
‡
2
0
1
6
‡
* 9
lC>= 0 , ‡/0 tp ‡6* Š * yNxTŠpŒx ‡/0 wBŠ?v 0 yNxTŠ yNxBu! * y…v *0 Š>w". v wv ƒ . Š } * !%p¥x ‡6*
r¥qv y
x * Š 0 Šu)wt5. q *@h
6
‡
*
1
‡
yNxTŠ?p Š q>.
H yNxTŠ‹x/t u !/. v p P!:‹, r } ‡/021 yNx%Š Q q67 , qF%D Š * GH u)q", r¥qv 0 y y qfr¥qv 0 y ‹‡6*9* x%q67 0 v 0Y v w3!
u)Š
‚_ =  =
-0 † }
‡ u ƒ Šu 6 KH q"! 02B1 8 yNxTŠjx/t 1 u ‡ !/. v p P!:‹, r–v 0 yNx%Š * xTqy * . Š>Š…TD Š47 xv pŒx¡xTŠ’p ‡ .(. Š j1 ‡ 6 7 ‡ D%Š 8‚=
ƒ
‡

9 Š 0 u Šu)Š¥wu t<ƒ pX!q v-.0Sy * ‡ Š¥u ,D ‡ q y1 v q ŠFŒ0 .>C>y =q 8 1 Š x¥* v *pŒub, v ƒ q Ša1 yNŠFx¥. v * w7v %D ‡Š D%h* Š ‡5} !T* ŠXyyav-. v TqFv H 0 ŠSw4C3, ! ‡ ‡6y*@v * q pX06q* 0Su)*Š>Š¥. ‡ u Dyv‡ 0 yw v q r/0 .(!‡/006w’1 Š† uŠ%D u ŠF0 . q3q!/pTv.(y]. vt \ * ‡/ŠS02C31 ! ‡7 y‡ v q TD 0Š
DTŠ>. qpTv y]tfy q7qyNxTŠu›wŠ/q3, Š>yNuKv p ‡ . ru)q‚r¥Š¥u)yv Š * q>H…yNx%Š * xTqy * . Š>ŠWD%Š = DTŠu S_ € t>Š ‡ u * Š ‡ u. v Š¥u } †ŠF . ‡/0 wŠ¥u
9_†Š> . ‡/0 wBŠ¥u  CU1 ŠF, q 0S* yNu ‡ y Š 1 yNx ‡ yAyNx%ŠhŠ 0 Š¥u!w¥t?v *1 v ** vr ‡ y Š 1 } ‡/061 yNx ‡ y Š 0 Š¥u!w¥tpXq 06* Šu D ‡ yv q 0 , q 1 
ŠF. * p ‡/0:0 q¥y ƒ Š ! * Š 1 y q * q". DTŠ7x/t 1 u ‡ !/. v p!/,r = Š 1 ŠF, q 0S* yNu ‡ y Š 1 yNx ‡ yyNx%Š 1 v *@* vr ‡ yv q 0 v 0 p¥u)Š ‡6* Š *
7Vv yNx?yNx%Š3v 0 pŒu!Š ‡6* ŠQq>.H yNxTŠ5. v C"¥! v 1 TD Š>. qpTv y]t ƒ Š…KH qu)ŠQyNx%Š P!:, r =R8 xv * p>q 0 p2.(! * v q 0 v * yNu%! ŠKH qu ‡/0 t%V v 021 q>H
wŠ/q3, Š>yNut =
) . v y Š¥u ‡ y;B! u!Š u)Š…¥D v Š…7 1 Š>, q 06* yNu ‡ y Š * yNx ‡ yQyNx%Š xTt 1 u ‡ !/. v p P!:, r v j
0 ‡ p%vu!pF!:. ‡ u›p¥u)q *@* ˆ * ŠTpNyv q 0 9 . v-V Š
0 ‡ * x%q¥y * . Š>Š…TD Š C‹‡ r
r¥Š ‡ u * v 0 q¥yNx%Š¥uVp ‡6* Š * } KH quaŠWT ‡ ‹, r:. Š ‡ Q q67 v 7
0 ‡ * y qu, * ŠW7 Šu * t * y ŠF, /* = )^0
v7
‡/%0 ‡ . tTyv p ‡ . * q3.(T! yv q 0 yNx ‡ y 1 Š * pŒubv ƒ Š * yNx%Š * q3.(T! yv q 0 v h
* †.‡ uˆ‰Š%vuz\ * KH qu,?!/. ‡Q‡/021 v * * x%q67 0 v 0Y v w3
! u!Š = # =
8 x%ŠaŠ 0 Š¥u!w¥t?. q *@* pXq 0 p>Š¥rTyE, ‡/0 v KH Š * y * v y * ŠF. .H v 0* Š…TD Šu ‡ . 1 Š * v w 0S* } * Œ! pŒx ‡6* v 0 yNx%ŠVŠ 0 Š¥u!w¥t/ˆ 1 v *@* vr ‡ yv 0 w
1 Š…¥D v p>Š * } v 0 Q7 x¥v p¥x xTt 1 u ‡ !:. v p !/, r <* ‡ u!Š v 0 yNu)q 1 %! p>Š 1 v 0 qu 1 Š¥u…y q 1 v *@* vr ‡ y Š–Š 0 Šu)wt = 8 x%ŠfŠ 0 Šu)wt>ˆ
1 v ** vr ‡ yv 0 w 1 ŠWD v pXŠ j
* ‡ u)Š * q:p>q3,?, q 0 yNx ‡ y 0 !/, Šu)q"! * u!Š * Š ‡ u!p¥x 7 quV * x ‡ TD Š ƒ Š>Š 0 r¥Š¥u KH qu, Š 1 q 0
yNxTŠ>, v 0 yNxTŠ . ‡6* y B€€ x/! 061 u)Š 1>* t>Š ‡ u /* =|)^0 Š;T¥pXŠF.(. Š 0 y3u!Š¥r¥qu)y ƒ t’yNx%Š …= [=A† !
u)Š ‡ ! qFHIŠ/pF. ‡ , ‡ yv q 0
9_† u ‡/0 p¥x † _ C* x%q67 * yNx%ŠVr¥Šu!p>Š 0 y ‡ wŠ qFH Š 0 Šu)wt. q */* = q67 Š…TD Šu }
‡ u ƒ Š¥u } ‡/061 . ‡ y Š¥u
q¥yNx%Š¥usu!Š * Š ‡ u!p¥xTŠu *
HGu)q", xv q  y ‡ y Š 0 v D%Š¥u * v y]t 9o† u)Š…D¥v pFV } ) u, Š 0 yNu)q"!/y ‡/021  x:! †:†F# C } H ‡ v-. Š 1 y q?V 0 q67 K ! 061 Š¥u * y ‡/021]K ! * Š
yNx¥v * v 0 KH qu, ‡ yv q 0 =

8

A3

6

6

6 6

6



6



6



1







6



%

pXqsr>tBubv wsxTy{|~
z }s€B€€‚}1ƒ tf„…u =V†.‡ uˆ[‰‹ŠŒvu

1 6

%

Ž>N‘’Ž>N“>”–•—B˜Œ™3š›”/šhœT”/™ŽTž#Ÿ¡ 
˜>”
 %—B¢>”¤£!—Œ™I•—B˜h‘*—¥ Œ•/¦jŸŒ§ X¨¥ž T™ž š…¦

‡Tª

 


 
 




 



   



   

 

%E021 Š¥u p>q 06* yNu!%pXyv q 0 r:. Š ‡6* Š‹v w 0 qu!Š yNx%Š’u)Š * y…qFHAyNxTŠ3pŒx ‡ rTy Š¥u =
 ( *W> ,+E 

0 yNx¥v * p¥x ‡ rTy Š¥ulyNxTŠ 1 Š * v * w 0‹‡/021 yNx%Š 1 v GIŠu)Š 0 yu)Š>. ‡ yv q 06* xvr ƒ ŠXy7 Š>Š 0 u! 0:0 Š¥u * ŠTp2, Š 0 y *V‡ u)Š * y;! 1 v Š 1
x%Š¥u!Š%v 0= 8 x%Š <[u * y * y Š¥r v 0 u! 0/0 Šu 1 Š * v w 0 v * y q 1 v DTŠ 1 Š 1 yNx%Š , q3. 1 v 0 y q * Š…DTŠu ‡ .. qwv p ‡ . * ŠTpNyv q 06*/=
8 x% Š D%3q .(!/, ŠjqFHhŠWD%Š¥u)t * ŠTpNyv q 0 x ‡6* y q ƒ Š p ‡ . pF!:. ‡ y Š 11= 8 x%Š 0 yNx%Š 1 Š * v w 0 x ‡6* y q Š 0S* !Bu!Š–yNx ‡ y3yNxTŠ
w ‡y|
Š D%FŠ . qpTv y]t ‡/061 yNx%Š|<‚.(. v 0 wyv-,QŠQq>HlŠWD%Š¥u)t * ŠTpNyv q 0 y q ƒ Š ‡6* u!Š/p>q3,?, Š 061 ƒ tŠWT
r¥ŠuKv-,QŠ 0 y ‡ .su)Š * !/. y */=
) y3yNx¥v *?* y ‡ wŠ yNx%Š¥u!Š¡v *0 q V 0 q67 0 u)Š>. ‡ v ƒ . Š–yNxTŠ/qut K , q 1 ŠF.V 0 q67 0 y q yNx%Š ‡ !TyNxTqu›y q r¥u!Š 1 v y * yNx%Š * Š
D ‡ .(!TŠ */= 8 xTŠ D ‡ .(!TŠ *<‡ u)Š ƒ 6‡ * Š 1 x ‡ D-v . t7q 0 * >Š ,?v oubv-. ‡ v ƒ . ŠfŠ;Tr¥Š¥ubv-, Š 0 y *T= 8 x%Š †.‡ p2VW7 qu 1 „dŠ * v w 0 v *
1 v * 2p !/! * Š 1IY= 8 x%Šfu!Š 2‡ 1 Š¥Eu 7hv yNx V 0 "q . Š>wBŠ v 0 >Š . Š/pNyNubv p ‡ .IŠ 0 wv 0/0 ŠuKv 0 w 9 ŠF. ŠTpNyNubv p ‡ .Ip%vu!pXy Š *C 7hv-.(. 0 q¥yv p>Š v 0
* "q , Š * -v ,?-v . ‡ ubv yv Š */= 6q 7 …Š DTŠu } xTt 1 u ‡ .(!:. v p p%vu!Fp !/y *‡ u!Š , qu)Š p>3q ,r/. Š;T =‚‡ uyqFH…yNxTŠ ŠWT
ru)Š *@* v q 0S*3‡ u)Š
* -v ,‹:r . v <sŠ 1 y q x ‡ DTŠ /‡ 0Œ‡ . t/yv p ‡ .1;Š Tr¥u!Š ** v q 06*/= Š>y } v 0f‡ pN;y ! ‡ . v y]t ‡ .(.syNxTŠ<y Šu , ** xT"q !:. 1 ƒ Š’y ‡ VNŠ 0 v 0 y q
* xT"q !:. 1 ƒ Š ! * Š 1I=
pXq 0S* v 1 Šu ‡ yv q 0S*a/‡ 021 pX3q ,4, Š¥upTv ‡ . * Fq Hy 7 ‡ u)Š * !ŒpŒxf„¤v Š  Š¥u HKŠ/pXy

1



 +10 +10 Z5OG^5   <6> L"!/N
 !
rBr¥q * ŠQyNx ‡ y7 Š‹x ‡ D%Š >?* Š/pXyv q 06* 7hv yNx > w ‡ y Š *T=M Š5V 0 q67 yNx ‡ yDTq".(!:, ŠQy q ƒ Š 1 ŠF. v D%Š¥u!Š 1 ‡ y…w ‡ y Š <
‡/021 v *91 Š 0 qy Š 1 ƒ t$# =R8 x%Š w ‡ y ŠDTŠ>. qp%v y t<x ‡6* y q ƒ Š?v 03‡ V 0 q67 0 u ‡/0 wŠ =A8 xTŠI<‚.(. v 0 w3yv-, Šx ‡6* y q ƒ Š
v 03‡ V 0 q67 0 Hz! 0 pNyv q 0?‡/061 7 Š‹u)ŠTpXq3,QŠ 021 y q! * Š  p2VNŠuy K†.‡ uˆ‰Š%vuz\ * HKqu,?!/. ‡=9 qu1yNxv *1 v * pF! ** v q 0 v y




v *V‡6*@*

!:, Š 1
 b


8 /x ! * }

yNx ‡ y…yNx%Š|<‚.(. v 0 wjx 6‡ * y q ƒ Š‹v 0

#%




w ‡ y Š ‡ u!Š ‡ KH qu.yNx%Š * /Š pXyv q

 b g' &



V 0 q67 0 u /‡ 0 wBŠ /‡ 021

0

yNx%Š

Q 6q 7

u ‡ y Šp ‡/0 ƒ Šp ‡ . 2p !/. ‡ y Š

1

ƒt

76

9 ‚= TC
9 ‚=  C



*"



6

Chapter 6. Runner Design

&  $  _$ &  k  0 $ '  , @& k'#$
  "*$ &>$ &  k  0 $ '  

) u , Š 1 7Vv yNx3yNxv * V 0 q67|. Š 1 wŠ } q 0 Š3p ‡/0?* y ‡ uy 1 Š * v w 0

0/0 Šu * t * y Š>,

yNx%Š<u!

vents

=

vents

Mold
i
κ

j
K

a

b
Biscuit

76 $ )

v w"!Bu!Š ‚ =

 +10 +

wŠ/q3, Š>yNutq>H¤u!

0/0 Šu pXq 0:0 Š/pXyv q 0

?(N NO<KG BML N ! dJ N NF< >M<(7 <&NKBU>
„dŠ * v w 0 qFHVpXq 0:0 Š/pXy Š 1 u! 0/0 Š¥u * Š/p2,QŠ 0 y * x ‡ D%Šjv 0S* !Bu!Š<yNx ‡ yyNxTŠ Q q67 u ‡ y Š ‡ yŠ ‡ pŒx * ŠTp2, Š 0 yx ‡6* y q
ƒ Š 1 Š * v w 0 Š 1 q 0 Š = 0 v w3!
u)Š ‚= /‡ ƒ u ‡/0 pŒx%Š * ‚‡/061?‡ u!Š<p>q 0/0 ŠTpNy Š 1 y q ƒ u ‡/0 pŒx ‡ yr¥qv 0 y =8 xTŠ
r¥u!Š *@* !Bu!Š 1 u)q‚r 91 v GŠ¥u!Š 0 pXŠ C q 0 ƒ u ‡/0 pŒx%Š * Œ‡/061  x ‡6* y q ƒ ŠVyNxTŠ *o‡ , Š * v 0 p>ŠayNxTŠ3ru)Š *@* !
u!ŠQv 0 yNxTŠ?, q3. 1
p ‡ Dv y t7v * yNxTŠ * ‡ , ŠYKH qu ƒ qyNx * ŠTp2, Š 0 y T* = 8 x%Š * !/, q>H›yNx%Š Q q67 u ‡ y Š * HKqu ƒ qyNx ƒ u ‡/0 p¥x x ‡6* y q ƒ Š
ŠJC"! ‡ .By q Q q67 u ‡ y Šv 0 ƒ u ‡/0 p¥x

 b   
|
b 
|b  

9 ‚= BC
8 xTŠ Q q67 u ‡ y Šv 0 Š…TD Šut ƒ u ‡/0 p¥x<v * u!ŠF. ‡ y Š 1 y q<yNxTŠ<r¥u!Š **
! u)Š 1 v G Š¥u!Š 0 pXŠ ƒ t
 b `Y; a
9 ‚ = # C
M x%Š¥u!Š?yNxTŠ * ! ƒ * p¥uKv y v 0 yNxv * p ‡6* Š ‡ . * q ,QŠ ‡/06a* ‡/0 t ƒ u ‡/0 pŒxŠ = w = } h‡/021* q’q 0 =9 qulŠWT ‡ ,r/. Š } q 0 Š
p ‡/0 Q
7 uKv y ŠKH qu ƒ u ‡/0 pŒx 

b `5; a
9 ‚ = B_ C

‡/061 yNx%ŠH ‡ pXyyNx ‡ yyNxTŠ
yv-. v Tv 0 w yNxTŠ , ‡6*@* p>q 06* Š¥u D ‡ yv q 0 HKqu r¥qv 0 y v 0 7 xv pŒx  b   
3
}
Y
`
a
}
@
*
*
1
0
*
*

‡
*
/
‡
0
r¥u!Š B! u!Š v IG Šu)Š p>Š
v yNx%Š , ŠyNx:! 7 Š3p Q
7 uKv y Š
Y
`
a
Y
`
a
; ];
  b ;  ;
b `Ya ; ;

9 ‚ = B C

7QxTŠu)Š7 Š3p ‡/0Y1 Š…< 0 Š?ŠJC"! ‡ . Š 0 yhu)Š * v * y ‡/0 p>Š ƒ t
; ;
; b
9 ‚ = BC
;
;








76

< <







<



<

%









h







pXqsr>tBubv wsxTy{|~
z }s€B€€‚}1ƒ tf„…u =V†.‡ uˆ[‰‹ŠŒvu

Ž>N‘’Ž>N“>”–•—B˜Œ™3š›”/šhœT”/™ŽTž#Ÿ¡ 
˜>”
 %—B¢>”¤£!—Œ™I•—B˜h‘*—¥ Œ•/¦jŸŒ§ X¨¥ž T™ž š…¦

%-,

Section 6.1. Introduction

3

Š>y * Hz!
uyNx%Š¥u‚, /‡ 0 v r¥q". y Š¤yNx%Š›ŠSC3! ‡ yv q
9*@
@
C…‡/061 ŠSC3! ‡ yv q 0 G9 @B@
C

`5a b `Ya
b 
Q q67 u ‡ y ŠQv 0 ‡ ƒ u ‡/0 pŒx

b ;;


b;



8

xTŠ







06*

y qwŠ>y * "q , Š,Qqu)Šhv-,r¥qu)y ‡/0 y u!ŠF. ‡ yv q

b 
;
p ‡/0 ƒ ŠQu!ŠF. ‡ y Š 1

<



yq

Q 6q 7:u ‡ y ŠQv 0 ƒ u ‡/0 pŒx %‡/061



%* v 0 w<ŠJC"! ‡ yv q 0–9*@
@BC…‡/021 ŠJC"! ‡ yv q 0 9*@
@
C q 0 Š?p ‡/0 q ƒ y ‡ v 0

;
 b ;
 ;
q3. Dv 0 w5HKqu.yNx%Š<u)Š * v * y ‡/0 pXŠ<u ‡ yv q * v 0 pXŠyNx%Š Q 6q 7
;
b  
;


&%

0S* x¥vr */= * v 0 w SŠ C3! ‡ yv q 0

p>qu u!Š * ¥r q

021 v 0 w‹u!Š * v * y ‡/0 pXŠ *
9 ‚ = † C





M



u ‡ y Šv *

t<6> LI>UBU58N&G <

76

9o‚= € C

V 0 q67 0

76G6

9o‚= %C



 +10 +.-

9 ‚=  C

1

x ‡ y 1 q
Š * Ny x%Š u)Š * v * y /‡ 0 Xp Š v 0 Fp .(! 1 Š O
6q 7 y q ‡ pŒxv ŠWD%Š !u Š * v * y ‡/0 p>Š u ‡ y v q v 0 yNxTŠ7r¥u)Š…D¥v q"!
9*@
@
C 7Vv-.(. ƒ Š 1 v * pF! ** Š 1 xTŠ u)ŠŒv 0 Hz!Bu)yNxTŠu = 8 %x ŠQy qy ‡ .‚u!Š * v * y Š 0 Xp Š<u!Š ‡21:*

* SŠ C3! ‡ yv q 0

θ1
θ2

v w3!
u)Š 1=  $lt<pXq
;

b
;

 

;  ;
 


&
"

 " * " 

0/0 Š/pNyv q 0

#  $ 

#    $ ;   ; "  
 ;



76

9o‚=  C

8 x%Šp>q 0 yNu ‡ pXyv q 0 u)Š * v * y Š 0 p>Š } ; #  $ 

#    $ } v * yNxTŠ 1 !TŠ‹yNxTŠ’pXq 0 yNu ‡ pNyv q 0 qFH¤yNxTŠ<w ‡ y Š =8 xTŠŠ;TBv y
u!Š * v * y Š 0 pXŠ } ; "   } v *I1 !%Š?y q¡u)Š * v y Š 0 pXŠ?q>H yNx%ŠY. v C3!v 1 , ŠXy ‡ .sv 0 , q". 1 p ‡ Dv y t = udv 0 q¥yNx%Š¥u7 qu 1:* } yNxTŠ
Š;TBv yu)Š * v * y Š 0 p>Š‹v *1 !%Š?yNxTŠ. q * y…qFHdŠ 0 Š¥u!w¥t‹q>HAŠ>, Š¥u * Š 1 ]ŠXy =8 x%Š ‡/0 w". Šu!Š * v * y Š 0 p>Š } ;
 v *1 !%Š?y q<yNxTŠ
pŒx /‡ 0 wŠ‹q>H 1 vu!Š/pXyv q 0=|8 xTŠ ;   v * yNxTŠfu)Š * v * y Š 0 pXŠ 1 !%Š‹y q Q q67 v 0 yNx%Š ƒ u ‡/0 pŒx q 0 ƒ u ‡/0 pŒx N=8 x%Š
wŠ/3q , Š>yNut u!Š * v * y Š 0 p>Š ; "  " *"‚} v *I1 !%Š?y qY7 x%qju!q3! 021 Š 1 yNxTŠ3pXq 0:0 Š/pXyv q 0=

&

`5a b
g 

X
e
k


h
d
M

 >Ž X‘ Ž>N“>”–•—B˜Œ™?š›”/šhœT”/™ŽTž#Ÿ¡ 
˜>”
 %—¢>”…£!—Œ™1•—B˜h‘*—¥ Œ•/¦jŸŒ§ >¨Œž T™!ž G”N¦

76

9o‚= k
C
p>qsrXt
ubv wsxTy{|~
z }€€B€‚}1ƒ tj„…u =a†.‡ uˆ[‰‹ŠŒvu

Chapter 6. Runner Design

b 
* v 0 p>Š g 
`Ya b
 
X
e
k  h 

d


76 # C

9o‚=



`Ya b 


X
e
k  h
d
ŠXy V* ‡6*@* !:,QŠ|Hz!
u)yNxTŠulyNx ‡ y e b e
X b X
b X



9o‚= J_BC



'&

(



 b 

}





9o‚= kBC

 X ke   
h b  X ke  

 h


9o‚= BC

k b 
k 



 !



&

(

'&







h

(



 q",r ‡ ubv * q 0 ƒ Š>y7 Š/Š 0?* pŒu ‡ r ƒ ŠXy7 Š>Š 0  ,?!/. yv . v 0 Š *C y 7 q=. v 0 Š *
<[u * y < 021 yNxTŠ 1 v ‡ , Š>y Š¥u.ŠJC"! ‡ . Š 0 y¤y q<y7 q . v 0 Š *



`Yacb

'&



X e h k    b

#

k    k
&

X eh
&

  
k  


(



 ! † C
 ! € C







(

y q’q 0 Y
Š .v0 Š



 b `Ya h k 
X e
* ! ƒ yv y;. v 0 w–v 0 y q
k  b

"

'&

(



C




 !  TC


n q67 7 Š V 0 q67 yNx%Š u!ŠF. ‡ yv q 0S* x¥vr
1 v G Š¥u!Š 0 pXŠ ƒ Š>y7 Š/Š 0 yNx%ŠF,
r:T! y 1 u ‡ 7hv 0 w’qFH yNxTŠ?yNu ‡ r¥Š >qv 1
. ŠXy * pŒu ‡ r 1 Š 0 q¥y Š 1 ƒ t'&
pXq 0 %D Š¥u)yv 0 w<yNx%Š?ŠJC"! ‡ yv q 0

ƒ ŠXy7 Š>Š

pXqsr>tBubv wsxTy{|~
z }s€B€€‚}1ƒ tf„…u V†.‡ uˆ[‰‹ŠŒvu

0

yNxTŠ x/t 1 u ‡

!/. v p u ‡21 -v ! *$%
Š>y * Š/Š7Qx ‡ y v *

yNx%Š

Ž>N‘’Ž>N“>”–•—B˜Œ™3š›”/šhœT”/™ŽTž#Ÿ¡ 
˜>”
 %—B¢>”¤£!—Œ™I•—B˜h‘*—¥ Œ•/¦jŸŒ§ X¨¥ž T™ž š…¦

* pŒu ‡
r

%/©

Section 6.1. Introduction

k  b











 &





 !  C

%e

yNx%Šu ‡ yv q’qFHAyNxTŠ * Œp u ‡ r’v *

&  &
&

b k  kh   k 

&





. ŠXy * Q7 uKv y Š k 
k   k 

 
k    k
 


‡/021=0 q67
&






(

 v 0 y Š¥u, q>H yNx%Šy7 q<q¥yNx%Š¥u

(



>_

 >Ž X‘ Ž>N“>”–•—B˜Œ™?š›”/šhœT”/™ŽTž#Ÿ¡ 
˜>”
 %—¢>”…£!—Œ™1•—B˜h‘*—¥ Œ•/¦jŸŒ§ >¨Œž T™!ž G”N¦

 !  
C
 !  # C

p>qsrXt
ubv wsxTy{|~
z }€€B€‚}1ƒ tj„…u a†.‡ uˆ[‰‹ŠŒvu

Chapter 6. Runner Design

pXqsr>tBubv wsxTy{|~
z }s€B€€‚}1ƒ tf„…u V†.‡ uˆ[‰‹ŠŒvu

Ž>N‘’Ž>N“>”–•—B˜Œ™3š›”/šhœT”/™ŽTž#Ÿ¡ 
˜>”
 %—B¢>”¤£!—Œ™I•—B˜h‘*—¥ Œ•/¦jŸŒ§ X¨¥ž T™ž š…¦

%&%



   

      

?(NKBU<&NOBU>


   

 

798;:<8#=>8;8@?A?CB D8;8@?FE GH8J ILKKM !8H#EH"$NPO QS%R '&( %) * +&&,-&( .$./102)354)6




T#UWV XZY[\5]#^`_;aD[cb ]`YdU'UeU'UeU'UeU'UeU'U'UeUeU'U'UeUeU'U'UeUeU'U'U'UfU'U'U'UfU'U'U'Uhg;i
T#U j kmlnpo$a]`qdq-]`Y;rts`u*vw^`b x)y(\5x1q UeU'U'UeUeU'U'UeUeU'U'U'UfU'U'U'UfU'U'U'Uhg;i
T#U z{kml1nd|+x1} b ^;b [<~d]19[l1n€oa+]`qdq-]`Y1rt^;b xy`\Cx1qUeU'U'UeUeU'U'U'UfU'U'U'UfU'U'U'UhT1‚
ƒ1„ …;„‡†‰ˆ<ŠŒ‹Ž(‘“’$”)•d•d”—–(˜f•d”1™`$šL›—œ—š‡Z™#žŸ„*„*„ „*„*„*„ „*„*„ „*„*„*„¡„*„*„*„ ƒ¢
ƒ1„ …;„ £ ¤¦¥Ž¡‹Ž`¡‹A¥Ž$–#™;Š§¥ŽDœ—ŠA”—–#œ—¨`š‡ž©„ „*„*„*„ „*„*„*„ „*„*„ „*„*„*„¡„*„*„*„ ƒ+ª
« š‡¬(–`­)¥/œ¥ŽDœ®+™`Zœ—•d‹Ž¥¡›—œ+¥ŽZœ+‹Ž‡”—–¯„*„ „*„*„*„ „*„*„ „*„*„*„¡„*„*„*„ ƒ+ª
° œ+‹Ž'œ+¥Ž$œ±›)œ¥ŽWœ‹Ž‡”)–J„*„¡„*„*„*„ „*„*„*„ „*„*„*„ „*„*„ „*„*„*„¡„*„*„*„ ƒ—ƒ
² –`¥Ž­—³’$”—–(ŠA¥Ž›—œ+‹Ž‡”—–J´¶µH”D·Œ¥§ŠA¬(µ`µ(š³d•œ—’c(‡–`/’c#œ¥cœ—’‹Ž¥Ž‡Š>‹Ž‡’¸pƒ—ƒ
² –`¥Ž­—³¹’$”)–`ŠA¥Ž›—œ+‹Ž‡”)–p´¶µH”D·º¥¦ŠA¬(µ(µ`š³#¸»„*„*„ „*„*„*„¡„*„*„*„ ƒ—ƒ
² –`¥Ž­—³¹’$”)–`ŠA¥Ž›—œ+‹Ž‡”)–p´5™;‡ŠAŠAZµ(œ+‹Ž‡”)–‘µ;¥Ž”)¨`šZ•¼¸½„*„*„*„¡„*„*„*„ ƒ—ƒ
¾ œ—ŠAŠ¦’$”)–`ŠA¥Ž›)œ‹Ž‡”)–p´¶Š>‹A¥Ž‡¿¸€„*„ „*„*„*„ „*„*„ „*„*„*„¡„*„*„*„ ƒ+À
¾ œ—ŠAŠ¦’$”)–`ŠA¥Ž›)œ‹Ž‡”)–p´¶³`™;¥cœ+¬(š‡‡’ µ(¬`•dµH¸ÁŒ„*„*„ „*„*„*„¡„*„*„*„ ƒ+À
ƒ1„ …;„ … ºœ¥ŽWœ‹Ž‡”)–(Šm”+ÃċŽ( ° œ‹Ž'œ+¥ŽDœ1ÅHÆ¡ÇȄ*„*„ „*„*„*„ „*„*„ „*„*„*„¡„*„*„*„ ƒ+À
T#U ‚ kml1n¼\5n—5]1\“q-n^‘s;u v ^;b xy`\Cxq UeUeU'U'UeUeU'U'UeUeU'U'U'UfU'U'U'UfU'U'U'UhT;É
ƒ1„ ¢`„‡†Ëʌ( ¥ŽÃ̔—¥Ž• •d”1™`šÍ„*„¡„*„*„*„ „*„*„*„ „*„*„*„ „*„*„ „*„*„*„¡„*„*„*„ ƒ+Î
ƒ1„ ¢`„ £ ²ÐÏ œ—•d‡–`Z–`­f‹Ž` ŠA”)š‡¬`‹Ž‡”—–Ñ„*„*„ „*„*„*„ „*„*„*„ „*„*„ „*„*„*„¡„*„*„*„ À1†
ʌ(*­œ‹Ž'œ+¥ŽDœ±ÒL$’‹ŽŠJ„¡„*„*„*„ „*„*„*„ „*„*„*„ „*„*„ „*„*„*„¡„*„*„*„ À1†
ÓeÔ9ÕDÖ ÒL$’‹×„*„¡„*„*„*„ „*„*„*„ „*„*„*„ „*„*„ „*„*„*„¡„*„*„*„ À1†
´5Æ¡ÇDØÆ'Ù¸AÚ¡ÒL$’‹ŽŠ9„*„*„*„ „*„*„*„ „*„*„*„ „*„*„ „*„*„*„¡„*„*„*„ À1†
ÛÜ ÒL’‹ŽŠÝ„*„*„¡„*„*„*„ „*„*„*„ „*„*„*„ „*„*„ „*„*„*„¡„*„*„*„ À)£
ʌ(*’$”—•-¨(‡–`D™¹ÒL’‹ŽŠ‘„ „*„*„*„ „*„*„*„ „*„*„ „*„*„*„¡„*„*„*„ À—…
° $–(¥cœ+šM’”)–(’šZ¬`ŠA‡”)–(ŠmÃÌ¥Ž”—• Ï œ—•dµ(š‡'ƒ„ ¢`„ £ „*„ „*„*„ „*„*„*„¡„*„*„*„ À)Þ
;ß

Chapter 7. pQ2 Diagram Calculations

ʌ('™;Z*’$œ—Š>‹Ž‡–(­±•œ+’`‡–( ’c#œ¥cœ—’‹Ž¥Ž‡Š>‹Ž‡’eÒL$’‹ŽŠ „*„*„¡„*„*„*„ „*„*„ À)ª
« š‡¬`–(­)¥¡œ¥ŽDœ®+™`Zœ—•d‹Ž¥¡ÒL$’‹ŽŠ€„ „*„*„*„ „*„*„*„ „*„*„¡„*„*„*„ „*„*„ À)Î
¾ œ—’c(‡–(*ŠA  'ÒL’‹ „*„*„*„ „*„*„ „*„*„*„ „*„*„*„ „*„*„¡„*„*„*„ „*„*„ Î)…
« ¥Ž’$”)–(™`‹Ž‡”)–‘ÒL$’‹'´F·§œD› ÃF”+¥Ž•œ+‹Ž‡”)–#¸ „ „*„*„*„ „*„*„¡„*„*„*„ „*„*„ Η¢
ƒ1„ ¢;„ … « ””—¥¡™`$ŠA‡­—–½ÒL$’‹ŽŠ „*„*„*„ „*„*„ „*„*„*„ „*„*„*„ „*„*„¡„*„*„*„ „*„*„ Η¢
ƒ1„ ¢;„ ¢ ÊM¥cœ—–`ŠA‡$–‹/ÒL$’‹ŽŠ „¡„*„*„*„ „*„*„ „*„*„*„ „*„*„*„ „*„*„¡„*„*„*„ „*„*„ Η¢
THU  Œnb y`Y\C]#an @U'U'UfU'U'U'UfU'U'U'UeUeU'U'UeUeU'U'UeUeU'U'UeU'UeU'UeU'UeUhÉ1‚
THU g{kml1n‘XZY[Žn Y b
Lax)[cb ]` Y Ð]` Y b ^;n\Cx)[cb ]`Y UeUeU'U'UeUeU'U'UeUeU'U'UeU'UeU'UeU'UeUh
É 
THU T L_`qdq-x)\C~ UfU'U'U'U'UfU'U'U'UfU'U'U'UeUeU'U'UeUeU'U'UeUeU'U'UeU'UeU'UeU'UeUhÉ;g
THU i u _n Ž[cb ]`Y  UfU'U'U'U'UfU'U'U'UfU'U'U'UeUeU'U'UeUeU'U'UeUeU'U'UeU'UeU'UeU'UeUhÉ;g



   "!#$

$

%'&)($*+,.-0/ 1)24351768/ 9;:<&)(=6>
9:@?A>46B6>DCE?A17F ?GHF 1:I/ >DCKJ4/ L 17CNME1:'17FOFPJ41
3Q($G)9(-SRM6>H9T:;-K/ (U?A1)9:I/PC2
(C)2K/PC)(A(
3Q9 V%W&(X/P6B*>K3Y:17C ?(Z>
L:<&/ 9[-0/ 1)2435176\?A17C]R(^-H(6>DC9:<3_1:T(-`RMa:<&(ZLb1 ?:$:<&)1:$:T(C)9>
L
6/PFOF / >4C)9>L'-
>DFOF 13_9=&)1c)(dR(A(
CS/PCNc)(A9:T(N-XRAMaefWgihjfWJ e lkmJn17C -d>:<&)(3W6o1qpr>K3;/PC)9T:I/ :<G:T(A9s&(
3Q(17C)17R3_>H1 -[/PCU:<&)($*+,`-K/ 1)2D3_176t3_(A9(135? & u%'&)(=*+,@-K/ 1)2D3_176v/ 9;>4C)(o>
Lw:<&)(=6x17C
/ Ly(A9T:1:I/ >DC9@>Lz9G7*7*HF M
17C)-^-
(
6x17C)-Z:<&(N>K3YM{x&/ ?&{i1)9U-
(Ac(
F >4*(-XRM[f;F L|3_(N-~}s1
3_9& 17FOF €7)‚ ƒ

€7„/PC:<&)( :<G73…C>L@:<&(
?(
CN:<G73YM '† :‡{i1)9@ˆj3Q9:'/PC:<3Q>0-DG)?A(N-$:T>=:<&)(-0/ (U?A1)9:I/PC2[/PC -4G)9T:<3QM$/PCU:<&)(sF 1:T(7‰ HŠ9 gu1c
/ 9 ƒ H‹H„ ‡†YCB:<&/ 9
-K/ 1)2D3_176=J17Cd(C)2K/PC)(A(
3'/PC)9G73Q(N9U:<& 1:U-0/ (?N1)9T:I/PC)2X6x1 ? &
/PC)([17R/PF / :rMS?N17CL|G7F ˆjFOFl:<&(-K/ (Z6x>4F -^-H(A9</ 24C
3Q(Œ4G
/P3_(6(
CN:T9:<&)(UF / ŒDG/ -$6x(:17F
/ 9@/PCp#(N?:T(N-B1:z:<&)(3y/ 2D&N:zc)(F >0?/ :rMB3517C2H(17C)-U:<&('ˆjFOF /PC)2o:I/P6(x/ 9 9A6x17FOF
(C)>4G)24&$:T>Ž*3_(c)(C:s*3_(6o1:<GH3_(=L|3Q(N(A/PC)2 xC)( ?A17C0Jl{'/ :<& :<&)(d&(
FO* >L@:<&(S*
+W,‘-0/ 1)2435176sJ"17C -ŽRM
GN:I/PF / )/PC2(’7*(
3y/P6x(C:17F4c)17FOG)(A9Ly>K3z-H(A9</P3Q(-ˆjFOF /PC)2 :I/P6(=17C)-2H1:T(Bc(
F >K?)/ :I/ (A9U/P6B*3_>c)(B:<&)(sŒDG)17F / :rMs>
L
:<&(B?N1)9T:I/PC)2
†PC:<&(-K/ ([?N1)9T:I/PC)2X*3_>K?A(A9q9 9(N(“kK/ 2DGH3_(
)„Jz1aF / Œ4G
/ -X6(A:17Fn/ 9*>4G73Q(-Ž/PC:T>d:<&(9A&>
:U9F (A(Ac(
{&)(3_(s/ :x/ 9*3Q>D*(FOF (-SRMB:<&)($*HFOG7C2H(3":<&73_>4G)24&U:<&)($3…G7CHC)(3z17C)- :<&(U271:T(s/PCN:T>=:<&)($6>4F - %'&)(U2H1:T(
:<&/ ?¡C)(A99/ 9;c)(3QM[C 13r3_>){`?A>46B* 1
3Q(-${'/ :<&U:<&)(B1c(
3_1)2H(N-d6x>4F -=:<&
/ ? ¡C)(A9q9;17C -$:<&)($3…G7C7C(
3n:<&
/ ? ¡C)(A9q9
:T>=/PC)9G73Q(;:<& 1:‡R
3Q(17¡<1)2H(o*>K/PC:z>
L¢:<&)(W9I? 3517*>0?A? G73_9i1:w:<& 1:u2H1:T(oF >0?A1:I/ >DC wfX9>4FOG:I/ >4CW>
L"/PC ? 3_(N1)9</PC2
:<&(-0/ 9q? & 1
3Q2H(?>K(£ ?/ (
CN:AJ0h"¤mJ F 1
3_2
(3j?>DC)-DG
/ :T9I„;3_(A9AGHF :T9'/PC1 F 13_2
(
3m9I? 3517* f¥?N13_(L|G7FH-H(A9¦/ 2DCx>
Lj:<&(
3…G7C7C(
3w17C)- :<&(2H1:T(E/ 9o3_(NŒDG/P3_(NkK/P3_9T:AJD:<&(X§|?>D6B6>DC)¨*
+W,©-0/ 1)2435176ªx/ 9/PCN:<3_>0-4G ?(- ;%'&)(B(
3…3_>K3Q9>Lz:<&/ 9B6>0-
(
FK1
3Q(s17C)17F M)(N1:T(3|J¢:<&(3Q(ALy>K3…6x(N-^6>0-
(
FD/ 9o-
(N9q?3y/PR(- =«7¬m(?<:T9x>Li-0/ ¬m(
3Q(
CN:Wc 1
3y/ 17R7F (A9o/ 9x9T:<G -K/ (-17C -SŒ4G)(A9:I/ >4C)9
Ly>K3n9T:<G -H(C:T9;1
3_(o20/ c(
C=/PCB:<&)(o(
C)->Ln:<&)(B? & 17*:T(3



ž

$

kY”P”P™• –P”P—9• —Yk™ŸQ˜4 5›k˜ '™œš7'™˜ ˜š ›–Q&_› ˜7 ˜ ”OœOš › &_l› 




ß



Ýß








­

®°¯±³²w‡ ´µ´¶$o·¹¸sº





v

s!#»x¼ 
»B´



%'&)( /PCqpr(?<:I/ >DC[*7&)1)9q( / 9 C)>K3…6x17FOF M„9(* 1
3_1:T(-d/PC:T>:<&73Q(N([6o1
/PC$9:1)2
(N9W{&
/ ? & 1
3Q(7½'9F >){¾*)1
3Y:AJ¢Lb1)9:
*)1
3Q:@17C -=:<&(E/PC:T(C)9¦/ ˆD?A1:I/ >DC 9(N(=k0/ 24G73Q(
7„ @†PCU:<&)(9F >){¿*)1
3Y:‡:<&(=*7FOGHC)2
(
3z6>c)(A9/PCU:<&)(?3y/ :I/ ?N17F
c(
F >0?/ :rMS:T>]*3_(c)(C:E{i1c)([Ly>K3r6x1:I/ >DCd17C -Ž:<&(
3Q(ALy>K3Q(S(<’K*(F 9S6x1N’H/P6BG76À1
/P3bÁ)271)9R(Ly>K3_(S:<&(aF / ŒDG/ 6(:17FH(C:T(3_9 :<&)(o?N1c/ :rM @†PC:<&)(WLb1)9:W*)1
3Q: :<&(o?A1c
/ :…MU9AGH*7*>
9q(N-U:T>R(xˆjFOF (N-=/PCU9AG)?&x{i1AMx:T>[*3_(c)(C:
Â#ÃIÄjÅrÆ<Ç ÄÈzÉNÊËIÌ Ç ÄjÊËTąÍIÎQÇ ÏËTÊoÇ ÐxÑ0Ò"ÓmÔ7ÒnÕ ÄwÏ<ÉNÉNÖTÄ

?>4*AMH3b/ 24&:ØÙ × J4
ŠHŠ
ŠDJ¢RM[g@3 'Ú"1
3P‚j}E( /P3

ێÜAÝ<Þ$ÜAÝ<ßAàáIâHã äUå‡àNåWæàNäPçIÜè™éSê7ãAàIç
ê)âHëAàiì_â ämáIâHãWÞ#âê ÝIáNíé î Ýïè Ýä5è çIå@í

ðñ

Section 7.2. The “common” pQ2 diagram

gate

mold
3
gate
runner
2

1

Shot sleeve

ß 7½ 
 

! "#$
"

k0/ 24G73Q(

*3_(6x1:<G73_(xL|3_(A(N/PC)2$17C -$:T>=>4R:1
/PCU:<&(=3b/ 24&:iˆjFOF /PC)2[* 1:|:T(3rC u%'&)(U/PC:T(C)9¦/ ˆD?N1:I/ >4C=*)1
3Y:/ 9@:T>=ˆjFOF:<&(
?A1c
/ :rM@{W/ :<&;1 -7-0/ :I/ >4C 17F 6x1:T(3b/ 17F:T>x?A>46B*(
C9I1:T( Ly>K3K:<&)(‡9A&H3b/PCH¡1)2H('*>K3Q>H9¦/ :rM;-DG73y/PC)2:<&)(@9>4F / -0/ ˆD?A1:I/ >DC
*3_>0?(A9q9 z%'&)(=*+,.-0/ 1)2435176©-H(N17F 9@{W/ :<&U:<&(U9q(N?>DC)-* 13Q:;>Ln:<&)(ˆjFOF /PC)2[*7&)1)9q(
†YC:<&)(Z*
+W,¶-0/ 1)2435176sJ:<&)(9>DFOGN:I/ >DCZ/ 9=-
(A:T(3r6/PC(- RMSˆjC -K/PC)2Z:<&)(d/PC:T(3_9(N?:I/PC2Ø*>K/PC:>
L':<&(
3rGHC7C(
3yÁK6>4F -d?&)1
3_1 ?:T(3b/ 9T:I/ ?[F /PC(s{'/ :<& :<&)(*HG76B* -0/ ($?A1)9T:I/PC)2a6x1 ? &
/PC()„o? & 1351 ?<:T(
3y/ 9:I/ ?F /PC)( s%'&)(
/PC:T(3_9(N?:I/PC2^*>K/PC:9>D6(:I/P6x(3_(Ly(3_(A(-S:T>S1)9x:<&)(s>D*(351:I/ >4C 17Fj*>K/PC: B%'&)(6x1 ?&/PC)($? & 1351 ?<:T(
3y/ 9:I/ ?
F /PC)(S/ 9E1)99AGH6x(N-Z:T>ØR(“G7C)-H(3_9T:T>K>0-Z:T>“9q>46(-H(A2D3Q(N([17C -X/ :$3_(NŒDG/P3_(A9EˆjC)-0/PC2Z(’7*(
3y/P6x(C:17FOF M[:r{ >
?>K(A£$?)/ (C:T9 n%W&(x3rGHC7C(
3yÁK6>4F -?&)1
3_1 ?:T(3b/ 9T:I/ ?F /PC(x3_(NŒDG/P3_(A9@¡C)>){F (-
2H( >4C':<&)(‡(A£$?)/ (C ?<M
Á -0/ 9q?&)1
3Q2H(
?>K(A£$?)/ (C:AJjh ¤ Jl:<&HG)9B/ :U/ 917C$(N99q(C:I/ 17F"*)1
35176(:T(
3i/PC :<&)($?A17F ? G7F 1:I/ >4C)9 $%iCN:I/PFwC>){J"h ¤ & 1)9ER(N(C
(c 17FOG 1:T(N-U( / :<&(
3D(<’K*(3b/P6(C:17FOF MNJ:T>sR(x1)99¦/ 2DC(-x:T>U9*(N?)/ ˆD?x3…G7CHC)(3|JH>K3jRMW:<&)(F / Œ4G
/ -$6(A:17F
*3_>4*(
'3 &
)(+* „ h">0? ¡A9 Nƒ
- ,H„"{&
/ ? &/ 9 -H('Lb1 ?:T>:<&(6(A:<&>0-$G)9(-U:T>0-71Mx17C -$3_(Ly(
3Q(N(N- &)(3_()/PC1)9z:<&(
:I/ (A9
§|?A>46B6x>4C ¨[*
+,V-0/ 1)2435176 , kKG73Y:<&)(3r6>K3_(HJmh ¤ / 9x1)99G76(-[?>DC9:17CN:o3_(A2H1
35-4F (N99;:T>[17CM=?&)17C)2
(s/PC
17CM>Lm:<&(6o1 ? &
/PC( Á)>4*(
3_1:I/ >DC*)1
3_176x(:T(3_9 -DGH3b/PC2o:<&)(W?A17F ?GHF 1:I/ >DC w%'&)(@(’7*(
3y/P6x(C:17F)17*7*3_>H1 ? &o/ 9
1
3_-DG>DG9 17C -B(’7*(
C9</ c(7J03_(NŒDG/P3b/PC)2U:<&(BRHG
/PF -K/PC)2>Ll:<&)(1 ?<:<G 17FH6x>4F -ULy>K3m(N1 ?&x1:|:T(6B*:z{'/ :<&x1c)(351)2
(
?>H9T:@>/
L .
‹DJ Š
ŠHŠ)
‚ . NŠ¢J ŠHŠ
Š17C)-[/ 9o3513_(F M[G9q(N-[/PCU:<&)(B/PC -DG9:<3Y1
M 0 zf]9A&>K3Q:@-0/ 9q?G9q9¦/ >DCU17R>DGN:‡:<&/ 9/ 9q9G)(
/ 9o*3_(A9(
CN:T(-[/PCB:<&)(of;*7*(C -0/ ’sf~?A>46B6x(C:T9‡:T>S3_(Ly(
3Q(N(B
2(3_()/PCs:<&(Ž§T?>D6B6>4C ¨6>0-
(
F ?>DC9:17CN:h"¤K„o/ 9?>DC9:<3…G ?<:T(- ;%'&)(E1)9q9G76B*N:I/ >DC96o1 -
(=/PCs:<&(
?>DC9:<3…G ?<:I/ >DCU>L:<&(=6>0-H(F71)9;Ly>DFOF >){'/PC)2



















!

h"¤S1)99AGH6(- :T>ZR(=?>DC9:17CN:W17C --H(*(
C)-H9W>4C7F M=:<&([6(:17F Uk >K3z(<’176B*7F (HJefWgihjf°3_(N?A>463&
6(C - -K/ ¬l(3_(C:@c)17FOG)(A9@Ly>K3w17FOG76/PC7GH6sJK)/PC)?17C -S6x1)24C)(A9</PGH6°17FOF >)M9

$

4TÒjÐIɦÅrÆIËIÎlÈuË|ÅrÆIÉAÊxÆ<ÃqÄzÏ<ËT˦Ї*Ä S6575<ËTÄbÅyËTÊoÇ Ð ÅrÆIË‡Ì Ç ÅyËIÎYÃ]Å SAΙË@Ç 9
Ð 8nÆ<Ç ÍIÆiÅrƦËiÔ ¤ Ç Äj;Ë :<ÃÌ S¦ÃqÅyËTÊxÏ<ÃqąËTÊWÉNÐ ÅrÆI
Ë :¦ÉNÌ SAÈzËwÅyÉ
Ï Ë=<
Ì Ì ËTÊ?>bÔ7ÉAÍIÖÄnÃÐIÊA@EÃÌ Ì B6C7D7EGF;HI"ÆIËuÃXSqÅrÆIÉÎ0ÊÉNËTÄnÐIɦÅnÖIЦÉ!8[ÉJ4ÃÐKÉNЦË8nÆIÉVSIÄbËÅrÆ<Ç Ä"ÈuË|ÅrÆIÉNÊ;ÃÐIʇÅrÆIËIÎPË;JQÉ<ÎPËiÇ Ä"ЦɦÅ
ÊNÇ ÄbÍSIąÄbËTÊÇ Ð ÅrÆ<Ç ÄzÏÉAÉNÖ HnÑ0Ë;:¦ËIΙÅrÆIËIÌ ËTÄbÄ!L ÅrÆ<Ç ÄzÈzË|ÅrÆIÉNÊxÇ Ä"ÃIÄNM5<ÉNÉAÊ7OÃIÄlÅrÆIËPM_ÍTÉNÈiÈuÉNÐOxÈzË|ÅrÆIÉNÊ
H
QqÇ JK/É S'ÐIÉ 8É J¢ÃÐ KqÉNÐI/Ë 8"ƦQ
É SIÄbËzÅrÆ<Ç ÄjÅyËTÍIÆAÐ<Ç RTS¦?
Ë SÌ ËÃIÄbËzÅyËIÌ ÌÈzËuÃÏ/É SqÅwÇ Å H
,
ƒ

ÛaÜAÝÞ ÜAÝ<ßAàáIâHã äå‡àNåWæàNäPçIÜè™éSê7ãAàIç
ê)â
ëAà@ì_â ä¢áIâHãWÞ#âê ÝIáNíé î ÝAï è Ýä_è ç|à<í

?A>4*M73b/ 24&:ØÙ × J0
Š
ŠHŠDJ¢RMg@3 ;Ú"1
3P‚j}E( /P3

Chapter 7. pQ2 Diagram Calculations

plunger location

liquid metal reaches
to the venting system
starging filling the cavity

{

liquid metal pressure at the plunger tip
or the hydralic pressure

cavity
filling

±ß

kK/ 24G73_(

Time

  
 
 "
G 
  
-'" 

¢½

 o}=17CMU:T(3r69x/PCÚj(3rC>DGHFOF /Q‰ 9;(NŒDG)1:I/ >DCE?A17C R($C)(A2DF (N?<:T(-



@%W&(=F / ŒDG/ -S6x(:17F0/ 9o3_(N1 ?&(-$:T>$2H1:T(

€ oe> 1
/P3bÁ)2H1)9W/ 9*3_(A9q(C:'/PCU:<&)($F / Œ4G
/ -S6(:17F
‹ oe>$9>DF / -K/ ˆD?N1:I/ >4C>0?A? G73_9;-DG73y/PC)2=:<&(ˆjFOF /PC)2

,

@%W&(=6x1
/PC 3_(A9</ 9T:17C ?(o:T>=:<&($6x(:17F 4>){

/ 9/PCB:<&)(s3rG7CHC)(3

ß ‡f¿F /PC)(N1
3u3Q(
F 1:I/ >4C)9&
/P*=R(A:…{ (N(CU:<&)(=*3Q(N99AGH3_(HJ
o17C -4>){¿351:T(  9IŒ4G 13_(N-K„J

f ?A?A>K3_-0/PC2$:T>:<&( F 1)9:W1)99G76B*:I/ >4C0JK:<&)( F / Œ4G
/ -Z6x(:17Fm*3Q(N99AGH3_(E1:':<&)( *HFOG7C)2
(3n:I/P*KJ

{3b/ :|:T(Cs1)9



 
~&)(3_(H½





 




 






J¢?N17C[R(



 ß!



:<&)(=*3_(A99AGH3_(B1:i:<&)($*7FOGHC)2
(
3j:I/P*
:<&)
( 4>){©3_1:T(
6o1N’
/P6BG76t*3Q(N99AGH3_({&
/ ? &E?N17C R(B1:|:1
/PC(-SRMU:<&(B-0/ (U?A1)9:I/PC2S6x1 ?&/PC)(
/PCU:<&)(U9&)>:@9F (N(c)(
6o1N’
/P6BG7
6 4>){V351:T(o{&
/ ? &E?N17CR(U1:|:1
/PC(-[/PCB:<&(9A&>
:‡9F (N(c)(





%'&)
(

17C -   c 17FOG)(A9=:T>~R(d-H(:T(
3…6U/PC(-ŽLy>K3W(c)(3QM^9(A:s>Lx:<&(Z-0/ (Z?A1)9T:I/PC)2]6x1 ? &
/PC(
17C)-Ž:<&)(d9&)>:E9AF (A(Ac( ¥%'&)(!
 c 17FOG(Z?A17C R(Z?N17F ? G7F 1:T(N-¥G9</PC2X1“9:1:I/ ?Ly>K35?(ŽR 17F 17C)?A( ¥%W&(



?>4*AMH3b/ 24&:ØÙ × J4
ŠHŠ
ŠDJ¢RM[g@3 'Ú"1
3P‚j}E( /P3

ێÜAÝ<Þ$ÜAÝ<ßAàáIâHã äUå‡àNåWæàNäPçIÜè™éSê7ãAàIç
ê)âHëAàiì_â ämáIâHãWÞ#âê ÝIáNíé î Ýïè Ýä5è çIå@í

"$#

Section 7.2. The “common” pQ2 diagram



-H(:T(3r6/PC 1:I/ >4C=>L   c 17FOG)($/ 9x-H>4C)( RMS6(1)9G73y/PC)2 :<&)(Bc)(F >0?/ :rMs>
Lu:<&([*HFOG7C2H(3w{&)(C=:<&(s9&)>:
9 F (N(c)(d/ 9s(6B*:…M Ž%W&(^6x1N’H/P6BGH6 c(
F >K?)/ :…MZ?>D6BR
/PC(-“{W/ :<&:<&)([9A&>
:B9F (A(Ac(S? 3_>
9q9|‚79q(N?:I/ >4C 17Fl1
3Q(1
M
/ (F -=:<&)($6x1N’
/P6EGH64>){¿351:T(HJ

$

  






 ß!




H„


{&)(3_( W3Q(
*3Q(N9(
CN:'17CNM[*>
99</PRHF (o9G7R)9q? 3b/P*:I/ >4CU( 2
%'&7G)9NJ7:<&)(Uˆj3Q9:xF /PC)(B?A17C[R(E-4351A{CE>DC*+ , -0/ 1)243517681)9x/ :'9&)>){C RMB:<&)($F /PC)(B-
(
C>
:T(N-1)9 E/PC
kK/ 2DGH3_(
 i%'&)( F /PC)(U9T:1
3Y:T9;L|3_>46t1&
/ 24&)(3‡*3Q(N99AGH3_(
 „':T>1[6o1N’
/P6BG76 4>){©3_1:T( 9qŒDG 13_(N-K„
f C)({~?A>46BR
/PC 1:I/ >4C>
Lj:<&(x9q176(-0/ (x?N1)9T:I/PC)2 6x1 ?&/PC)(17C -s1U-0/ ¬m(
3Q(
CN:'*7FOG7C2H(3m-0/ 176(A:T(3j? 3_(N1:T(A9@1
-0/ ¬m(
3Q(
CN:WF /PC)( fØ9A6x17FOF (3*7FOGHC)2
(
3j-0/ 176(A:T(3&)1)9;1=F 13_2
(
3z6x1N’
/P6EGH68*
3Q(N99G73_(
 „i17C -$-K/ ¬l(3_(C:
6x1N’H/P6BG76 4>){©351:T(1)9'9A&>){xC$RMB:<&)(sF /PC)(U-
(
C>
:T(N- 1)9
%'&)(Z6x1N’H/P6BG76 4>){‘3_1:T(Z/ 9s1L|G7C)?:I/ >4C>
L':<&(^6x1N’H/P6BGH6 *7FOG7C2H(3ic)(F >0?)/ :…MZ17C)-“:<&(^*HFOG7C)2
(3

-0/ 176(:T(
3 1
3Q(1„ %W&(s*HFOG7C)2
(3n1
3_(N1 / 9;1E>4Rc/ >DG9‡L|G7C)?:I/ >4CB>L:<&)(s*7FOG7C2H(3n-0/ 176(:T(
3#J
2>){ (c)(3|Jm:<&(6x1N’H/P6BG76 *7FOGHC)2
(
3c)(F >0?)/ :…MS/ 91$Lb1
3P‚m6>K3Q($?>D6B*7F (<’ L|GHC ?<:I/ >DC E%'&)(ELy>K35?(=:<& 1:x?A17C
R((’:<351 ?<:T(-sL|3Q>D6¿1U-K/ (o?A1)9:I/PC2 6o1 ? &
/PC(U/ 9i(A9q9(
CN:I/ 17FOF Mx:<&(x9q176(Ly>K3l-0/ ¬m(
3Q(
CN:*HFOG7C2H(3l-K/ 176(A:T(3_9
%'&)(?&)17C)2
(Z/PC:<&)(a3Q(N9¦/ 9T:17C ?(S1)9[3_(A9AGHF :T9s>Lx?&)17C)2K/PC)2Z:<&)(“*7FOGHC)2
(
3 -0/ 176(:T(
35„s-
(
*(C -
9s>4CS:<&(
?>DC)-0/ :I/ >4C)9>Lm:<&(U*7FOG7C2H(3 n%'&)(§|-D3QM)¨oL|3b/ ?<:I/ >DCW{'/PFOFHR(W9q176(@{x&)1:u-K/ ¬l(3_(C: -4G)(;:T>U? & 17C2H(*HFOG7C)2
(3
{ ()/ 2D&N:AJ;(Ac(
C]/ LB:<&(¥*HFOG7C)2
(3U?>DC)-0/ :I/ >4C)9 {x&(
3Q(^:<&(a9q176(
l(:AJ9>D6(Ø3_(A9q(N1
3_?&(
3Q9S? F 1
/P6¶:<& 1:
*7FOGHC)2
(
3Dc)(F >0?/ :rMB/ 9@17FO6>
9:‡/PCNc 13b/ 17C:@/PCE3_(A2H1
35-B:T>E:<&(E*HFOG7C2H(3l-K/ 176(A:T(3 ;ew(Ac(
3Y:<&)(F (N99J:<&
/ 9'*
/ (N?(
>Lu/PCNLy>K3r6x1:I/ >4Cs&)1)9xC)>R(N1
3b/PC2s>4Co:<&(-
(
3y/ c 1:I/ >4CE/PC:<&/ 96>0-
(
F>K3z3Q(ALy>K3…6(-E>DC(7J79¦/PC ?(W{ (o-
>C)>:
G)9(E/ :
f~9¦/P6B*7F / ˆ4(N-sLy>K35?(=R)17F 17C ?(>DCU:<&($3_>0-
(oM
/ (F -H9 9(N($6>K3Q(U-H(:1
/PF 9/PCB9(?<:I/ >DC
€ * 1)2
(U
ƒ7„



¼ß










 




  





      
  









 

¼ß!

 ß! 

„

{&)(3_(o9AGHR)9q?3y/P*: ‘-H(C)>:T(N9@:<&(U1 ?<:<G 1:T>K3

!#"
  '%$'&(
)+*-,/.0 12.3*/465873491:1<;-7=4>,/.?.3*/465A@B;-CEDF4<7G.30 5IHJ*/4<CK.3*/4L5873491:1<;-7=4>,/.M.3*/4>,-NO.P;,/.RQ-70 12
TS2U=VT,7W1YX
HJ0B.3*2Z/0 ,-[4O.34E7\Q8]\S ^_
<U=[`Xa,-b/ZcHJ0B.3*>,5A@B;-b<Dd4<7#Z/0 ,-[4O.34E7=e  edQ8]\S ^fSOg-UR[aXh
-fi 6'-"
j ;TV1<.30B.P;/.30kbEDl.3*/4MZT,/.R,20kb8.RQ+4Em8;,/.30 Q/bonqpO^ rsut/0k4E@kZ1
vAw   w v Uz
X

 Ov  
vxw v/y 
†YCB:<&(^§T?>46E6>4C ¨*
+,`-K/ 1)2D3_176vh"¤S/ 9;-H(ˆjC)(N- 1)9


„#„

ßA‹

¤







a{}|~


 ß!

 E€ €


‚<ƒ‡Î™ËqÉ<ÃqÊWÎPˇÅrÎPÆIËTËuąËÍTÃIÉNÎPÈiÍIÆ'ÈuÇ ÄËIÐqÐIÅwËTËÈuÊWÃIÊÉNËiÐiÏÅrK'Æ<Ç ÄwÎPË;ÃqJQËIÄ;S<ÎPËTˈÍ|Å…fH …AÅyÉ@ÅrÆIË
ÛaÜAÝÞ ÜAÝ<ßAàáIâHã äå‡àNåWæàNäPçIÜè™éSê7ãAàIç
ê)â
ëAà@ì_â ä¢áIâHãWÞ#âê ÝIáNíé î ÝAï è Ýä_è ç|à<í

S¦ÃGSËIÎDÉNÐ?Sˆ‡
,

ÉNÐ?S<Ã5<Ë

B9‰ˆŠ H

?A>4*M73b/ 24&:ØÙ × J0
Š
ŠHŠDJ¢RMg@3 ;Ú"1
3P‚j}E( /P3

€7„

Chapter 7. pQ2 Diagram Calculations

Pmax

2
smaller
plunger
2

2

2 A 3 CD
2
Q=
ρ

1

Pmax

2

dß!  ½

kK/ 2DGH3_(

|+~

ew>
:T(HJK:<&)(3_(Ly>K3_(
:I/ >4C





Qmax

6G$$"  
- !"

/ 9W17F 9>-H(ˆjC)(N- 1)9W1=?>DC9:17CN:@Ly>K3n(c)(3QM[6x(:17F

3%n:I/PF / /PC)2SÚj(
3…C)>4G7FOF /Q‰ 9'(NŒDG)1 &

 ß!

 

*

‹H„

%W&(4>){V3_1:T(B1:‡:<&(U271:T(U?A17C R(U(<’K*3_(A9q9(N- 1)9

  

 

*

 ß! ,





% &)( 4>){v3_1:T( /PC -0/ ¬l(3_(C:UF >K?N1:I/ >4C)9o/ 91=L|GHC ?<:I/ >DC=>
Lu:<&(s:T(6B*(
3_1:<G73_( 2w>){ (Ac(
3#Jz«0?¡¦(
3Y: «0? ¡G&
'
(3Q: NƒH
ƒH„U-
(
6>4C)9T:<351:T(N-[:<& 1:W:<&(&)(N1:W:<3517C9Ly(3@/ 9B/PC9</ 24C
/ ˆD?A17C:x/PC=:<&)($-4G73_1:I/ >DC >L :<&)(EˆjFOF /PC)2>
L
:<&(B?N1c/ :rMNJ¢17C)-=:<&)(3_(Ly>K3_(:<&(:T(
6B*(351:<G73Q(B>
Lw:<&)($F / ŒDG/ -S6(A:17FK?N17CR(B1)99AGH6x(N- 17FO6>H9T:@?A>4C)9T:17C:
-4G73b/PC2^:<&([ˆjFOF /PC2 *(
3y/ >0- {x&/ ?&“/PCŽ6>H9T:E?A1)9q(A9 / 96BG ? &ŽF (A9q9 NŠHŠX6/PFOF / 9q(N?>DC)-H9I„ “fu9s9G ? &0J:<&(
9>DF / -K/ ˆD?N1:I/ >4C[/ 9s/PC9</ 24C
/ ˆD?A17C: :<&)(dF / Œ4G
/ -Ž6(:17Fl-
(
C9</ :…M[?&)17C)2
(N9=F (A99o:<& 17CŠ \/PC :<&(d3rGHC7C)(3y„
? 4>){V3_1:T(U?N17CR(B1)99AGH6(-$?>4C)9T:17C:A½
š I— ”  P”O˜ š › QI—! ™šI—™˜ ˜ :<&(
3Q(ALy>K3Q(7JK:<&)(xc)>4FOG76(A:<3y/ 
!P—YŸ —YPœO”

&

‹



' & &'





!f‹

     "  

 ß! ß



# I"ÆIËiÃXSqÅrÆIÉÎ8DÉ/SÌ ÊoÌ Ç Ö#ËzÅyÉÌ ËæÎ_Ð98"ÆIÉ'ÍqÃ<ÈuË%$AÉ/SqÅ 8"Ç ÅrÆiÅrÆ<Ç ÄNM_ÍIÌ Ë;:I˦ΠOxÇ ÊËà H
& QJ É<ÎmÈzÉÎPËÊAË|ÅbÃ<Ç Ì ÄwÄbËTËuąËTÍ|Å…Ç ÉNÐ ' H (N¦S Ã6<5 Ë)'7C H
* ÎPËÃIÊoÈuÉ<ÎPËuÃÏ<É/SqÅwÇ ÅnÇ Ð;Ô4ƦÃGqS ÅyËIÎ E H
?>4*AMH3b/ 24&:ØÙ × J4
ŠHŠ
ŠDJ¢RM[g@3 'Ú"1
3P‚j}E( /P3

ێÜAÝ<Þ$ÜAÝ<ßAàáIâHã äUå‡àNåWæàNäPçIÜè™éSê7ãAàIç
ê)âHëAàiì_â ämáIâHãWÞ#âê ÝIáNíé î Ýïè Ýä5è çIå@í

"+

Section 7.2. The “common” pQ2 diagram

Pmax



Q max

1
2

∼ DP

2

DP

Pmax
Q max

dß! €¢½


kK/ 2DGH3_(

$  

2(C ?(HJ4{

9>DFOGN:I/ >DCs/ 9




D1

 
" !  
?
PYi" G " 
  _i"#- 3
$  3
-   '" #  6G$$"

($&)1c)(U:r{ > (NŒDG)1:I/ >DC9

 ß!f‹

„'17C -

 ß! ,

H„‡{'/ :<&s:…{ >SG7CH¡
C>){xC9



17C -




„@Ly>K3n{x&/ ?&B:<&(

 ß!


  
 

  


  

H„

!#"
  '%$'&
)+*-,/.†0 12.3*/4587=4q1 1E;T734>,/.`5x@B;TbEDF4E7G.30 5 n3[4.R,-@'1 0kZ 4 sEeu.3* 4-Q8H7Y,/.34>,-b/Z%DA,/.34 4<@ QAN<0B. t HJ*/4<b
.3* 4%]fQ/@k@ Q8 H#0kb<D ,734GDd0ˆ4EbL@k0km ;T0kZ
[4.R,-@[M,/.34<730 ,-@0 1,-@B;-[0kb8;-[e
     y"! z
e #   
vAw v $ U   % X,-b/Zl.3*/4Dx,/.34 ,7=4 ', &  O)v (+* U   XT-h ,'1ˆ'4 .0/21435/76 1L734<NˆQ8[[4Eb Z/4<Z89,-@B;-4 Q ]
~ < & w &s^
3:9+; S/^ g gcn |+=
-fi 6'-"
,\.30k@k0 >0kbEDc4Em8;,/.30 Q/bcnˆpE^ ? s
y






 A@+BCD * *F EHG CL@ @* C@+D C B  M@ CIKJ EHG
*
G
.3* 4 DA,/.34N 4<@ QAN<0B. t+Nˆ,-bVˆt%Q/V .R,-0kb 4EZ2Vˆto;/.30k@k0 > 0kb<D
4<m ;,/.30 Q/bcnqpO^ gs

   vAwky-y5O   & y-
v
P'*/4-Q8H}7R,/.34?N ,-b+V 4?Q/V .R,-0kb/4<Z%Vˆtc;/.30k@k0 > 0kbEDc4Em8;,/.30 Q/bonqpO^ s
 &  E v (+*
 

ß

ÛaÜAÝÞ ÜAÝ<ßAàáIâHã äå‡àNåWæàNäPçIÜè™éSê7ãAàIç
ê)â
ëAà@ì_â ä¢áIâHãWÞ#âê ÝIáNíé î ÝAï è Ýä_è ç|à<í

?A>4*M73b/ 24&:ØÙ × J0
Š
ŠHŠDJ¢RMg@3RQ;Ú"1
3P‚j}E( /P3

Chapter 7. pQ2 Diagram Calculations

!#"
$>$&
4q5d4ˆ,/. 5 7=4Aˆ0 QA;E1 4 -,-[ [email protected]*
_i 6'-"
;-b/Z 4E7 NˆQ8b1E.37 ;-NO.30 Q8b




&

' &
& ' &

› P˜ ”P• šI—) _› ˜ œ P˜ ˜ › Q)›  • ” ž —P•  Q˜
š Nš –P”Iš • ”P™ Q˜
› P˜ ”P• š#š –P”IœO—YŸ œ QŸ —™š › _ › š –• ”

˜ kP”OœOš|š 
 —YP
  








®°¯±W»r!#=!…

~w¯±

7Y,-bEDF0kbED]7YQ8[ S/^ o.RQS ^ >Z 7R, H ,2Z/0 , DF7R,-[

3 9



²n@$´

´

 x·



s!#»x¼ 
»E´

†PCd:<&)(S?A>4C)9T:<3rG)?:I/ >4CS>LW:<&)(`§T?>D6B6>4C ¨X6>0-H(FPJ:r{ >Ø6x1
/PCZ1)99AGH6E*N:I/ >DC9E{ (3_(“6x1 -H(H½ >DC(“h"¤Ø/ 9
1 ?>4C)9T:17C:={&
/ ? &Ž-H(*(
C)-H9 >4C7F Ma>DC“:<&)( F / Œ4G
/ - 6(A:17F;6x1:T(3b/ 17FPJ'17C)- :…{ >K„6x17CNMŽ:T(3r69S/PC^:<&(
X
(C)(3_2Mo(NŒDG)1:I/ >DC Új(3rC)>4G7FOF /Q‰ 9u(Œ4G 1:I/ >4C„?A17CBR(UC)(A2DF (N?:T(N-+Q % CLy>K3Q:<GHC 1:T(F MNJ:<&('(’ 176U/PC)1:I/ >DCW>Lm:<&(
c)17F / -0/ :rMs>L:<&)(A9(B1)9q9G76B*:I/ >4C)9‡{i1)96U/ 99¦/PC)2[/PC=17FOF7:<&($*
3Q(Ac/ >DG9'9:<G)-0/ (A9 QN2(3_(HJ4:<&(BŒDG(N9T:I/ >DCB{&)(C
:<&(X§|?>D6B6>DC)¨6>0-H(F7c)17F / - >K3‡*(3r&)17*)9'{x&(A:<&(
3":<&(X§|?>D6B6>DCK‰m6>0-H(F7c)17F / -1:W17FOF4/ 9W(’ 176U/PC(- Q
! >46x($1
3_24G)(s:<& 1:(Ac(
Cd/ Li:<&)(S6>0-
(
Fj/ 9o{3_>4C)2S17C -Z-H>^C)>:o9T:17C -d>4C 9>DGHC -d9q?)/ (C:I/ ˆD? *3b/PC)?)/P*HF (N9NJ
/ : 9T:I/PFOF@&)1)91ac 17FOG(Ž/ Ls/ :S*3_>K-DG ?(A9d3_(N1)9q>4C 17RHF (d:<3_(C -H9 QV%'&)(3_(Ly>K3_(HJ‡:<&/ 9d6x>K-H(Fz9&)>4G7F - *3_>0-4G ?(
3Q(1)9>DC)17R7F ($3Q(N9G7F :T9W17C)- :<3Q(
C)-H9'{&)(CEc)1
3YM
/PC)217CNM*)1
3_176x(:T(3u/PCs>K35-
(
3":T>d&)1c)(E17CMBc 17FOG( Q#"D1
3Q:@>
L
:<&(U(’ 176U/PC)1:I/ >DCE/ 9W-H>4C)(=RMUc 13QM/PC)2d* 135176(:T(
3Q9'17C - ? &)(N?¡)/PC2s:T>$9(N({& 1:& 17*H*(
CU:T>s:<3_(C -H9 Q
$&%('&%*)

+-,/.0214357698:8;69<=>8?6&@A12B9C DEBGFH@9I

† 9z:<&)(6x1)9q9‡R 17F 17C ?(o3Q(17FOF M9q1:I/ 9ˆ4(N-E/PC':<&)(§|?A>46B6>DC)¨E6>0-H(F JLK (:T9u(<’176/PC)(;:<&/ 9@*>0/PCN: @
Q «0Œ4G 1:I/ >4C

Q 7„@9T:1:T(A9@:<& 1:i:<&)($6x1)9M
9 bc>DFOGH6(7JmGHC -H(3w?A>4C)9T:17C:‡-
(
C9</ :…M„xR 17F 17C)?A(B/ 9;(’
/ 9: Q

“ß ß

“ß5Q ƒH„
>¢Jj{x&)1:E/ 9:<&)($?A>4C -K/ :I/ >DC>4CSh ¤ :T>d9q1:I/ 9L5M:<&/ 9B?A>4C -K/ :I/ >DC 8hn17Cdh ¤ R(1S?>4C)9T:17C:o1)9U9:1:T(N/PC=1)9q9G76B*N:I/ >DC+‹ X%l> 9:<G)-
ME:<&
/ 9*>K/PC:xF (A:W-
(
3y/ c)(E17Cs(’7*
3Q(N99¦/ >DCBLy>K3zh ¤ Q %n:I/PF / /PC2 (Œ4G 1:I/ >4C “ß5Q ‹H„
 <    



!

NJ

OJ

P

M/ (
F -
9

  



*

 

<ß5Qf‹NŠH„


<ß5Qf‹„AJ¢/ :@?N17C R(U9&)>){C:<&)1:

kK3_>46V:<&)($6x1 ? &
/PC(U?&)1
3_1 ?:T(3b/ 9T:I/ ?HJK(NŒDG)1:I/ >DCQ

!





<ß5Qf‹-‹„

 

GHR)9T:I/ :<G:I/PC2=(NŒDG 1:I/ >4C
QB‹ ‹„'/PC:T>=(Œ4G 1:I/ >4C 5Qf‹NŠH„iM
/ (F -mJ

 <  
  
   
*




R




“ß





S

T

R

<ß5Qf‹NH„


<ß5Qf‹NH„@?N17C R(:<3_17C)9TLy>K3r6(N-[/PC:T>

† :'?A17C R(U9&)>){C:<& 1:@(Œ4G 1:I/ >4CT


¤





 


V

 *

K
F (
U

<ß5Qf‹  „






?>4*AMH3b/ 24&:ØÙ × J4
ŠHŠ
ŠDJ¢RM[g@3RQ'Ú"1
3P‚j}E( /P3

ێÜAÝ<Þ$ÜAÝ<ßAàáIâHã äUå‡àNåWæàNäPçIÜè™éSê7ãAàIç
ê)âHëAàiì_â ämáIâHãWÞ#âê ÝIáNíé î Ýïè Ýä5è çIå@í

"

XW

Section 7.3. The validity of the “common” diagram

f ?N?>K35-K/PC)2:T>S:<&)(
%'&)( :T(
3…6



V

§T?>D6B6>4C ¨Z6x>K-H(F



 (







J"17C -!




1
3Q([/PC -
(
*(C -
(
CN:x>L :<&)($2H1:T($13_(N10J

/ 9‡C)>:w1W?A>4C)9T:17C:n17C)-B/ 9z1;L|G7C)?:I/ >4C;>L







Q

*>
9q9¦/PR
/PF / :…M;>:<&)(3l* 135176(:T(
3Q9¦„





%l>d6x1
/PC:1
/PCU:<&($6o1)99R 17F 17C)?A(sh ¤ 6EG9:oR(B1EL|G7C)?:I/ >4Cs1:F (N1)9:‡>
L:<&)(U2H1:T(B1
3_(N10J  Q ! /PC)?A(:<&(
§|?A>46B6x>4C ¨X*+,\-0/ 1)2435176 1)9q9G76(A9E:<&)1:$h ¤ / 9=1“?A>4C)9T:17C:s/ :s-K/ 176x(:<3b/ ?A17FOF Md>4*7*>
9¦/ :T([:<&(^6x1)99
?>DC9q(3Qc)1:I/ >DCa*
3y/PC ?/P*7F
( Q~}E>K3_(A>
c(
3#Ji/PCd:<&)(`§T?>D6B6>4C ¨Ž6>0-H(FPJu1X6x1qp#>K3W1)99G76B*:I/ >4C“/ 9E:<& 1:U:<&(
c 17FOG(=>LWh ¤ -H(*(C -H9o>DC$:<&(6(:17FPJm:<&)(3_(Ly>K3_(HJj:<&(6x1)99sR 17F 17C)?A( / 9s*3_>4R 17RHF MdC)(c)(3i1 ? &
/ (c)(N-“/PC
6x17CMS?N1)9(A9 Q[%W&/ 9oc
/ >4F 1:I/ >4C[-H(6x>4C)9T:<351:T(A9NJw>4C ?(=Ly>K3;17FOFPJ":<& 1:x:<&)(]§|?A>46B6x>4C ¨^*
+, -0/ 1)2435176 / 9
(3r3_>4C)(A>4G)9Q

!#"
  '%$'&
,d1ˆ4 .3*/4?0kb8]fQ-73[M,/.30 Q/b%]7YQ8[ 4 T,-[?5A@k42pE^ %,-b Z%N<*/4<N %H#*T,/.J*-,O5/5d4<b/4<Z.RQ.3* 4-Q8H 7R,/.34 ,/. . HQ
@ Q N ,/.30 Q/bon
qsuDx,/.34s 5A@B;-bEDF4<7`.30 5Ts6HJ*/4<b2Z/0 1ˆNE*T,7BDd4MNˆQA4 LN<0k4Eb8.J0 1#q,7=0k4EZ 3:9+; S/^ PS/^
-fi 6'-"
;Tb/Z 4E7#NˆQ8b1E.37 ;-NO.30 Q8b












P

ß Q ‹¢½


k0/ 24G73Q(

ß
‹

ÛaÜAÝÞ ÜAÝ<ßAàáIâHã äå‡àNåWæàNäPçIÜè™éSê7ãAàIç
ê)â
ëAà@ì_â ä¢áIâHãWÞ#âê ÝIáNíé î ÝAï è Ýä_è ç|à<í






A1

   '
 

?A>4*M73b/ 24&:ØÙ × J0
Š
ŠHŠDJ¢RMg@3RQ;Ú"1
3P‚j}E( /P3

Q

Chapter 7. pQ2 Diagram Calculations

Pbar

ß5Q ,D½


kK/ 24G73_(
$&%('&%

 1:.01

A3


-4&    '
1  

. 1A<@A, 1 D2, 69<2DEB 1EI

e>){¿9(?>DC)-^*)1
3Q:AJj13_(E:<&)(B:<3_(C -H9E*3_(N-0/ ?<:T(-aRMs:<&)(ا|?>D6B6>DC)¨d6x>K-H(FD1
3_([3_(A9AGH6x17R7F ( …?>K3r3_(N?<:q„J
% >B(<’176/PC)(':<& 1:AJ{ ('c 1
3YMo:<&(E*HFOG7C)2
(3m-K/ 176(A:T(3|J  W>K3
l
„i17C)-B:<&(2H1:T(1
3Q(10J ':T>B9q(A(o/ Ln17CM
c/ >DF 1:I/ >4C>
Ll:<&(U*7&M9</ ?9;F 1A{‡9u>0?A?GH3_9i1)9;3_(A9G7F :T9Qz%W&(W?A>46B* 13b/ 9>DCUR(:r{ (A(
CW:<&(B3Q(17F:<3_(C -H9i17C)-U:<&(
§|?A>46B6>DC)¨E:<3_(C -
9/ 9W-0/ 9q? G)99q(N-/PCU:<&)(Ly>4FOF >){'/PC)2E9q(N?:I/ >4)
C Q




!#"$%&'(







kK/P3_9T:AJ
:<&((¬l(N?<:z>Lz*7FOGHC)2
(
3¢-0/ 176(:T(
3D9¦/ (Wc)1
3y/ 1:I/ >DCo/ 9 (<’176/PC)(N-+Qi†YCx9q(N?:I/ >4C 5Q E/ :{i1)9u9&)>){C':<& 1:
  (   Q'«0ŒDG)1:I/ >DT
C  5Q H„;-H(6x>4C)9T:<351:T(A9‡:<&)1
:
 U/PC ? 3_(N1)9q(A9@{'/ :<&E17C /PC)?3Q(1)9(>L

) Q
%'&)(Zc 17FOG(

?N17CX1:|:1
/PC)(N- / 917CØ/PCNˆjC
/ :T(Zc 17FOG( …1 ?A?A>K3_-0/PC)2X:T> :<&(°§|?A>46B6>DC)¨~6x>K-H(F „

:<&(
3Q(ALy>K3Q(
/ 9/PCNˆjC
/ :T( 1)9l{ (FOF Qw%'&)(u2H1:T(zc)(F >0?/ :rMNJ  J/PC)?3Q(1)9(A9"1)9":<&('*7FOG7C2H(3H-0/ 176(:T(
37-H(N?3Q(1)9(A9
1)9'9&)>){Cs/PCkK/ 2DGH3_( 5Q 5Qf;3r6(N- {'/ :<&U:<&
/ 9¡C>){xF (N-H2
(EC>){JH9q(c)(3517FK?N1)9(N9;?N17C R(U(<’176/PC)(N-/ Lw:<&(

“ß

T






ß ß

q… Å"ÃÌ Ä…É@ÊAËIÈzÉNÐIÄbÅrÎYÃÅyËÄ"ÅrƦÃqÅjÅrÆIË:<ÃÌ IËzÉJ
*

+

.

,/

,

ÐIË;:¦ËIÎ4ÍÃЇË-<ÍTËTËTÊ

> ' H B ( F

03254

,10325476 0325498:;#<9>@
= ?BA3C1D@E

?>4*AMH3b/ 24&:ØÙ × J4
ŠHŠ
ŠDJ¢RM[g@3RQ'Ú"1
3P‚@FE( /P3

ێÜAÝ<Þ$ÜAÝ<ßAàáIâHã äUå‡àNåWæàNäPçIÜè™éSê7ãAàIç
ê)âHëAàiì_â ämáIâHãWÞ#âê ÝIáNíé î Ýïè Ýä5è çIå@í

"ð

Section 7.3. The validity of the “common” diagram

P1

Q


1
2

∼ DP

2

DP

1



DP
P1
u3

Q

D1

kK/ 2DGH3_(5Q D½ 66 i 6
1 _i"#-  
 6  
1 6  
"  6#-

 G'   
-

Yi" G " 
/_i"#- 3
$G 6  
:<3_(C -
9W1
3Q(=3_(N17F / 9:I/ ?KQ




 



$ 

"$ 5&(7

 

   

  

 

 
(7 5"5&(7
(




 


$ 
% 55
K (:A‰ 9 1)99AGH6x(‡:<& 1:@6x1)99u?>D
C &
9(
3Yc 1:I/ >4Ca/ 9=L|G7F ˆjFOF (N-mJ 17C)-mJ'&)(C ?(S:<&)(^*7FOG7C2H(3'c)(F >0?/ :rM“?A17C^17*7*3Q>71 ? &^/PCNˆjC
/ :rMNJ

{&)(C

TG7C)-H(3;?>DC9:17CN:
   „ QS%'&)(S&NM -D3_17G7F / ?S*/ 9:T>4C17F 9q>Ž&)1)9:T>X6>
c(${W/ :<&:<&)( 9q176($c)(G&
F >0?/ :rMNJ Q l(:AJl1 ?A?A>K3_-0/PC)2 :T>:<&)(6x1 ?&/PC)(E?&)1
3_1 ?:T(3b/ 9T:I/ ?B:<&(=-43b/ c/PC)2“*
3Q(N99G73_(HJl17*H*
3Q>71 ? &)(A9W(
3Q>



Qw%W&(
3Q(ALy>K3Q(7J :<&)(@(
C(
3Q2
M9G7*7*HF M':T>:<&)(;9TM)9T:T(6¿/ 9 17*7*3_>H1 ? &
/PC)2x(
3Q+> Q l(:AJ
(C)(3_2M
>4R:1
/PC)(N-L|3Q>D6¾:<&)($9TM)9T:T(
6‘/ 9E/PCNˆjC
/ :T(=9¦/PC ?(pr(:B/ 9U/PCqpr(?<:B/PCS/PCNˆjC
/ :T(Bc)(F >0?/ :rM[17C -[ˆjC
/ :T
( 4>){¾351:T
( Q
%'&
/ 9'?A17C7C>
:i(<’H/ 9T:/PCB>4G73"{ >K3rF -=>K3u*(3r&)17*)9'>4C)(U?A17C *3_>K>L:<&(>4*7*>
9</ :T( Q



%!

& \



v

 
 (' ! v

) 



"!$#



*+  ,  

 
(7 5"5&(7
(




fu99G76/PC)2:<& 1:W:<&)(6x1)9q9ER 17F 17C)?A(3_(NŒDG/P3_(6x(C:/ 9x>DR &
:1
/PC)(N-mJ":<&)(“*3_(A9q9G73Q(1:=*7FOG7C2H(3 :I/P*0J
17C)-^2H1:T( c)(F >0?/ :rMNJ  Ji/PC)?3Q(1)9( …17C -Ž?A17C^3_(N1 ?&Z/PCˆjC&
/ :rMNJ b{&)(C

:<&)(C 
]„s{&)(Cd:<&(Ž*7FOGHC)2
(
3W-K/ 176(A:T(3o/ 9S3_(N-DG)?A(N-+Q¥%'&)(3_(Ly>K3_(HJ :<&(
(C)(3_2Mo9G7*H*7F MW:T>:<&)('9TM)9T:T(
6°&)1)9z:T>$R(o/PCˆjC
/ :…M r1)99G76/PC)2B1?>4C)9T:17C:w(
C(
3Q2
Mo-0/ 99</P*)1:I/ >DCKJ 1 ?:<G)17FOF M
:<&)(-0/ 99</P*)1:I/ >DCB/PC ? 3_(N1)9q(A9‡{'/ :<&$*7FOGHC)2
(
3j-0/ 176(A:T(3/PC$6>
9:W3517C2H(A9I„ 2>){ (c)(3|JH:<&(o(C)(3_2MB9AGH*7*7F Mo:T>
:<&)(s9M9:T(6 rK
? Q
c Q>DCHF M=:<&([F / Œ4G
/ -^6(:17F „9TM)9T:T(
68{ >4G7F -“R(

TyˆjC
/ :T(=176x>4G7CN:q„17C)-[:<&(
(C)(3_2ME:<&(9TM)9T:T(
6¾*
3Q>
c/ -H(=*HFOG)9;{ >4G7F -R(s/PCNˆjC
/ :…T
M |/PCNˆjC
/ :T(2H1:T(oc(
F >0?/ :rM „*7FOG9W-0/ 99</P*)1:I/ >D
C Q

!-#



!-#



  



1 

2 3 4

5 6 

 
(7 5"'(7
7
 1'(7
%( 
1
f‘-K/ ¬l(3_(C:${i1M^:T> F >7>D¡“1:s:<&
/ 99¦/ :<G 1:I/ >4CŽ/ 9
? &)(N?¡W{& 1:W& 17*H*(
C:T>[*7&NM)9¦/ ?N17F
Œ4G 17C:I/ :I/ (A9Q‡k >K3j(<’176B*7F (HJH:<&(s3_(A9¦/ 9:17C)?A(:T>E:<&(sF / ŒDG/ -6(A:17F 4>){
/PC ? 3_(N1)9(N9E{x&(
C:<&)(S2H1:T(c(
F >K?)/ :…MSc)(F >0?/ :rMa/ 9 /PC ? 3_(N1)9q(N+
- QXfu9s9A6x17FOF (3;:<&)(^*7FOGHC)2
(
3;-0/ 176(A:T(3;:<&(



ÛaÜAÝÞ ÜAÝ<ßAàáIâHã äå‡àNåWæàNäPçIÜè™éSê7ãAàIç
ê)â
ëAà@ì_â ä¢áIâHãWÞ#âê ÝIáNíé î ÝAï è Ýä_è ç|à<í

?A>4*M73b/ 24&:ØÙ × J0
Š
ŠHŠDJ¢RMg@3RQ;Ú"1
3P‚@FE( /P3

&&

& ' /& . & 0

š I— ”I—  P”O˜ š › _<› • ” ž —P•  Y˜
š A 5› ˜ ˜ › k™—Pš › QI—Q™  O”PŸ QœP› š

Chapter 7. pQ2 Diagram Calculations

P1
2

ρ Qmax
2

2

2 A 3 CD

5Q D½

?
PYi" G " 

 

Pmax

kK/ 2DGH3_(

F 13_2
(
34:<&)(W2H1:T(@c)(F >0?/ :rMx17C -U:<&)(F 13_2
(
34:<&(3_(A9</ 9T:17C ?( QA2>){ (c)(3|J):<&)(W(C)(3_2Mx9G7*H*7F MW:T>:<&)('9TM)9T:T(6
&)1)9W16x1N’H/P6BGH6817R
/PF / :…M Q 2(
C)?A(HJ7:<&
/ 9‡:<3_(C -$L|3_>46©:<&
/ 9x3_(A9A*(N?:W/ 9oG7CH3_(N17F / 9:I/ ?KQ

3, 






$(7 5"'(7
55  
f ?N?>K35-K/PC)2U:T>U:<&)(d§T?>46E6>4C ¨=6>0-
(
FPJ :<&)(271:T('c(
F >0?/ :rM-H(N?3Q(1)9(A9
{&)(CU:<&)(E*7FOG7C2H(3"-K/ 176x(:T(3/PC ? 3_(N1)9q(A9 Quh">4Cc)(3_9(F MJ7:<&(o2H1:T(oc)(F >0?/ :rMs/PC)?3Q(1)9(A9‡{&)(C:<&)(=*HFOG7C2H(3
-K/ 176x(:T(30-H(N? 3_(N1)9q(A9 AQ"f ?A?A>K3_-0/PC)2':T>(Œ4G 1:I/ >4C# 5Q H„j:<&(F / Œ4G
/ -U6(A:17F 4>){ 3_1:T(;1:j:<&)(i2H1:T(;/PC)?3Q(1)9(A9
1)9'{ (FOF Q2>){ (c)(3|J41 ?N?>K35-K/PC)2$:T>$:<&(X§|?>D6B6>DC)¨*
+ , -0/ 1)2435176sJ0:<&)( *7FOGHC)2
(
3w?A17C6>c)(B>4C7F M$/PC$1
  ª LQ%W&(
3Q(ALy>K3Q(7JH:<&( 4>){ 351:T(o1:i:<&(s*HFOG7C)2
(3l:I/P*
ˆjC/ :T(xc)(F >0?/ :rMsF (A:T9‡9I1Ms/PC:<&)(x(’:<3_(6(?A1)9q(
-
(? 3_(N1)9q(A9 QUhuF (N1
3…F MNJm:<&)(A9q(s-0/ 176(:<3b/ ?A17FOF M$>4*7*>
9</PC2:<3Q(
C)-H9x?N17CHC)>:?A>7(’
/ 9: Qs«D/ :<&)(3:<&)(X§|?A>46B6x>4C ¨
*+,.-0/ 1)2435176¿{x3Q>DC2$>K3j:<&)($6x1)99oR 17F 17C)?A(U?>4C ?(
*N:'/ 9;{3_>4C)2¢JH:17¡<(xMN>4G73 */ ?¡ Q



3  

+

  


$(7 5"'(7
  
&
 7
\%'&)('6x1)9q9 R 17F 17C)?A(‡17F 9q>U&)1)9n:T>(’
/ 9:/PCx&M)-D3517GHF / ?*HG76B*
b>DRNc
/ >4G)9F M„ QE† Lu:<&)(*7FOGHC)2
(
3nc)(F >0?/ :rMS&)1c)(B:T>^R($/PCˆjC/ :T(U:T>“6x1
/PCN:1
/PC6x1)99ER)17F 17C ?($/PCs:<&)(6(A:17F
9¦/ -H(HJH:<&)(B6x1)9q9 4>){`351:T(o1:u:<&)(B&M)-D3517GHF / ?9¦/ -H(>Lj:<&)(B3_>0-
(17F 9>&)1c)(W:T>[R(U/PCˆjC/ :T( QA2>){ (Ac(
3#J:<&(
š k Pš0š —!QŸ ” › š –" _› b”P• ”P™š *HG76B*& 1)9o6x1N’H/P6BGH6°?A17* 1 ?/ :rMULy>K3 4>){V3_1:T( Q?2(C ?(HJm6o1)99oR)17F 17C ?(U?N17CR(U>4R:1
/PC(- Q
š • ”PP Q˜N—™˜—
Q™œOš › Q
 
—YP I— !P” › š –<—
ž Q• ” 


& '

0 ' & $'&

$&%('&%('

TD

 FGD . FG69<,

6T.021TD . 1

D

 1 D

GHC -H(3w?A>4C)9T:<3rG)?:I/ >4C
|ÍIƦËTÍIÖ@6
à 5Ã<Ç 
Ð NÇ 5 +AÎ™Ë ' H (
Â|ÅrÆ<Ç ÄÇ ÄlÅrÆIË:¦ËIÌ ÉNÍqÇ ÅK@ÃqÅ5ÅbÃ<Ç ÐIËÊ?8"ƦËIЇÅrÆIË Ä|ÆIɦÅ"Ä#Ì ËTË;:¦ËiÇ ÄjËIÈASqÅK

?>4*AMH3b/ 24&:ØÙ × J4
ŠHŠ
ŠDJ¢RM[g@3RQ'Ú"1
3P‚@FE( /P3

ێÜAÝ<Þ$ÜAÝ<ßAàáIâHã äUå‡àNåWæàNäPçIÜè™éSê7ãAàIç
ê)âHëAàiì_â ämáIâHãWÞ#âê ÝIáNíé î Ýïè Ýä5è çIå@í

"ñ

Section 7.4. The reformed pQ2 diagram



®8¯o±


± 
 U0´¶±W

¸=º

=!#»¼
»B´

%'&)($6(A:<&>0-SR 1)9(N->4CB:<&)($F / Œ4G
/ -S6(A:17F¢*3_>4*(
3Y:I/ (N9x/ 9;{'/ :<&E-0/ 9q1)2D3Q(N(6(
CN:@{'/ :<&E?A>46B6>DCHF ME1)2D3Q(N(N> CŽ/PCjG
/ -~6(? & 17C/ ?A9P"D1)> ƒ, 7J;*7*Q   ‹1&|
ƒHƒH„ Q † :/ 9 ?>46E6>4C7F M^1)243_(A(-Ž:<&)1:h"¤]/ 9 1“L|GHC ?7&
4
:I/ >4C>
Lm(M7C)>4F -H9EC7GH6ER(3i17C -S:<&($2
(N>46(A:<3YM>
Li:<&)(S3…G7CHC)(3@-
(N9¦/ 24C)Q=%'&)(=17G:<&>K3 qÚ"13&5FE( /P3i17C)¥/PCH¡F (
3 ƒ
ƒ
€7„@9G)2
2H(A9:T(N- 1 -H>4*:I/PC217C 17*H*
3Q>71 ? &B{x&(
3Q(E:<&(=h ¤ / 9o?A17F ?GHF 1:T(-dRMSGN:I/PF / /PC)2-71:1s>
L
4>){°3_(A9¦/ 9:17C)?A(B>Luc 1
3y/ >DG9U* 1
3Y:T9 …9(N246(
CN:T9¦„;>Lu:<&)( 3rGHC7C(
3 Qx%'&)(E1c 1
/PF 17RHF (E-71:1/PCE:<&)(F / :T(
3_1:<G73Q(
-H(6>DC9:<3_1:T(N9z:<&)1: 1x:…M7*
/ ?A17F)c)17FOG)(W>
Lnh ¤ ?A17Co?&)17C)2
(W1)9W6BG)?&o1)9 Š
Š ©>K3n6x>K3Q(pIG9:@RAM?&)17C)2K/PC)2
:<&)(s271:T(=1
3Q(1 F /P¡¦(Ec)17F c)($>4*(
C/PC)27„ QB%'&7G9Jm:<&($1)99AGH6E*N:I/ >DC$>
L‡1[?A>4C)9T:17C:oh ¤ Jl{x&/ ?&[/ 9sG)9(N-“/PC
§|?A>46B6x>4C ¨$*+, ?A17F ?GHF 1:I/ >DC9<ªTªJD/ 9xC)>: c 17F / - Q?2(
3Q(1B9M9:T(6x1:I/ ?o-
(
3y/ c 1:I/ >4CU>
L":<&(=*
+W, -0/ 1)2435176
/ 9u2K/ c)()
C Q%'&)(;17*7*3_>H1 ?&x1 -H17*:T(N-E/PC:<&/ 9;R>K>4¡/ 9z:<& 1:(Ac(
3YM:<&/PC)T
2 #/ Lz*>H99¦/PR7F („w9A&>DGHF -=R(U*
3Q(N9(C:T(N/PCE-0/P6(C)9¦/ >DCHF (N99‡Ly>K3…6 Q

x‹ A‹



$&%





%*)



8?6&@A12B

5Q „@?A17C[R(:<3_17C)9TLy>K3r6(N-[/PC:T> -K/P6x(C)9¦/ >4C7F (A9q9

«0ŒDG)1:I/ >DCQ




 1  68

021

R

5Q N‹7„








3Q(-4G ?(-S*3Q(N99AGH3_(HJ

3Q(-4G ?(
- 4>){¿351:T(HJ 








]&)(3_(H½



L|3_>4681)9

‹



«0? ¡<(
3YM
: q«0?¡¦(
3Y: ƒ
HƒH„@17F 9>[-H(6x>4C)9T:<351:T(N-$:<& 1:;:<&(s24351c/ :rMs(A¬m(?<:T91
3Q([C(N24F / 20/PRHF ( ª , Q'fu9q9G76/PC)2
9T:T(1 -Mo9T:1:T( ª 0‡17C - G:I/PF / /PC)2 Új(3rC>DGHFOF /Q‰ 9u(NŒDG 1:I/ >4CBR(A:…{ (N(CB*>0/PCN:  )„z>4CE*HFOG7C2H(3¢:I/P*o17C -$*>K/PC:   „
1:@:<&(2H1:T(U1
3Q(1S…9(A( k0/ 24G73Q( Q )„ M
/ (F -H9



*

{   







*

‹



{    {










5Q ,7„

{&)(3_(H½



*



c(
F >K?)/ :…MB>
Ln:<&)($F / Œ4G
/ -S6(A:17F
:<&(=F / ŒDG/ -S6(A:17F7-H(C)9¦/ :rM
(C)(3_2M F >
9q9oR(:r{ (A(C$*7FOGHC)2
(
3j:I/P*s17C -$2H1:T((<’H/ :



9G7R)9q? 3b/P*:

‹

*HFOG7C2H(3j:I/P*
(C:<3_17C ?(o:T>S3…G7C7C(
3n9TM)9T:T(
6
2H1:T(





† :W&)1)9xR(A(
CB9&)>){Co:<&)1:i:<&(s*3_(A99AGH3_(B/PCo:<&)(U?A1c
/ :…MB?N17C=R(U1)9q9G76(N-E:T>[R(U17R>DGN:‡1:<6x>
9*7&)(3b/ ?
yLy>K3n1
/P3jc)(C:I/PC)2E>K3jc 1 ? G7GH6¿c(
CN:I/PC)27„W*3_>c
/ -K/PC)2Ec)(C:T9;13_(=*3Q>D*(3rF MB-
(N9¦/ 24C)(N-SÚ"1
3P‚@FE( /P3"1:i(F7Ú"1
3'&
Fs()/P3|J «0? ¡<(3Q:o17C -
w>4F -H9T:T( /PC ƒ
ƒ-,DÚ"13&5FE( /P3#J‡«0? ¡<(3Q:x17C -
w>4F -H9T:T()/PC NƒHƒ 7„qª Q=%W&/ 91)99AGH6E*N:I/ >DC[/ 9







†…f…

ÂyÂ#ÉÎDÃqÄnÇ ÅnÇ Ä"Ä +6575<ËTÄyÅyËÊÏKiÅrÆIˇÎPË;JQËIÎPËTË
Â4TąËT/
Ë JYÉÎmÈzÉΙËzÊËTÅbÃ¦Ç Ì ÄwÍIƦÃGSqÅyËIÎ E
ÂQIÎPËÃIÊÇ ÐiÅrÆIË ÄbËÍ|Å…Ç ÉN
Ð ' H (1H (;ÉNÐiÅrÆIË ÅrÎPÃÐIÄ#Ç Å…Ç ÉNÐ3S<˦ÎYÇ ÉAÊWÉJDÅrÆIËAS
  ËÃIÊWÃ@ÈzÉÎPËuÊË|ÅbÃ<Ç Ì ËTÊWÊNÇ Äb!Í +¦ÄbÄrÇ ÉNÐ'Ç Ð;Ô4Æ<7à SIÅyËIÎ C

‚

ƒ

ÛaÜAÝÞ ÜAÝ<ßAàáIâHã äå‡àNåWæàNäPçIÜè™éSê7ãAàIç
ê)â
ëAà@ì_â ä¢áIâHãWÞ#âê ÝIáNíé î ÝAï è Ýä_è ç|à<í

ˆ‡



3

,

?A>4*M73b/ 24&:ØÙ × J0
Š
ŠHŠDJ¢RMg@3RQ;Ú"1
3P‚@FE( /P3

Chapter 7. pQ2 Diagram Calculations

C>
:ic 17F / -={&)(CU:<&)(oc(
CN:T9'1
3Q(=*>K>K3…F ME-H(A9</ 24C)(N+
- Q ]&)(CU:<&)(Ms1
3_(s*>K>K3rF ME-
(N9¦/ 2DC(-¢JH:<&)(s351:I/ >$>Lw:<&(
c(
CN:13_(N1 :T>d?3y/ :I/ ?N17F4c)(C:x13_(N1-
(A:T(3r6/PC)(A9x:<&(RHG
/PF -aGH*Z*
3Q(N99G73_(HJ
 Jm{x&/ ?& ?N17CZR(=?N17F ? G7F 1:T(N1)9U/ :U/ 9o-H>4C)($/PCZÚ"1
3P@
‚ FE( /P3(A:x17F Ú"1
3 & Fs()/P3|Ju«0? ¡<(3Q:17C -
w>DF -
9:T()/PC NƒHƒ H„ QP2>){ (Ac(
3#J¢:<&
/ 9/ 9sC>
:1
-
(N9¦/P3517RHF ($9</ :<G)1:I/ >DC9¦/PC ?( 1?A>4C)9¦/ -H(3517RHF (=2H1)9<Á 1
/P3'*>K3_>
9</ :…MS/ 9U? 3_(N1:T(-“17C -d9&)>4G7F -ŽR(1c>0/ -
(- QS† :
17F 9>[&)1)9R(A(C9&)>){Cx:<&)1:u:<&)(x?&(
6/ ?A17FK3_(N1 ?:I/ >4C)9‡-H>C)>:;*HF 1AMU1U9¦/ 2DC/ ˆD?N17CN:@3Q>DF (x-DGH3b/PC)2B:<&)(WˆjFOF /PC)2
>L:<&(U?N1c/ :rMs17C - ?A17CR(=C)(A24F (?<:T(- Ú"1
'3 &5FE( /P3 ƒ
ƒH‹0R„ Q
%'&)(d3Q(N9¦/ 9:17C)?A(S/PC[:<&)(Z6>DF -d:T> F / ŒDG/ -X6x(:17F 4>){v-
(
*(C -
9U>DC[:<&)(2
(N>46(A:<3YMS>L;:<&)(Z*)1
3Q:o:T>
R(d*3_>K-DG ?(N+
- Qd† L‡:<&
/ 9$3Q(N9¦/ 9:17C)?A(/ 9U9</ 24C
/ ˆD?A17C:AJn/ :s& 1)9o:T>ŽR($:17¡¦(
CS/PCN:T>Z1 ?N?>4G7C:o?A17F ?GHF 1:I/PC)2:<&(
:T>:17Fm3Q(N9¦/ 9:17C)?A(B/PCE:<&($3rGHC7C)(R3 QW†YC[6x17CME2
(N>46(A:<3y/ (N9NJ7:<&)($F / Œ4G
/ -d6(A:17F¢* 1:<&=/PCB:<&)($6>4F -S/ 9'9&)>K3Y:AJ
:<&(
CW:<&)(3Q(N9¦/ 9T:17C ?(x/ 9‡/PC)9¦/ 2DC/ ˆD?N17CN:?>46E*)1
3Q(-:T>o:<&(B3Q(N9¦/ 9T:17C ?(/PCW:<&)(3rGHC7C(
3m17C -B?A17CER(o/ 24C)>K3Q(- Q
2(C ?(HJ7:<&)($*3_(A9q9G73Q(U1:@:<&(2H1:T(7J
 J4?N17C R($C(N24F (N?:T(N+- Qw%W&HG)9NJK(Œ4G 1:I/ >4S
C  5Q ,7„;/ 9o3_(N-DG)?A(N-=:T>







{        {



*







5Q (H„




%'&)((C)(3_2M F >
9q9NJ HJ4?A17C R(U(’7*
3Q(N99(-[/PCU:T(3r69'>L:<&)(o271:T(oc(
F >K?)/ :…ME1)9

| ~   

 



|+~



5Q NH„


{&)(3_(
/ 9:<&( 3_(A9</ 9T:17C ?(E?A>K(£ ?/ (C:AJj3_(*
3Q(N9(C:I/PC)2[1=9*(N?)/ ˆD?$3rGHC7C(
3z-H(A9</ 24C$17C)-[9*(N?)/ ˆD?U2H1:T(
13_(N1)Q
hj>D6BR
/PC/PC)2s(Œ4G 1:I/ >4C)9  5Q H„AJ  Q H„‡17C)-  5Q N7„@17C)-S3_(N1
3…3517C)2K/PC)2sM
/ (F -H9



  

B‹/

 

*





5Q NƒH„


{&)(3_(


 &  9 '   
    {}| ~
hj>DCNc)(3Q:I/PC)2=(Œ4G 1:I/ >4C 5QfN‹ ƒ7„;/PC:T>$1s-0/P6(C)9¦/ >DCHF (N99‡Ly>K3…6VM
/ (F -H9
 


 


¤



<



5Q 
ŠH„



5Q 



5Q 
H„

 D

S

A‹„

R

]&)(CE:<&(s@A(3‡e‡G76BR(3/ 9W-H(ˆjC)(N-$1)9
  G
F
     
 



*
 
 
  
<






D



%'&)(9¦/ 24C
/ ˆD?A17C ?(o>L:<&)(B;$CHG76BR(3u/ 9‡:<& 1:@:<&/ 9/ 9@:<&($351:I/ >$>L:<&(a§|(¬l(N?:I/ c(¨[6o1N’
/P6BG76©(C)(3_2M
>L:<&(=&M)-D3_>
9T:1:I/ ?s*3_(A9q9G73Q(:T>=:<&)(=6x1N’
/P6EGH6 ¡)/PC)(:I/ ?x(C)(3_2MQ'e>
:T(x:<& 1:i:<&)(s@(
3 C7GH6BR(
3z/ 9oC>
:
1* 1
3_176(A:T(3j:<& 1:;?N17C R(B?A17F ?GHF 1:T(- 1 *3b/ >K3y/09¦/PC ?(o:<&)(Bh ¤ / 9@c 13QM/PC)2${'/ :<&U:<&)(>4*(
3_1:I/ >DC *>K/PC: Q
ª k >K3@*3_1 ?:I/ ?A17Fl3_(N1)9>DC9W:<&(s2H1:T(s1
3_(N10J =?A17C7C>
:oR(s(<’):<3Q(
6(F MdF 1
3Q2H
( QxCs:<&)(E>
:<&(
3‡& 17C -¢J
:<&(d271:T(S1
3Q(1^?N17C R(a3_(F 1:I/ c)(F M“9A6x17FOF

/PCZ:<&
/ 9$?A1)9(^@A(3UC7GH6BR(
3
  {x&(
3Q(^/ 9$1
„Q
CHG76BR(
3 F 13_2
(
3j:<&(
Cs 



…


  v

  



Â# j
Å Ä#Æ¦É + Ì ÊoÏˇÈuæΠ5AÇ Ð …ÐIɦÅyËiÃÐIÊ'ąÉNSÌ ËÃIąËiÇ 5NÐIÉÎPËuÅrÆ<Ç ÄJYÉAɦÅrЦɦÅyËGH
?>4*AMH3b/ 24&:ØÙ × J4
ŠHŠ
ŠDJ¢RM[g@3RQ'Ú"1
3P‚@FE( /P3

ێÜAÝ<Þ$ÜAÝ<ßAàáIâHã äUå‡àNåWæàNäPçIÜè™éSê7ãAàIç
ê)âHëAàiì_â ämáIâHãWÞ#âê ÝIáNíé î Ýïè Ýä5è çIå@í

ñ$#

Section 7.4. The reformed pQ2 diagram
!

M
/ (F -H9

x‹„‡{W/ :<& BQ ‹‹H„‡Ly>K3



>DF c/PC)2$(NŒDG)1:I/ >DC9M


a{ 






J¢17C)- :17¡)/PC2$>DCHF Ms:<&($*>H99¦/PR7F ($*7&NM)9¦/ ?N17F79q>4FOG:I/ >4C0J






{&
/ ? &=/ 9@:<&(U-0/P6(C)9¦/ >DCHF (N99‡Ly>K3…6°>
Lw(NŒDG 1:I/ >4CS
$&%



%



DA8

F <F <

5Q  


.021

, 6

„

Q 7„ Q



B 2. FG69<

%'&
/ 9o9>4FOG:I/ >4Cd*3_>c
/ -H($1“*>){ (3QL|GHFD:T>7>DFD:T>S(<’176/PC)(sc 1
3y/ >DG9=* 135176(:T(
3Q9U17C -S:<&( /P3 (¬l(N?:T9o>DC :<&(
-H(A9¦/ 2D
C Q%'&)(o/P6B*>K3Q:17C:Lb1 ?:T>K3Q9i:<&)1: (Ac(
3YM(C)2K/PC)(A(
3n& 1)9 :T>UˆjC -UL|3_>46¿:<&(N9(?N17F ? G7F 1:I/ >4C)9 13_(H½271:T(
1
3Q(10Jz*HFOG7C)2
(3 -0/ 176(:T(
3Q9Jl:<&)(6o1 ? &
/PC($9¦/ A(HJj17C -Ž6x1 ? &
/PC(S*(
3YLy>K3r6x17C ?($(:? ª%
Q=%W&(N9(/ 99AG(N9o1
3Q(
(<’K*7F >K3Q(-=L|GH3Q:<&(
3z/PCB:<&)(oLy>4FOF >){'/PC)2=9(N?:I/ >4C)9 Q

 1

 

$ 


 +
 

1:T([1
3Q(11¬l(N?:T9:<&(d3_(N-DG ?(N- *3Q(N99AGH3_(HJ
J/PC:…{ >S{i1AM9½oc/ 1[:<&(d@(3xCHG76BR(
3 {&
/ ? &d/PC ? FOG -H(
:r{ >B:T(3r69½w>DC(7J
    17C -¢JH:r{ >¢J7-K/ 9I? & 13_2
(o?>K(£ ?/ (
CN:  #Qz%'&)(x-0/ 9q?&)1
3_2
(x?A>K(£ ?/ (C:AJ0h ¤
/ 9'17F 9>=1¬m(?<:T(N-SRAMU:<&(2H1:T(1
3Q(1B1¬m(?<:T9@:<&73Q>DG2D&o:r{ >$-K/ ¬l(3_(C:i:T(
3…69W/PCU:<&)(-H(ˆjC
/ :I/ >4CQb(Œ4G 1:I/ >4C
5Q 
Š7„JK>DC(7J   17C)-=:r{ >SRM
Q

&



ˆ

&



'

|+~

'

 
 / 917FO6>H9T:/PCNc 1
3y/ 17C:;{'/ :<&[3_(A9A*(N?:@:T>:<&(B271:T(B13_(N1G7*E:T>9A6x17FOF02H1:T(B1
3Q(1=9¦/ (N9¦ª%AQ
2(C ? (o:<&
/ 9x* 1
3Y:/ 9;9>46x({& 1:‡?F (N1
3w17C)-SC)> -K/ 9I? G)99</ >4Cs/ 9oC(N(N-+Q
Yk ”P• –P—9kP˜uš & k'™šz 5› ˜ œ'P˜ ˜ › &Q
Yk ”PP _›  &Qjš –™”l• ”O—™ Q”P• ˜D• ”
˜ k &QP˜ ” ž
&  O ˆ '  
  (:T9^F >K>4¡“1:[1:$:<&(^-H(ˆjC
/ :I/ >4Ca>L=h"¤](Œ4G 1:I/ >4C 5Q 
Š7„ Q k >K3U/PFOFOG)9T:<351:I/ >4C
*7GH3r*>
9q(A9ZF (A:[1)99G76(Z:<& 1: | ~ / 9ZC)>:1ŽL|G7C)?:I/ >4Ca>
LU2H1:T(^1
3Q(10J | ~ &  
Q f 9A6x17FOF
'  
 € °


K



*(3Q:<G73…R 1:I/ >4CB>
Lw:<&)(2H1:T(U13_(N1[3_(A9G7F :T9/PCE%j1M7F >K3"9(
3y/ (N9NJ

 






¤
V



&  
{ 



   G
G

{ | ~





&  '

 '  

{



  





  G

{

G


 G < (  GG  
  < ( GG D
 
    G {}| ~
G








D









V

{


{ |+~

 <    G
G

D

G











5Q €K„

{ &    ' 



ÆIÉ8!"TËIÎmÐ'+ȇÏ<ËIÎmÏËIƦÃ:IËÄwÃIÄ"Ã

J+ÐIÍ|Å…Ç ÉNÐ@ÉJ0ÅrÆIË 5ÃqÅyËiæÎPËÃ$#

%'&

, 0

254

A3C

()+*-,, /.
: =
E
E103254
 & I"ÆIËBÈuÃIÍIÆ<Ç ÐIËoÄrÇ "ËxÃÌ Ä…É$Ì Ç È Ç ÅyËTÊ$ÏKBÃÄbËTÍÉNÐIÊ S¦ÃIÎYÃÈzËTÅyËIÎ Ö¦ÐIÉ"
8 ÐsÃIÄiÅrƦËoÍ¦Ì ÃÈ9S<Ç Ð65 JQÉ<ÎPÍTËTÄ@ÅyÉ Ï<ËoÊNÇ Ä…Í!+IąÄbËTÊ[Ç Ð
Ô4ƦÃGSqÅyËIÎ B76
 * I"Æ<Ç ÄwÇ ÄwÎPËÃIÄbÉNÐ<Ã<ÏAÌ ËiÄ;S<ËÍ!+Ì ÃqÅ…Ç ÉNÐ'ÃÏ<É +IÅjÅrÆ<Ç Ä SÉAÇ ÐIÅH ƒiÉÎPËuÄyÅ +IÊG'
K Ç Ä D8 ËIÌ Ì)ÍTÉNÈzË
8

032 4






ÛaÜAÝÞ ÜAÝ<ßAàáIâHã äå‡àNåWæàNäPçIÜè™éSê7ãAàIç
ê)â
ëAà@ì_â ä¢áIâHãWÞ#âê ÝIáNíé î ÝAï è Ýä_è ç|à<í

?A>4*M73b/ 24&:ØÙ × J0
Š
ŠHŠDJ¢RMg@3RQ;Ú"1
3P‚@FE( /P3




Chapter 7. pQ2 Diagram Calculations

†YCB:<&
/ 9'?A1)9((Œ4G 1:I/ >4CS

5Q H„‡9T:I/PFOF¢&>DF -SRHG:'h

¤ & 1)9‡:T>SR($3_(A(Ac)17FOG 1:T(N-+Q

!#"
$>$&
73495d4 ,/.a.3*/4M4 -,-[ 5x@k4+pE^ oH#0B.3* |+~  & w &
_i 6'-"
x0k71E. N ,-@kNO;-@ ,/.34L.3* 4MZ/0 1ˆNE*T,7BDd4MNˆQA4 LN<0k4Eb8.3e3:9]fQ-7 q ,7=0 QA;E1`DA,/.34 ,7=4 ,1E.R,7P.30kbEDl]7RQ/[ x ^ Ov)( M
U   X?.RQ6r O)v ( U   X ;O1ˆ0kbED
4<m ;,/.30 Q8bpE^  S ^
%'&
/ 9j(<’176B*7F (i-
(
6>4C)9T:<351:T(u:<&)(uc)(3QMoF /P6U/ :T(N-x/P6B*>K3Q:17C ?( >
L7:<&)(@/PC ? FOG)9¦/ >DCi>L0:<&)(u:T(3r6 &     
'












/PCN:T>=:<&)(B?A17F ?GHF 1:I/ >DC9

|+~

Q

 +



%'&)(^? & 17C)2
(Ž/PCa:<&(a2H1:T(^1
3Q(1Ø/PC)?3Q(1)9(A9:<&(¥3Q(N9¦/ 9T:17C ?(“:T> :<&( 4>){ c/ 1Ž9q(c)(3517F
? >DCN:<3b/PRHG:I/PC)2xLb1 ?:T>K3Q9{x&/ ?&o/PC)?FOG)-H(H½":<&(W?&)17C)2
(/PCW:<&)( 4>){ ?3Q>H99z9(?<:I/ >DCKJ?&)17C)2
(/PC':<&)(W-K/P3_(N?:I/ >4C
>L:<&( 4>){JHL|3y/ ?:I/ >4C 17FDF >
9q9'-4G)(o:T> 4>){]:<&73Q>DG2D&U:<&(271:T(sF (
C2
:<&KJ017C -$:<&)(=F >
99'-DG(:T>=:<&)(B17R3rGH*:
(<’K*)17C)9¦/ >DCd1L5:T(
3;:<&(2H1:T
( QŽ%'&)(“F >H99E-DG)([:T>^:<&(S17R3…G7*:B(<’K*)17C)9¦/ >DCZ/ 9$1Ž6x1qpr>K3'?>DCN:<3b/PRHG:T>K3'17C)/ :T9Ec 17FOG)(? & 17C)2
(A9s-4G73y/PC)2“:<&)(ˆjFOF /PC2 *
3Q>0?(N99 Qa%W&(^F / Œ4G
/ -Ø6x(:17F"(C:T(3_9B:<&)(a6>4F -Ž?A1c
/ :…M^/PCS:<&(
/PC/ :I/ 17Fm9T:1)2H($1)9U1`§rL|3_(A(op#(:¨d17C)-“9>46x(:I/P6(F 1:T(3;/ :x:<GH3rC)9s/PCN:T>Z17Cd/P6B6x(3_9(N-sp#(:o{&
/ ? &Z& 17*H*(
C9
/PCd6x17CNM 2H(A>46x(:<3b/ (A9'{W/ :<&/PC‹  &|
Š ‘>
L :<&(EˆjFOF /PC+
2 Qx%W&($? & 17C)2
($/PC=:<&)( 4>){8* 1:|:T(3rC/ 9BR(
F / (c)(N:T>~R(S2D3_1 -DG 17Fw17C)-¥/ 9 1“L|GHC ?<:I/ >DCd>
L:<&)(Ž6>4F -Ž2
(N>46(A:<3YM Q¥f¾2
(A>D6(:<3QMZ{'/ :<&X6x17CMa?&)17C)2
(N9$/PC
:<&(=-K/P3_(N?:I/ >4C$>Lu:<&)( 4>){¿17C -0Á)>K31SC 1
3…3_>){86>DF L
- 3Q(
F 1:I/ c(
F Ms:<&
/PCs{i17FOF 9¦„;{W/PFOFm& 1c)(B:<&)(s? & 17C)2
(B:T>
/P6B6(
3Q9q(N-xpr(A:i(N1
3rF / (R3 Q9Fs17CMU9>4G735?(A9x*3_>c
/ -
(B/PCLy>K3…6x1:I/ >DCU>4C
Ly>K3jc 13b/ >4G)9x*)1
3Y:T9@>Lw:<&(U-H(A9</ 24C)9
>L :<&)(3rG7CHC)(3 17C -[271:T
( Q %n:I/PF / /PC)2:<&
/ 9/PCLy>K3…6x1:I/ >DC[*3_>0-4G ?(N9':<&)(E2H1:T(Ec(
F >0?/ :rM$1)9o1$L|GHC ?<:I/ >DCs>
L
:<&(20/ c(
Co2H(A>46x(:<3QM Qz%l>s9:<G)-
ML|GH3Q:<&(
3":<&
/ 9*>0/PCN:i?A>4C)9¦/ -H(3"1B?A1)9q({x&(
3Q(
/ 9@1U9</P6B*7F (L|G7C)?:I/ >4C
>L":<&)(271:T(1
3Q()
1 Q ~&)(C  / 9 c)(3QM$F 13_2
(':<&)(C:<&)((A¬m(?<: >4C
1
3Q(E3Q(
F 1:I/ c(
F MU96x17FOF Quhj>DCNc)(3_9(
F MNJ

|+~

|+~

|+~



KF

K0



!

 Q ƒ¢½

kK/ 24G73_(

v

{&)(C 
:<&)(“3_(A9</ 9T:17C ?(7J
3Q(
*3_(A9(
CN:;9G ? & R(
&)1c
/ >K3/ 9

| ~



{ 



|~

| ~


-?
PYi" 7 6'-" 
/#-
1 6
6
 &
A3

! # Q“%'&)(9</P6B*HF (N9T:L|G7C)?:I/ >4C0Jw9A&>){xCZ/PCŽkK/ 24G73_(5Q ƒDJn:<& 1:



?>4*AMH3b/ 24&:ØÙ × J4
ŠHŠ
ŠDJ¢RM[g@3RQ'Ú"1
3P‚@FE( /P3



ێÜAÝ<Þ$ÜAÝ<ßAàáIâHã äUå‡àNåWæàNäPçIÜè™éSê7ãAàIç
ê)âHëAàiì_â ämáIâHãWÞ#âê ÝIáNíé î Ýïè Ýä5è çIå@í

5Q 
‹H„

ñ+

Section 7.4. The reformed pQ2 diagram

 17C -   1
3Q(S?>4C)9T:17C:T9s17C -Ž?A17CŽR(S?N17F ? G7F 1:T(N- r17*H*
3Q>’H/P6x1:T(N-K„Ly>K3'1Z9A*(N?/ ˆD?2
(A>D6(:<3QMQ
%'&)( c 17FOG([>L  -H(:T(
3…6/PC)( :<&)(c 17FOG([>L;:<&(^3Q(N9¦/ 9:17C)?A( {&)(3_(  (¬l(N?:=/ 9 6/PC
/P6BGH6 17C -  
-H(:T(3r6/PC)(E:<&)(3517C)2
( T*>K/PC:q„W{&)(3_(  *7F 1M)9x19¦/ 24C
/ ˆD?A17C:'(¬l(N?: Q$†PCS*351 ?<:I/ ?A17FPJ"/ :/ 9xLy>4G7C -:<& 1:
  / 9E/PC :<&(S3517C2H(E{x&(
3Q($2H1:T( 1
3Q(1[1
3Q( -H(A9</P3Q(-Z17C)-S:<&)(3_(Ly>K3_(S*3Q>H2435176¾9AG)?&[1)9$gi/ ( "4(3QLy(N?:
1
3Q(s/P6B*>K3Q:17C:i:T> ?A17F ?GHF 1:T(-E:<&)(B1 ?<:<G 17FD3_(A9</ 9T:17C ?( Q





!#"
  '%$'&
, b/Z 4E7#NˆQ/b1<.37P;-NO.30 Q/b
N<734ˆ,/.34 ,%m ;-491<.30 Q8bHJ0B.3*273491 5d4ENO. .RQo.3* 4]Y;-b N.30 Q/bpO^  g
-fi 6'-"
, b/Z 4E7#NˆQ/b1<.37P;-NO.30 Q/b
 1

6

 

(7  1 

h">4C)9(NŒDG)(C:<F MNJ 1'c)(3QM96o17FOFN13_(N1B3_1:I/ >s3_(A9G7F :T9i/PC1'c)(3QMUF 13_2
(o3_(A9</ 9T:17C ?(HJ
:<&)(3_(Ly>K3_(x:<&(=3_(A9¦/ 9:17C)?A(
3_(A9AGHF :I/PC)2$/PCB1UA(3_>=271:T(Wc)(F >0?/ :rT
M TF /P¡<(1B? F >H9(N1 C -E{x&(
C 
7
 
c 17F c()„ Qh">4Cc(
3Q9q(F MNJ4Ly>K31F 13_2
(s13_(N1351:I/ >¢J0:<&)( 3_(A9</ 9T:17C ?(s/ 9o/PC)9(
C9</ :I/ c(:T> c 1
3y/ 1:I/ >DC9'>
L:<&)(B271:T(
1
3Q(1W17C)-x:<&)(ic)(F >0?)/ :…Mx/ 9‡3Q(-4G ?(-{W/ :<&x/PC)?3Q(1)9(‡:<&(@2H1:T(@13_(N)
1 Q%'&)(3_(Ly>K3_(‡1B6x1N’
/P6EGH6~2H1:T( c)(F >0?)/ :…M
6BG)9T:@(<’H/ 9T:AJ417C - ?A17CR(oLy>DGHC -dRM



!

 





 

v

! #

v


5Q ,7„

{&
/ ? &$?A17CR(E9>DF c(-ZC7GH6x(3b/ ?A17FOF MQW%W&(E9>4FOG:I/ >4Cs>L (NŒDG 1:I/ >4CP 5Q ,7„o3Q(Œ4G
/P3_(A9'L|G7FOFm/PCNLy>K3r6x1:I/ >DCE>4C
:<&)(-0/ (B?A1)9:I/PC26x1 ?&/PC)
( Q
f 2
(
C(
3_17F?A>46B*7F / ?A1:T(-$3…G7C7C(
3l-H(A9</ 24Cx?A>4Cˆ424G73_1:I/ >DCx?A17CsR(x?>DCNc)(3Q:T(N-$/PCN:T>s19T:<351
/ 24&:u?A>4C -4G
/ :
{'/ :<&;:<3517*(A>0/ -H17F? 3_>
99T‚79q(N?<:I/ >DCKJH*3_>c
/ -H(N-x:<&)1: / :"{i1)9‡*3Q>D*>K3Y:I/ >DC)17FOF M'-H(A9¦/ 2DC(-x:T>o?3Q(1:T(‡(Œ4G 17FN271:T(
c)(F >0?/ :rMLy>K3n-K/ ¬l(3_(C:i2H1:T(sF >0?A1:I/ >DC9<ª Qu%W&(x:<3517*(A>0/ -H17F
9A&)17*(B/ 9;?>46E6>4C7F M$G9q(N-R(N?N17G9q(x>
L":<&(
)
9¦/P6E*HF / ?)/ :…MNJ7:<&)(3r6x17FPJ017C -$Ly>K3n?>H9T:x3Q(1)9>4C)9 Q

!#"
  '%$'&B$
PTQc0k@k@B;O1<.37R,/.34 Q/b/@ t.3* 4>4
x4<N.W1MQ ]`.3* 4GDA,/.34L,734ˆ,NE*T,-bEDF4%.3HQ
4 -,-[ 5x@k491?,734M5873491 4<b .34<Z Q/b/4<e
,KNˆQ8b1E.R,-b8.†5873491:1<;-7=4c0 12,O5 5x@k0k4<Z}.RQ .3*/4
7 ;-b/b 4E7=eM.3HQ8e ,KNˆQ8b1E.R,-b8.†5xQ8H4E7?0 12,O5/5A@k0k4EZ .RQ .3* 4
7 ;-b b/4<7P^ P* 467=4q1ˆ0 1<.R,-b/N<4>.RQ
.3* 74 -Q8H 0kb
.3*/4 1 *TQA.\1 @k4<4Aˆ460 1G1ˆ[ ,-@k@dN Q/[ 5 ,7=4EZc.RQo73491 0 1<.R,-b/N<40kb
.3* 4%7P;Tb/b 4E7=e */4<b/N<4<eu.3* 4273491 0 1<.R,-b/N<4%0kb .3*/4L1ˆ*-Q .`1 @k4<4Aˆ42N ,-bV 42b 4 [email protected]<Z ^ P'*/4%Z 0k42N ,O1<.30kbED
[M,-N<*/0kb 4\5d4<7 ]fQ-7=[M,-b/N<4aN<*-,7R,-NO.34E7=0 1E.30kN91,734`0 19Q8@ ,/.34<Z/e ,-b Z .3* 4 DA,/.34J,734ˆ,G
4 x4<N.W1\Q8bM.3*/4 .3*/4Dx,/.34
ˆ4E@ Q NE0B.kt%Nˆ,-b>V 4?4 -,-[0kb 4EZ8
^ P<tT5A0kN ,-@ Z 0k[L4<b1ˆ0 Q/b1aQ ] .3* 4 Z 4q1ˆ0 Ddb,7=4u5873491ˆ4Eb8.34EZ60kb x0 D';-7=4>pE^_
TS ^
P'*/41ˆ*-Q-7 .FN Q/b/Z8;-0B.8Q ] S ^ -g-UR[aX73495873491 4<b .W1,-b 4 NE4<@[email protected];Tb/b 4E7FZ/491 0 DFb,-b ZM.3* 4a@ Q/bEDF491E.AN Q/b/Z8;-0B.
Q8]A
-^ g SOU=[`X\7=4q587=4q1ˆ4Eb8.W1J, ˆ4E7Bt 5xQ8 Q-7dZ 4q1ˆ0 Ddb8^ P'*/4`Nˆ,-@kN;T@ ,/.30 Q8b1aH4<734`Nˆ,737=0k4EZM]fQ-7F,-M @B;-[0kb ;T[ ,-@k@ Q t
HJ0B.3*o,
Z/4<b1ˆ0B. tcQ8]#-)r ?gTU ˆD
 X ,-b Zc, T0kb/4<[M,/.30kN ˆ0 1 NˆQT1ˆ0B. toQ ] vxw y -+ E)v ( U  
/1 4<N3X ,-b Z
7 ;-b b/4<7J1<;-73]f,-NE4L7RQ ; DF*/b 4q1 1GQ ]#S ^fS
U=[[`Xˆ^ Q-7 .3*/4LN Q/b1<.R,-b .5 7=4q1 1<;-734Nˆ,O1 46.3* 46@k0km8;-0kZ+[4.R,-@
587=4q1 1E;T734 ,/..3*/4>7 ;-b b/4<7u4Eb8.37R,-b NE460 1M,O1 1E;T[4EZ.RQcV 42
-^ TU ',:X,-b/Z
]fQ-7†.3*/4>NˆQ/b1<.R,-b .#5xQ8H4<7
Nˆ,O1ˆ4.3*/45xQ8H4<7#@ Q1:1 0 1 U 
 HAXq^
 IÎPËÃIÊWÃÏÉ qÅ S<ÉNÉ<ÎDÊËÄrÇ 5NÐ;Ë
ËTÍ|Å"ÉNÐ?S ‡ , ÊNÇ Ã5NÎYÃÈ
















*



+

ÛaÜAÝÞ ÜAÝ<ßAàáIâHã äå‡àNåWæàNäPçIÜè™éSê7ãAàIç
ê)â
ëAà@ì_â ä¢áIâHãWÞ#âê ÝIáNíé î ÝAï è Ýä_è ç|à<í

?A>4*M73b/ 24&:ØÙ × J0
Š
ŠHŠDJ¢RMg@3RQ;Ú"1
3P‚@FE( /P3

. & & &

Ÿ ”O— O”
› š
Y•A  Y! ”Oš š ”P•(kY• ”

˜ ”P™š —™š › _™”O”O Q”O 

Chapter 7. pQ2 Diagram Calculations

_i 6'-"
P* 4DA,/.34'

4<@ QAN<0B. to0 14 /* 0kV/0B.34<Z+,O1?,o]Y;-b N.30 Q/b+Q8]#.3* 467Y,/.30 QQ8] .3*/4DA,/.34 ,734ˆ,o.RQl.3*/4N Q/b/Z8;-0B.
, 734ˆ,+,O1M1ˆ*-Q8HJbc0kb A0 D;T734
pE^_
-
o]fQ-7`,
NˆQ8b1E.R,-b8. 5 7=4q1 1<;-734,-b/Zl0kb A0 D';-734
pO^f
Ol]fQ-7 ,oN Q/b1<.R,-b .
5xQ8H4E7 ^






3
0.01 [m]

gate
area

mold

gravity

0.008 [m]

A-A
flow direction

L
0.01438 [m]

A

A
A2
2



runner
entrance

shot
sleeve

1

:i

"



5Q NŠ¢½#"
"  $ " '-" A 6  " "     
$       "#  
 6 " 6   6 "  ""  '#-" 
'' 
  #
1  '#-"  
  ! 
# '"  
 #
1 6

 6
"#
$!$$G 6
 #
1 6  
kK/ 2DGH3_(

:i

/i

5Qf‹-‹7½

"
-   6'
?
Yi" G " 
 


1 6'   3G"  
" ?  :i 6 

kK/ 2DGH3_(

?>4*AMH3b/ 24&:ØÙ × J4
ŠHŠ
ŠDJ¢RM[g@3RQ'Ú"1
3P‚@FE( /P3

ێÜAÝ<Þ$ÜAÝ<ßAàáIâHã äUå‡àNåWæàNäPçIÜè™éSê7ãAàIç
ê)âHëAàiì_â ämáIâHãWÞ#âê ÝIáNíé î Ýïè Ýä5è çIå@í

ñXW

Section 7.4. The reformed pQ2 diagram

 QB‹D½

1 6
- G' ?
?
PYi" 7 "  6
6
6
   3G-" ! 6
"     

k0/ 24G73Q(




   

1%


(7 


(





%(7



 

c$'& &






k >K3l:<&(?>DC9:17CN:'*
3Q(N99G73_(x?A1)9q(:<&)(“§|?>D6B6>DC)¨ ª 1)99G76B*:I/ >4CxM/ (
F -
9;1B?>DC9:17CN:uc)(F >0?)/ :…MU(c)(CLy>K3
1s(3_>$2H1:T(U13_(N1)Q



f‹-‹

%'&)(U9>DF / -SF /PC(s/PCSkK/ 2DGH3_( 5Q $3_(*3_(A9q(C:T9;:<&(U271:T(c(
F >0?/ :rM=?A17F ?GHF 1:T(-SR)1)9q(N-[>4CB:<&)(B?>D6B6>4C
1)99AGH6E*N:I/ >DCd>
L?A>4C)9T:17C: h ¤ {&
/PF (S:<&(Z>
:<&(
3BF /PC)(A9 13_(XR 1)9(N-X>DC^?A17F ?GHF 1:I/ >DC9s{&
/ ? &“:17¡<(^/PC:T>
1 ?A?A>4G7CN: :<&)(]3…G7CHC)(3U2H(A>46x(:<3QM 17C -¥:<&( m(¥C7GH6ER(3RQ‘%'&)(¥3_(A9AGHF :T9[Ly>K3U?A>4C)9T:17C:Sh ¤ 3_(*3_(A9q(C:
§|1c)(351)2
(-H¨E>L":<&)(o>:<&)(3z3Q(N9G7F :T9Qz%'&)(?A17F ? G7F 1:I/ >4C)9i>
L":<&)(c)(F >0?/ :rM$R)1)9q(N-=>4CU1E?A>4C)9T:17C:@h ¤ c 17FOG(
1
3Q(UG7C73Q(17F / 9T:I/ K
? Q‡† : >c)(3_(A9T:I/P6o1:T(A9u:<&)('c)(F >0?/ :rMLy>K3F 13_2
('271:T(1
3Q(1U17C)-GHC -
(
3Q(N9T:I/P6x1:T(N9zLy>K3¢:<&)(1
3Q(1
351:I/ >R(F >){ V
Š °Ly>K3m:<&)(x9A&>K3Q:'3…G7C7C(
3l17C -  ‹ 8Ly>K3m:<&(sF >4C)2 3rGHC7C)(R3 Q‡k0/ 24G73Q( 5Q (<’K&/PR
/ :T9 :<& 1:
:<&)(3_(=/ 9W1$? F (N1
3 6x1N’H/P6BG7682H1:T(c)(F >0?/ :rMB{x&/ ?&s-
(
*(C -
9>4CB:<&)($3…G7C7C(
3z-H(A9</ 24S
C T&)(3_( 3_(*3_(A9q(C:T(NRM:<&)( ?>DC)-DG/ :sF (C)2:<&„ Q %W&(S6x1N’H/P6BG76 /PC -0/ ?A1:T(A9o:<& 1::<&)(d*3_(Ly(3r3_(N-Z9</ :<G)1:I/ >DCS/ 9:T>aR( >DC :<&(
§I3b/ 24&:U& 17C)-9¦/ -H(R3517C ? & ¨dR(N?N17G9q(E>L‡9&)>K3Y:T(
3wˆjFOF /PC)2 :I/P6( Qx%W&(B271:T(Bc)(F >0?/ :rM[/ 9x-H>4G7RHF (-Ly>K3:<&(
(<’?(
FOF (C: -
(N9¦/ 24Co?>46E*)1
3Q(-{'/ :<&x:<&(2H1:T('c)(F >0?/ :rM>DRN:1
/PC)(N-L|3_>46 :<&(U*>K>K3l-
(N9¦/ 24)
C Q%'&
/ 9‡/PC)-0/ ?A1:T(N9
:<& 1:B:<&(Ž3rGHC7C)(3-H(A9¦/ 2DC“/ 96>K3_(Z/P6E*>K3Y:17C:B:<& 17CS:<&)(d9*(?/ ˆD?[?&)1
351 ?<:T(3b/ 9T:I/ ?>Lx:<&(d-0/ (S?N1)9T:I/PC)2
6x1 ?&/PC)(S*(3QLy>K3…6x17C ?( Qx*(351:I/PC2S:<&)( -K/ ( ?A1)9:I/PC2a6x1 ?&/PC)( /PC :<&)(]§I3b/ 24&:B& 17C)-d9</ -
(¨“3_(A9AGHF :T9E/PC
96o17FOF (3n3_(NŒDG
/P3Q(
6(C:T9u>4Cx:<&(W-0/ (?A1)9:I/PC2$6o1 ? &
/PC(R(?A17G)9('>L"1o96o17FOF (3DˆjFOF /PC)2o:I/P6(HJH17C)-B:<&(
3Q(ALy>K3Q(
{'/PFOF¢3Q(Œ4G
/P3_(B1B96o17FOF (3w-0/ (U?A1)9T:I/PC)26x1 ? &
/PC( Q





f‹-‹

k >K3:<&(=?>4C)9T:17C:U*>){ (3u?A1)9q(HJ¢:<&)(E2H1:T(Ec(
F >0?/ :rM 1)9o1$L|G7C)?:I/ >4C$>Lu:<&)(=1
3Q(1S3_1:I/ >“/ 99A&>){xC /PC
k / 2DGH3_( 5Q N Q%'&)(?>D6B6>DC[1)99G76B*:I/ >4C>
L'?A>4C)9T:17C:Uh ¤ M
/ (F -H9:<&( 271:T($c(
F >0?/ :rM
K
 ( 
9&)>){C RAME:<&)(U9>4F / -ZF /PC( Q fu2H1
/PC0J0:<&)(B?>D6B6>DCs1)99AGH6B*:I/ >4C *
3Q>0-DG)?A(A9G7CH3_(N17F / 9:I/ ?E3_(A9AGHF :T9J0{W/ :<&B:<&(
2H1:T(Wc(
F >K?)/ :…M17*H*
3Q>71 ? &
/PC2s/PCˆjC/ :rMx1)9u:<&)(x1
3_(N1s3_1:I/ >s17*H*3_>H1 ?&(N9u(3_> Q xRc
/ >4G)9F MNJ
:<&(B3Q(N9G7F :T9u{'/ :<&
1S?>4C)9T:17C:Uh ¤ >
c(
3Q(N9T:I/P6x1:T(N9x:<&)( 2H1:T(=c)(F >0?/ :rMLy>K3WF 1
3_2
( 13_(N1^351:I/ >
9U17C)- GHC -
(
3Q(N9T:I/P6x1:T(N9E/ :xLy>K3
96o17FOFj1
3_(N1a3_1:I/ >H9 Qd%'&)( >:<&)(3xF /PC(N9E-H(A9q?3y/PR(:<&([?N17F ? G7F 1:T(N-Z271:T($c(
F >0?/ :rM^R 1)9(N-^>4C:<&(Z3rG7CHC)(3
2
(N>46(A:<3YM QBfu9=R(Ly>K3_(HJj1? F (N1
3;6x1N’H/P6BGH6‘?A17C17F 9q>^R($>4R)9(
3Yc)(N+
- Qk >K3;F 1
3Q2H(=1
3_(N1Z351:I/ >
9Jm:<&($271:T(
c)(F >0?/ :rM{W/ :<&S17Cd(<’?(
FOF (C:U-H(A9</ 24C“/ 9s17FO6>H9T:B-
>DGHR7F (N-a?>D6B*)1
3_(N-Z:T>“:<&([c)17FOG)(A9s>4R:1
/PC(-Z{'/ :<&d1
*>K>K3w-H(A9¦/ 2D
C Q2>){ (c)(3|JK{&)(Cs:<&(B1
3Q(13_1:I/ >17*7*3_>H1 ? &)(A9;(
3Q>mJ0:<&)(B2H1:T(c)(F >0?)/ :…M$/ 9/PC9q(C)9¦/ :I/ c)(x:T>
:<&)(s3rG7CHC)(3 F (
C2
:<&E17C)- 1:|:1
/PC)9'16o1N’
/P6BG76Vc)17FOG)(B1:;17FO6x>
9T:i:<&(U9I176(=*>K/PC: Q





 

†YCs?>DC)?FOG9</ >4C0J
:<&
/ 9* 13Q:x& 1)9R(A(
CE9&)>){CU:<& 1:@:<&($G)9(U>
Lw:<&)(a§|?A>46B6>DC)¨[*
+W,¿-K/ 1)2D3_176V{'/ :<&
:<&)(1)9q9G76B*:I/ >4C>L1E?>4C)9T:17C:;h"¤d6x1AM F (N1 -s:T>Ec)(3QME9q(3b/ >4G)9‡(
3…3_>K3Q9 Q %n9</PC2s:<&(s*
+W,`-0/ 1)2435176sJH:<&(
(C)2K/PC)(A(
3z&)1)9‡:T>E:17¡<(U/PCN:T>$1 ?A?A>4G7CN:u:<&)((¬l(N?<:T9@>Ln:<&(oc 13b/ 1:I/ >4C>Lw:<&(o2H1:T(13_(N1B>4C:<&(-0/ 9q? & 1
3Q2H(
?>K(A£$?)/ (C:AJjh ¤ Jlc)17FOG)
( QE%'&)(E:r{ >[(’ 176B*7F (A9o2K/ c)(C/PC7&(
3Q($-H>^C)>:B3_(*
3Q(N9(C:W:<&)( ? & 1351 ?<:T(
3y/ 9:I/ ?9>
L
:<&)(x-0/ (?A1)9:I/PC2 6o1 ? &
/PC( Q 2>){ (Ac(
3#J46>K3Q(o-
(A:1
/PF (N-s?A17F ? G7F 1:I/ >4C)9u9&)>){‡9 :<&)1:z:<&)(x?>DC9:17CN:;*3_(A9q9G73Q(
/ 9i/PC?>DCN:<3_>4FN{&)(C':<&)(x*7FOG7C2H(3m/ 9z96x17FOF)?>D6B*)1
3_(N-x:T>o:<&(;>:<&)(3j6o1 ? &
/PC('-0/P6(C)9¦/ >DC9z17C)-o{x&(
C':<&(
3rGHC7C(
3w9M9:T(6t/ 9'c)(3QM*>K>K3rF Ms-H(A9¦/ 2DC(- Q'‡:<&)(3Q{'/ 9q(HJ0:<&)(E?A>46BR
/PC)1:I/ >DCB>Lz:<&)($*3Q(N99AGH3_(E17C -Z*>){ (3
F /P6/ :1:I/ >DC9x3Q(N9G7F :T9/PCB:<&(U?&)1
3_1 ?:T(3b/ 9T:I/ ?A9@>
Ln:<&)(B-K/ (U?N1)9T:I/PC)26o1 ? &
/PC(o{&
/ ? & & 1)9@:T>SR(U9>4F c)(N-+Q
ÂTÒ¢ÄwÇ Å"Ç Ä8"ÎQÇ Å5Åy˦Ð'Ç ÐxÑ0ÒnÓmÔ7Ò"Õ ÄwÏÉAÉNÖÄ

‹

ÛaÜAÝÞ ÜAÝ<ßAàáIâHã äå‡àNåWæàNäPçIÜè™éSê7ãAàIç
ê)â
ëAà@ì_â ä¢áIâHãWÞ#âê ÝIáNíé î ÝAï è Ýä_è ç|à<í

?A>4*M73b/ 24&:ØÙ × J0
Š
ŠHŠDJ¢RMg@3RQ;Ú"1
3P‚@FE( /P3

Chapter 7. pQ2 Diagram Calculations

U3
‘‘common’’ model

realistic velocity

A3

5Qf‹  ½ 
?
PYi" G " 
/#-

6
  

kK/ 2DGH3_(

 

 

7

 5' 









 
$ 

 
 +

% 55

 

%'&)(3_(E1
3Q(:r{ >$:…M7*(B>
L>D*(351:I/ >4CE>
L:<&)(B-0/ (E?A1)9:I/PC2S6x1 ?&/PC)(HJD>4C)(„‡:<&)(E-K/ ($6o1 ? &
/PC(s/ 9W>D*(351:T(N-K/P3_(N?:<F M“RMa&NM -43517G7F / ?[*7G76B*LT6x>
9T:<F M>4C:<&)( >4F -Ž6x1 ?&/PC)(A9¦„ Q$:r{ >7„EG:I/PF / /PC)2:<&)(dC)>4C[?>DCN:I/PC7G)>4G)9
-
(
6x17C -Ly>K3w:<&([*>){ (3|J4:<&)( *>){ (3 / 99:T>K3Q(-S/PC 1=?A>4C:1
/PC(
317C -“3_(F (1)9(- {&)(CSC)(A(N-LT6>H9T:<F M$>4C
:<&(dC)({ (
3'6x1 ? &
/PC)(A9I„ Q$%'&)($?A>4C:1
/PC(
3@/ 9=C>K3r6x17FOF M[1ZF 1
3_2
(=:17CH¡ ?>DCN:1
/PCZC
/ :<3_>
2
(
C17C)-Ž&M)-D3517GHF / ?
F / Œ4G
/ - , AQ[%'&)($(¬l(N?:T9U>L@:<&($:17C7¡=9</ (17C -d2H1)9¦ÁKF / Œ4G
/ -a3_1:I/ >Z>DC:<&)(*
3Q(N99G73_(17C)!
- 4>){t351:T([?A17C
(N1)9</PF MR(U-
(
3y/ c)(N-+Q
o&)(*>){ (3 9G7*7*HF M$L|3_>46 :<&(=:17C7¡E{W/ :<&[?A17C?>DC9</ -
(
3i17FO6>
9:x1)9U1[?>DC9:17CN:E*3Q(N99AGH3_([R7G:
:<&)(F /PC)(U:T>[1 ?:<G)1:T>K3 / 9W{W/ :<&Ec 13b/ 17RHF (3Q(N9¦/ 9T:17C ?(E{&
/ ? &/ 91=L|GHC ?<:I/ >DCs>
Lu:<&([F / Œ4G
/ - c)(F >0?/ :rMQ
%W&(3_(A9¦/ 9:17C)?A(=?N17CdR($?A>4C)9¦/ -H(3|J¢Ly>K3i1[?(
3Y:1
/PCd3517C2H(HJj1)91ZF /PC)(N1
3zL|GHC ?<:I/ >DC$>
L :<&)(sc)(F >0?)/ :…M
 ¨ Q32(C ?(HJ7:<&)(Lb176>DG9'1=1)99G76B*:I/ >4CB>
Lw:<&)(a§|?A>46B6>DC)¨s-K/ (B?N1)9T:I/PC)2S6x1 ? &
/PC(
9IŒ4G 1
3Q(7J‡§

$5

 (  Q





@

%'&)([? & 1
3_1 ?:T(3b/ 9T:I/ ? >
L@:<&)(c 1
3y/ >DG9 *7G76B*9&)1c)(“R(N(C9:<G)-0/ (N-^(<’):T(C)9¦/ c)(F M^/PC[:<&)(“* 1)9T:Tk1
/P3&
R 17C7¡A9 Nƒ
‹HƒH„ Qu%'&)(B-K/ (B?N1)9T:I/PC)26o1 ? &
/PC(s/ 9W1[*HG76B*B{W/ :<&E9>D6(s/P6B*3_>c)(6x(C:T9‡{x&/ ?&s1
3Q($* 1:T(C:T(N› P˜ ”P• šDš –™”j 5› ˜ œ ™˜ ˜ › _j—! Pš )
k (k œP–™—P• —™œOš ”P• › ˜ š › œ › š – š –™” R M -K/ ¬l(3_(C:B6x17C7GNLb1 ?:<GH3_(A9 Q%W&( C)({©?>DCNˆ42DGH351:I/ >4C)9NJ09AG)?&$1)9o-
>DGHR7F ( *7G9A&/PC)2[?MHF /PC -
(
3Q9J¢?&)17C)2
(
Q• ”
• sš –P”• ”O 
_Ÿ  Y”P•
 Pž š ”O˜
9>D6({x&)1:‡:<&(B?&)1
3_1 ?:T(3b/ 9T:I/ ?A9'>L:<&(B-0/ (B?A1)9:I/PC2S6x1 ?&/PC)(A9 Q'kK/P3_9T:oF (:'-K/ 9I? G)99'9q>46(2
(
C(
3_17F0? & 1
3'&
1 ?<:T(
3y/ 9:I/ ?>L1a*7GH6E/
* |/ 99G)(A9F /P¡¦([(6B*(
F >K3#J9*(N(N-Ž13_([>DGN:U>
L':<&(9q?>D*(>L':<&
/ 9s-0/ 9q?G9q9¦/ >DC „ Qdf
*HG76B*E/ 9W6(? & 17C/ ?N17F-
(Ac/ 9q(W:<& 1:u:<3_17C)9TLy(
3Q9;17C)-s(F (?<:<3b/ ?A17FK*>){ (
3 T6>H9T:<F M„@/PC:T>Ž§¦&NM -43517G7F / ?A¨$*>){ (
3 Q
f¥:rM7*/ ?N17F7? & 1
3_1 ?:T(3b/ 9T:I/ ?o>Lu1 *7GH6E*s13_(U-
(N9q?3y/PR(-/PCkK/ 2DGH3_( 5Q A€ Q

' ' & ' & & &'
&







4  I"Æ<Ç ÄjÄ#Ç ÈiÇ Ì Ã¦ÎÅyɇÉ SËIÎYÃqÅ…Ç ÉNЇÉJ8¢ÃqÅyËIÎKÄ KIÄbÅyËIÈaÇ ÐiÃuÄ#Æ<Ç SL
ÈuÃÐKuÉJHÅrƦËuÍIƦÃIÎYÃIÍ|ÅyËIÎQÇ ÄyÅ…Ç ÍÄnÃIÎPËwÅrÆIËuąÃÈzË H  +ΙÅrÆIËIÎ_ÈuÉ<ÎPË7L
ÅrÆIËEÄrÃÈzËBÊNÇ 
ËIÎPËIÐqÅ…Ç ÃÌjËR +¦ÃqÅ…Ç ÉNÐIÄUÃIÎPË 5<É:¦ËIÎ_Ð<Ç Ð65ÅrÆIËsÄrÇ Å +¦ÃqÅ…Ç ÉNÐ H I"ÆIËEÅ'K S<Ç ÍqÃ<Ì R +IËTÄbÅ…Ç ÉNÐIÄÄ +IÍIÆ[ÃqÄWÅrÆIË$ÐIËÍTËTÄbÄrÃIÎQÇ Ì K
ÍTÉNÐqÅbÃ<Ç Ð¦ËIÎiÄrÇ "ËÃÐIÊ=ÅrÆIËsÎYÃqÅ…Ç É=ÉJ 5ÃIÄ;ÅyÉ Æ6KIÊÎYÃ'+Ì Ç ÍsÌ Ç R +<Ç ÊP8¢ËIÎPËPS¦ÃIΙÅ;ÉJ@È KUÄyÅ +IÊGK=Ç Ð$Æ<Ç 5NÆsÄbÍIÆIÉNÉNÌ> S¦ÎPÉNϦÃÏÌ KEÅrÆIË
ÄrÇ 9
È SÌ Ç <)ËTÊ :I˦ΙÄ#Ç ÉNЇÉ J0ÅrÆIË;ΙËqÃ<Ì)ÍÃIÄbË FH J0ÊËIÈ Ã<ЦÊ;ÅyÉ;ÅrÆ<Ç ÄÈ ÃqÅyËIÎQÇ ÃÌ ÎYÃ¦Ç ÄbËT
Ê L 8"Ç Ì Ì)Ç ÐIÄb˦ÎOÅwÇ ÅwÆIËIÎPË‡Ç Ð ÅrÆIË J +qÅ +ÎPËGH



?>4*AMH3b/ 24&:ØÙ × J4
ŠHŠ
ŠDJ¢RM[g@3RQ'Ú"1
3P‚@FE( /P3



ێÜAÝ<Þ$ÜAÝ<ßAàáIâHã äUå‡àNåWæàNäPçIÜè™éSê7ãAàIç
ê)âHëAàiì_â ämáIâHãWÞ#âê ÝIáNíé î Ýïè Ýä5è çIå@í

ñð

Section 7.4. The reformed pQ2 diagram

pressure
efficiency

power

P
power

η

 QB‹N€¢½

Q

 "  
  

G  6

A i$

kK/ 24G73_(

%u{ >$9</P6/PF 13i*HG76B*)9W?A17CR(E?A>4C7C(?<:W/PCE:r{ >s{i1AME9q(3b/ (A9W17C -Z* 13517FOF (F Q‡%'&)($*)1
3_17FOF (
FK?A>4C7C(?<:I/ >DC
P/ C ? 3_(N1)9(=6>H9T:<F MU:<&)(4>){¿351:T(B1)9;9&)>){Cs/PCkK/ 2DGH3_( 5Q A€+Qw%W&(9(
3y/ >DG9'?A>4C7C(?<:I/ >4CE/PC ? 3_(N1)9($6x>
9T:<F M
:<&)(U*3_(A99AGH3_(1)9 9A&>){xC/PCsk0/ 24G73Q( 5Q A€ Qw%'&)(W9(
3y/ (N9i?>DCHC)(N?:I/ >4Co/ Lo§¦C>K3r6x17F / (-H¨B/ 9uc)(3QM?F >
9q(;:T>U:<&(
>K3b/ 2K/PC 17F*7G76B
* Q 2>){ (c)(3|JN:<&(x*)1
3517FOF (FA?>DCHC)(N?:I/ >4C‡{&)(C[§IC)>K3…6x17F / A(N-7¨'9&)>){Ž1R(A:|:T(3l*(3QLy>K3r6x17C)?A
( Q
%l>[9:<G)-
M$:<&(=(¬l(N?:T9x>
Li:<&)(=-0/ ($?A1)9T:I/PC)2“6o1 ? &
/PC([*(3QLy>K3…6x17C ?(N9NJm:<&)(=Ly>4FOF >){'/PC)2 L|G7C)?:I/ >4C)9x1
3Q(
(<’176/PC)(N- …9(A( k0/ 24G73Q( Q ‹H„½











&    1
'


&     '


 
 

&    1 '
 
%'&)(UL|G7C)?:I/ >4C)9 5Q H1„J 5Q 4R „;17C - 5Q H?N„x3_(*3_(A9q(C:'1 -0/ (B?A1)9:I/PC2“6x1 ? &
/PC({W/ :<&=1*>K>K3i*(
3'&




R

R







Ly>K3r6x17C)?A(HJ
:<&(x?>46E6>4CB*(
3YLy>K3r6x17C ?(7JH17C -E1-0/ (?A1)9:I/PC2$6x1 ?&/PC)('{W/ :<&o17Cx(’ ?A(FOF (
CN:;*(3QLy>K3r6x17C)?A(HJ
3_(A9*(?<:I/ c)(F MQ
h">46BR
/PC/PC)2=(NŒDG)1:I/ >DQ
C  5Q  )„ {W/ :<S
&  Q  H„iM/ (
F -
9

R
R



 


 
 


U




 


 




U


U





3_(N1
3…3517C20/PC2=(NŒDG 1:I/ >4CS

 {

   &a





'
{





Q HH„iM
/ (F -H9
 

v

ÛaÜAÝÞ ÜAÝ<ßAàáIâHã äå‡àNåWæàNäPçIÜè™éSê7ãAàIç
ê)â
ëAà@ì_â ä¢áIâHãWÞ#âê ÝIáNíé î ÝAï è Ýä_è ç|à<í

&   
'
&     '
&     '
&    
'

?A>4*M73b/ 24&:ØÙ × J0
Š
ŠHŠDJ¢RMg@3RQ;Ú"1
3P‚@FE( /P3

Chapter 7. pQ2 Diagram Calculations
1

0.8

0.6

P
0.4

P= 1 − Q
P= 1 − Q

2

P= 1 − Q

0.2

0

4

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Q

 QB‹‹D½
6' i  
! "#$
"    6$
" G

k0/ 24G73Q(




&     '

& a
 {  '  v
&     '

{
   v
>4F c
/PC)2=(Œ4G 1:I/ >4C)9 5Q 
ƒ7„iLy>K3
J417C)-=:17¡ /PC2$>4C7F MU:<&)(s*>H99</PRHF (=*7&NM)9¦/ ?N17FH9>DFOGN:I/ >DCKJHM
/ (F -H9
& { '
&  & v
'
 {


 a

&  & v  '


a { 
a { $   
&  & v  '



%'&)(o3Q(-4G ?(-=*3Q(N99AGH3_(HJ

JK/ 9@*HF >
:|:T(N-1)9 1'L|G7C)?:I/ >4CW>
LD:<&)(
CHG76BR(3DLy>K30:<&(;:<&73Q(N('-K/ ('?A1)9:I/PC2
6x1 ? &
/PC)(s*(
3YLy>K3r6x17C ?(N9W1)9@9A&>){xCs/PC[kK/ 2DGH3_(5Qf‹,5Q







!

R

kK/ 2DGH3_(









R








i




i

i

Yi

5Q ,¢½?   $ 66 
   
1
6' 
 '"?    6
"  
-
 " G "  

"8i   






k / 2DGH3_( 5Q ,'-H(6x>4C)9T:<351:T(A9l:<& 1:
V6x>4C)>:T>4C
/ ?A17FOF Mi-H(N?3Q(1)9(N9j{'/ :<&‡17C/PC ? 3_(N1)9(‡/PC@:<&)(
K
C7GH6ER(3
Ly>K3W17FOFm:<&)(“6o1 ? &
/PC(^*(3QLy>K3…6x17C ?(N9Q^f;FOFj:<&(:<&H3_(A(^3Q(N9G7F :T9s?A>4Cc(
3Y:U:T>Z:<&)([9I176(“F /PC)({x&/ ?&Z/ 9=1
  QBk >K3‡F 1
3Q2H(
*HF 1:T(17G$1L5:T(
3
CHG76BR(3_9W:<&)(3_(N-DG ?(N-“*3_(A99AGH3_(HJ
$Jl?A17CSR(s?A>4C)9¦/ -H(3_(N- :T>
 Qw%W&(271:T(xc)(F >0?)/ :…MNJm/PCU:<&/ 9'?A1)9q(HJD/ 9
R(B?>DC9:17CN:








v

vAw v y

  xv w   




*




5Q 

‹„

%'&)(d@A(3oCHG76BR(3'9:<3Q>DC2DF MS-H(*(C -H9E>4C:<&(S-K/ 9I? & 13_2
(?>K(£ ?/ (
CN:AJ h ¤ Ju17C -
  Qa%'&)( c 17FOG(

>L   / 9$3_(F 1:I/ c)(F M“/PC9q(C)9¦/ :I/ c)(s:T>“:<&( 9</ ( >L;:<&)(-K/ (?N1)9T:I/PC)2X6x1 ? &
/PC( Q[%W&HG)9NJ":<&/ 9U(Œ4G 1:I/ >4C



?>4*AMH3b/ 24&:ØÙ × J4
ŠHŠ
ŠDJ¢RM[g@3RQ'Ú"1
3P‚@FE( /P3

ێÜAÝ<Þ$ÜAÝ<ßAàáIâHã äUå‡àNåWæàNäPçIÜè™éSê7ãAàIç
ê)âHëAàiì_â ämáIâHãWÞ#âê ÝIáNíé î Ýïè Ýä5è çIå@í

ññ

Section 7.4. The reformed pQ2 diagram

/ 9E17*7*HF / ?N17RHF ($:T>a1S{ (FOFj-
(N9¦/ 24C)(N-

3…G7CHC)(3MTF 1
3_2
(Sh ¤ „E17C)-0Á)>K3@1ŽF 13_2
(-0/ ([?A1)9:I/PC2Ø6x1 ? &
/PC(  F 13_2
(


   „ Q
%'&)(X3_(N-DG)?A(N-`*
3Q(N99G73_(ZLy>K3o1ac)(3QMŽ9A6x17FOFzc)17FOG)(Z>LU:<&)(
C7G76BR(3o(NŒDG)17F 9$:T>Ø>DC(7J
 
>K3
  
Jw-DG($:T>d:<&)(ZF 1
3Q2H(d3Q(N9¦/ 9:17C)?A(/PC:<&(“3…G7CHC)(3 y{x&(
C:<&(“3Q(N9¦/ 9T:17C ?(/PC[:<&(Z3rG7CHC)(3

17*7*3Q>71 ? &)(A9E/PCˆjC/ :rMNJ | ~ !
# J":<&)(C
  „ Q 2 (C ?(7Jj:<&)( 2H1:T($c)(F >0?/ :rMS/ 9B-H(:T(3r6/PC)(N-XRAM:<&(





17*7*3Q>’H/P6x1:I/ >DC>
L



 
 

*

  



5Q 

7„

%'&)($-K/ ¬l(3_(C ?(R(:r{ (A(
Cs:<&)(Ec 1
3y/ >DG9s6x1 ? &
/PC)(*(3QLy>K3r6x17C)?A(A9B/ 9E6x>K3Q($?>DC9</ -
(
3_17R7F ($/PC$:<&)([6/ -7-DF (
3517C2H(U>L:<&(s@$C7G76BR(3_9Qif¿R(A:|:T(3 6o1 ? &
/PC($*(
3YLy>K3r6x17C ?($*3_>0-4G ?(N9W1&
/ 24&)(3 3_(N-DG ?(N-Z*3Q(N99AGH3_(HJ

Qz%'&)(U*3_(Ly(
3…3_(N-s9¦/ :<G 1:I/ >4C/ 9 {&)(C:<&)(o@BCHG76BR(3n/ 9'F 1
3Q2H(W17C)-E:<&7G9@/PC -0/ ?A1:T(A9z:<& 1:z:<&(E6x1 ? &
/PC)(
*(3QLy>K3r6x17C)?A( / 9EF (A9q9/P6B*>K3Q:17CN:':<& 17C=:<&(3…G7C7C(
3u-H(A9</ 24C*)1
3_176x(:T(3_9 Q%W&/ 9W>DR9q(3Qc)1:I/ >DC/ 9L|GH3Q:<&)(3
(FOG ?/ -71:T(N-[/PCUc
/ ({`>
L@k0/ 24G73Q(N9 Q U17C)Q 5 Q

B‹ ‹





%


 +


19!

 

0 &

”  kQŸ —Y›  –P—™š7#”nš • P›  ž š
—PœP–Y› ” O”<–P”P• ”

.

PB 2

DR

atmospheric
pressure
P1

D B PB
1

rode

D1

plunger
hydraulic
piston
kK/ 2DGH3_(5Q (¢½   
1 6 
    "#3
"   6"!

" G   G



fi

%'&)(x*3Q(N99AGH3_('1:w:<&)(o*HFOG7C2H(30:I/P*?N17CUR('(c 17FOG)1:T(-oL|3Q>D6`1BR)17F 17C ?(@Ly>K35?(N9z1 ?:T9z>4C':<&)(x&M -43517GHF / ?
* / 9T:T>4C=17C)-d*7FOG7C2H(3w1)9W9A&>){xC=/PC[kK/ 2DGH3_( Q 5Qi%W&(B1:<6x>
9*7&)(3b/ ?E*
3Q(N99G73_(U:<&)1:'1 ?<:I/PC)2 >4CE:<&( F (AL5:

9¦/ -H(W>
Lm:<&)(U*7FOGHC)2
(
3l/ 9'C)(A2DF (N?<:T(- Qnfu99AGH6/PC)2E1o9T:T(1 -Mo9T:1:T(17C -$C)(A2DF (N?<:I/PC)2:<&)('L|3y/ ?:I/ >4C0J :<&)('Ly>K35?(A9
R 17F 17C)?A(o>DCU:<&(=3_>0-$M/ (
F -
9

 B‹/

    &






 ' {  


 



 






5Q  



5Q 

kY”P• –™—9kP˜ š &0œP• ”O—™š ”H—
 'P”O–˜ 0 š 2
› &_ &Y•rš –P”I˜ š 'P Y”PPš ˜


„

†PC * 13Q:I/ ? G7F 1
3#JD/PCB:<&)(9T:1:I/ >DC)1
3YME?N1)9(o:<&)($6x1N’
/P6EGH6t*3_(A99AGH3_(>4R:1
/PC9

    &



%'&)(B(Œ4G 1:I/ >4C
 :T>3_(N1 -







ƒ



    &
\




5Q 



' 




{  






 

 








€K„/ 9B3_(N-DG ?(N-{&)(C=:<&(3Q>0-H(s1
3Q(1[/ 9BC)(A24F / 20/PRHF (7j*7FOG9J"C)>:I/ ?A(U:<& 1:


\ /'



 

 


ÛaÜAÝÞ ÜAÝ<ßAàáIâHã äå‡àNåWæàNäPçIÜè™éSê7ãAàIç
ê)â
ëAà@ì_â ä¢áIâHãWÞ#âê ÝIáNíé î ÝAï è Ýä_è ç|à<í


  




€K„

 




5Q 

?A>4*M73b/ 24&:ØÙ × J0
Š
ŠHŠDJ¢RMg@3RQ;Ú"1
3P‚@FE( /P3

‹7„










Chapter 7. pQ2 Diagram Calculations



kK/ 2DGH3_(
Q D½ m(N-DG ?(N-^F / ŒDG/ -^6(:17Fn*3Q(N99AGH3_(=1::<&([*HFOG7C2H(3z:I/P* 17C)-a3_(N-DG)?A(N-S2H1:T(Ec(
F >K?)/ :…M1)9o1
L|GHC ?<:I/ >DCB>L:<&(=3_(N-DG)?A(N-d*7FOG7C2H(3n-0/ 176(:T(
3

m(N1
3…3517C20/PC2=(NŒDG 1:I/ >4CT

 




Q

‹H„iM/ (
F -
9






&
 
  '  


&
\  \
  '  

 

 






 





5Q  ,H„

, ª
% &)( 2H1:T(zc)(F >0?)/ :…Mx3Q(
F 1:T(A9j:T>':<&)('F / ŒDG/ -B6(:17F)*3_(A9q9G73Q(‡1:*7FOG7C2H(3
:I/P*;1 ?A?A>K3_-0/PC2@:T>':<&)( Ly>DFOF >){'/PC)2
'
(NŒDG)1:I/ >DCE?>D6BR/PC
/PC)2s(Œ4G 1:I/ >4CT Q ‹7„;17C)-  5Q  Š4R „iM
/ (F -H9


kY”P• –P—9k™˜ _ 5› ˜ œ'P˜ ˜




 O
*





 

&
 
  '     
  
    &
 
  '  
 
 


`{



<

D

<





5Q 

D

<







D

   J
%iC)-H(3n:<&(U1)99AGH6E*N:I/ >DCo:<& 1:@:<&(=6x1 ?&/PC)(U? & 1351 ?<:T(
3y/ 9:I/ ?U/ 9
3(    
 
$5
6 !-f i "     '" 6 ! 7 "  -'" P#-
- "    /i
1 6'-" =  9i   / i
1 6'-"
&   &  ' G  3  "
 

*
5Q  H„

 O & \
  \

  
 
/ '   






"  6   i   #-
1 6
 G' 

  



 "#  !   "' " ( / i
" &   &  ' NG"
-   
$!$ ?  

  

  O






{




5Q 



5Q €HŠH„

ƒH„

4…Â Ñ0ɦÅyË'ÅrÆ<ÃÅ , / 03254 , / 03254 H I"ÆIËWÊNÇ 
ËIÎPËIÐIÍTËÇ ÄuÅrÆ<ÃÅ , / 03254 ΙËSIÎPËTąËIÐqÅyÄ@ÅrÆIËoÈ Ã -Ç È +È S¦Î™ËÄbÄ+AΙËxÉJ"ÅrÆIË
 Ç ÐBÅrÆIËÄyÅbÃqÅ…Ç ÉNÐ<ÃIÎ KsÍÃIąË7L 8"ÆI˦ΙËBÃIÄ , / 0 254 ÎPË6S¦ÎPËTąËIÐqÅyÄWÅrƦË:¦ÃÌ +¦ËxÉJzÅrÆIËEÈuà -AÇ È#+È
Ì Ç R +<Ç Ê[ÈuË|ÅbÃÌDÃqÅNSÌ +AÐ65<ËIÎu8
Å…Ç Ss
¦S ΙËÄbÄ+AΙËuÉJ7ÅrÆIËiÌ Ç R +<Ç ÊWÈuË|ÅbÃÌÃqÅ¢ÅrÆIË9SÌ +Ð5<ËIÎ7Å…Ç SzÅrƦÃqÅlÍÃЇÏËuÃIÍIÆ<Ç Ë :IËTÊ 8nÆIËIÐ;ÆK¦ÊÎYÃ'+Ì Ç ÍS¦ÎPËTÄbÄ +ÎPË/8jÇ ÅrÆ<Ç ÐuÅrÆIË9S<Ç ÄyÅyÉNÐ@Ç Ä
:¦Ã¦ÎQÇ ËT
Ê H I"ÆIË JYÉÎ_ÈzËIÎmÎPË6S¦ÎPËTÄbËIÐIÅyÄÉNÐAÌ KiÅrÆ¦Ë ÊNÇ ËiÍÃIÄyÅ…Ç Ð5xÈuÃIÍIÆ<Ç ÐIËiÃÐIÊ'ÅrÆIËiÄ#ÆIɦÅ"Ä|Ì ËTË;:¦Ë7L18nÆ<Ç Ì ËzÅrÆIË;Ì ÃqÅ5ÅyËIÎlΙËSIÎPËTąËIÐqÅyÄÅrÆIË
ÍTÉNÈiÏÇ Ð¦ÃqÅ…Ç ÉNÐ;É J4ÅrÆIËuÊNÇ Ë ÍÃIÄyÅ…Ç 6Ð 5ÈuÃIÍIÆ<Ç ÐIA
Ë >5ÃÐIÊWÄ|ÆIɦÅ"Ä#Ì ËT;Ë :¦Ë FjÃÐIÊ'ÅrƦˇΠ+AÐÐIËI뢀 KIÄbÅyËIÈ H
Ð > ' H B ( FjÊ˦ÈzÉNÐIÄbÅrÎPÃqÅyËTÄnÅrƦÃqÅjÅrÆI
Ë :<ÃÌ +IËzÉ J ,/  032 4 Ç ÄnÇ ÐIÊ6Ë SËIÐIÊAËIÐqÅzÉ J,10 254 >JQÉ<ÎmÌ Ã¦Î 5</
Ë :<ÃÌ +IËÄ"É J,1032 41F
 R +¦ÃqÅ…Ç ÉNN
+ÐIÊ˦ÎmÅrÆIË;ÃIÄb
Ä +A9
È SqÅ…Ç ÉNÐIÄzÇ Ð 8nÆ<Ç Í¦Æ;ÅrÆ<Ç Äw!Ë R +¦ÃqÅ…Ç ÉN3
Ð 8¢ÃIÄz ÃÅ5ÅbÃ<Ç ÐIËTÊ >QÅrÆI
Ë M_ÍTÉNȇÈzÉNÐ OWÊNÇ Ë‡ÍqÃqÄbÅ…Ç 6Ð 5UÈuÃIÍIÆ<Ç ÐIË SËIÎ JYÉÎ_ÈuÃÐIÍTGË L
Ë|ÅyÍ FH I"Æ<Ç ÄlÄ +575<ËTÄyÅyÄjÅrÆ<ÃÅjÃzÄ#È ÃÌ Ì Ë¦ÎHÊNÇ ËÍÃIÄyÅ…Ç 6Ð 5'È ÃIÍIÆ<Ç Ð¦ËwÍÃÐiÃIÍIÆ<Ç Ë :IËÅrÆIËząÃÈu
Ë 5ÉNÏ ÃIąÄ +ÈiÇ 6Ð 5ià :¦ËIÎY6à 5<
Ë SËIÎ JYÉÎ_ÈuÃÐIÍTË
ÊNÇ ËuÍqÃqÄ#Ç 6Ð 5xÈ ÃIÍIÆ<Ç Ð¦GË H
?>4*AMH3b/ 24&:ØÙ × J4
ŠHŠ
ŠDJ¢RM[g@3RQ'Ú"1
3P‚@FE( /P3

ێÜAÝ<Þ$ÜAÝ<ßAàáIâHã äUå‡àNåWæàNäPçIÜè™éSê7ãAàIç
ê)âHëAàiì_â ämáIâHãWÞ#âê ÝIáNíé î Ýïè Ýä5è çIå@í

$#

Section 7.4. The reformed pQ2 diagram

'     "' " 
"   " 
"#
     
  


5Q €x‹)„
 
* #
  
 " 
"   6
"  -  /i
" &   & v  '  
& 
-
/i  6'-"
 -i ?  $'  '

5Q €H7„
 

 { 
 G  '"- $

"   i
1 " &    '
"   "  /i
1 6'-" &  & '

6 i   
G"  
"
G "#  6  $$"    " 
# 6
  8i     
 
"  


Y i" 7 6'-")

6  6 "  
 G 
  fi "# 
$G 6  -" 6 6 i G #
1 6

 G' 
"    i    66 i     #-

-   
"  6   i  $ 6
A 66 i 6
1
fi "#?   
 ?' 
" '"  
 '" 6 _i"#- N
  6(
! ?" "  '# i 6
  
   "# 6$ /i
1 6'-" &    v '
"  &     ' 






 › 

”r 5š › ˜–™œ”'P•˜ ”O˜ ˜ ›
Q'Q Ÿ š ˜
Q<š –™” I”O—Y

1

ž




liquid
metal out

the moving part of
the control volume
atmospheric
pressure

UP

air flow
in
PB 2
PB 1



friction is neglected

kK/ 2DGH3_( 5Q Nƒ¢½jfŽ2
(C)(3517FN9I? &)(6x1:I/ ?@>
L¢:<&)('?>4C:<3_>4FAc)>4FOG76(;>Lm:<&)(x&M -43517GHF / ?o*
/ 9T:T>DC'{'/ :<&':<&)(*HFOG7C)2
(3
17C -S*)1
3Y:;>Lw:<&($F / ŒDG
/ -S6(:17F





{

   

f8?>DCN:<3_>4Flc)>4FOG76([1)9 / :E/ 9s9&)>){Cd/PCXkK/ 2DGH3_(
Q ƒ^/ 9s?A>4C)9T:<3rG)?:T(N-Z:T>^9T:<G -MS:<&([(¬l(N?<:B>
L':<&(
*7FOGHC)2
(
3l-0/ 176(:T(
3#J7b{&
/ ? &E/PC)?FOG)-H(A9i:<&(E*HFOG7C2H(3m{'/ :<&:<&)(B3_>K-H(HJ¢&M)-D3517GHF / ?E*/ 9:T>4C0JH17C -s9&)>: 9F (N(c)(HJ
R7GN:‡{&
/ ? &E-H>7(N9C)>:W/PC)?FOG)-H(x:<&(=&M)-D3_17G7F / ?sF / Œ4G
/ -$>K3l:<&(=F / ŒDG/ -S6x(:17Fp#(:q„ Qu%'&)(o?A>4C:<3Q>DF
c)>4FOG76(U/ 9
9T:1:I/ >DC)1
3QM;1
3Q>DGHC -x:<&(@9&)>:w9F (A(Ac(;17C -U/ 9‡6>
c/PC)2W{W/ :<&@:<&)(x&NM -43517G7F / ?W*
/ 9T:T>D
C Qnf;*H*7F M/PC)2x:<&(‡ˆj3Q9: F 1A{
>Lu:<&)(3r6>0-
MHC 176/ ?9J¢{&)(C=:<&)1:':<&)(s1:<6>H9*7&(
3y/ ? *3Q(N99AGH3_( / 9o1)99AGH6(-ZC)(A2DF / 2K/PR7F (E17C)-^C)(A24F (?<:I/PC)2
:<&)(-0/ 99</P*)1:I/ >DCU(C)(3_2MNJKM
/ (F -H9
– @˜ –
QŸ   Y
! ”H› ™œPŸ P Q”O H› 
š –™”¦”PP  

{       {   










  



 

{ €








 D 

D

%{ 

 D D




{

40 '

   DD Q€



†PCU{x3y/ :I/PC)2$(NŒDG)1:I/ >DS
C  5Q €  „JD/ :@9&)>4G7F -SR(sC)>:I/ ?A(N-=:<& 1:i:<&)(U>4C7F ME? & 17C2H(E/PCU:<&(B?A>4C:<3Q>DFc>DFOGH6x(B/ 9
P/ C$:<&(s9&)>:W9AF (A(c)( Q%W&(&(1:':<3_17C)9TLy(
3i?A17CSR([C)(A2DF (N?:T(N-mJ¢9</PC)?A(B:<&)(BˆjFOF /PC)2“*3_>0?(N99/ 9c(
3YMZ3517*
/ - Q
%'&)(3_(“/ 9[C)> 4>){ /PCN:T>^:<&(d?>DCN:<3_>4Fnc>DFOGH6( TC)(A2DF (N?<:I/PC)2“:<&)(d1
/P34>){‘/PC:T>“:<&)(^R 1 ? ¡S9¦/ -H(>
LW:<&(
*7FOGHC)2
(
317C - :<&)(E? & 17C2H(U>L;¡)/PC)(:I/ ?(
C(
3Q2
Ms>Lu:<&)(E1
/P3|J0{x&NM J)„Jl17C)-:<&(
3Q(ALy>K3Q(B:<&(B9q(N?A>4C -$:T(3r68>4C
:<&)(E3b/ 24&:W& 17C)-=9¦/ -H(?A17C R(o>46/ :|:T(- Qf;*7*HF M
/PC26x1)9q9@?A>4C)9(3Qc 1:I/ >4C>4C:<&(?>DCN:<3_>4F
c>DFOGH6(xLy>K3l:<&(
F / ŒDG/ -S6(A:17F
M
/ (F -H9




ƒ





€





 D

D

 

 

ÛaÜAÝÞ ÜAÝ<ßAàáIâHã äå‡àNåWæàNäPçIÜè™éSê7ãAàIç
ê)â
ëAà@ì_â ä¢áIâHãWÞ#âê ÝIáNíé î ÝAï è Ýä_è ç|à<í



5Q €
€K„

?A>4*M73b/ 24&:ØÙ × J0
Š
ŠHŠDJ¢RMg@3RQ;Ú"1
3P‚@FE( /P3

„

'




Chapter 7. pQ2 Diagram Calculations

%'&)(UR>4G7C -H1
3YMx{ >K3…¡'>DC:<&)(?>DCN:<3_>4F)c)>4FOG76(o/ 9i-H>4C)(RMo:<&(UF (AL5:'&)17C -B9</ -
(>Ll:<&(E*HFOG7C)2
(3m17C)-=?A17C
R(U(<’K*3_(A99q(N-SRM

   D
%W&(=6x1)9q9

\   

\


D   &

 '
4>){¿351:T(U>4G:@?N17CR(=3Q(
F 1:T(N-$:T>=:<&)(o271:T(oc(
F >K?)/ :…M

  
)*8

F=1)99'?A>4C)9(3Qc 1:I/



 

GHR)9T:I/ :<G:I/PC2=(NŒDG 1:I/ >4C)9

&
  
 ( ' 

  < 



 





5Q €-,H„

5Q €H7„  

=%

 

&

=%

 

{   
'

5Q €H„


'

5Q € 

„iM/ (
F -
9

{   

 






 


 

5Q €HH„



5Q €HƒH„



5Q ‹
ŠH„





  

  &



 /'    


 < $ # 

.

 



H„‡/PC:T>$(NŒDG)1:I/ >DCT

)*8  

&
 
  '   *  &

  
!"

    


 

5Q €
€& Q €


 
 
 
NΠ S

!



>4CU>4CU:<&)($F / Œ4G
/ -S6(A:17F0/PCU:<&)(U9&)>:‡9AF (A(Ac(U17C -=:<&($3rGHC7C)(3"M
/ (F -H9

 <    
!

5Q €H‹H„





&



 %



'
6



 D

%& '( )*!+-,).N’)' )/0 123!+-,,4   56 ((



 

  B
 ( 
 79G8 E
F




:, '-,%( )



 



 



 
  
$# 








<



 D

&




&   =% '  % ;
 ;5(; =<
 &
\ (
\ G '
F  
798








<





$#



 D





'

A‹„



5Q ‹



5Q ‹
H„

 !">  Œ ?)@A  „






Q ‹HH„>  

B+ ).    
C-,D
(% E5  CNŒ0  T

  

  
 

 %





 
  a{  
!





Ù × G 
ŠHŠ
Š GJI LKMRQ'ÚNP‚@FC0
562F
,ØH

<



$# 
 D



5Q ‹ 


ێÜAÝ<Þ$ÜAÝ<ßAàáIâHã äUå‡àNåWæàNäPçIÜè™éSê7ãAàIç
ê)âHëAàiì_â ämáIâHãWÞ#âê ÝIáNíé î Ýïè Ýä5è çIå@í

+

„

Section 7.4. The reformed pQ2 diagram

U3
‘‘common’’ model
realistic velocity
po

ssi

ble

ma

x

 Q HŠD½


 



 5Q A‹7½
/
(

,



,D
(% E5   G

 05

A1

D

'!  05-  '!+-,6 1 
9
; G

6= !M-, E  52A 

).05,  '





!  05-  L!M-,


 ).   ;

 , < ’6
2     5Q ‹  „' C   5)C6  5;(;?!  5  L! AQŽ† D5; I  2,. -,@,
-, 61 
 E  )@2(  6 6
050,2@ ˆ$    G

 @,

¥„ -, -,
(. E5  
G ., -, 6 1 
%E  )@( G
 6 6  050,2 
Q N     G -,
(  5   G 

Q
 , CE5;50   I ;52 A )@A- 
 0 
Q  , G -,
    ;A' 
6 1 
EE  )@2(E-,0+50
;(;M).N
 ’)C): E5   FA;@ˆ
   5Q 
Š7„ Q )@
MA %(-0 2,M
-,06 E 
' .-,C6,- 5M .-,.  -0  G )@
 -,0 .   E5;  )%N’)' ) 5; .E525RQ   -,
 )% 1+6 1 
ME  )@2( G -,
(  E5    6 6
050,2U
 2
 I ;5; 
  ¤  6 6  050,2 ˆ$   Q
0$ 
C61 
$  ).( G -,%
(  E5    66  050,2   I ;5;   -,'6
2   % ¬ 
 05
05- 
C D-,   + M 6 6
050, E
 +
 Q , ).-,). 5; < ’6
2A-  D!" -, ).N
 ’)' )/
(
 E5   A7
 ¡-23A2
 J6
2 G  0-,
!"
  . M,
 @ ,

 Q?2+
 = G !"=6405- 5; 6  6A; G
-, ).N
 ’)')  E5   5;   P
 A   
 „ I  52  5 ( I  - 
 5)'6 ;(=6

4 ) 050,
 K>  " !"5- 4Q





v

!

v

!

|



! #

! #



!

!



v

v

! #

   / 


 





 3



,a
 Œ2(  ,  
 -, E  52( 
)%050,  6 0  , £ 5  ?     ;+Q 
).N’)D  -,D;  2  @! -,  .52( 
).05, =D)'(3 0
(A 0  0.,=52 0  
 L,0 6 6 Q.†   L)'6 A C(     ?-, -,   ;5  !.-,   Œ  )@2A  ( -, 52  

N
 Œ
2 6
 = Q ,?6
 = G = 52 ’-405-%! 
)  )%050,  G 6 0  -,?61 
 E5  
 0.-,$64 )@(  Q  
 =    P ¡-=( ; 
 3'6 E522A+A.-,0>6=<’-405-  %  ).N’)D  Q
K0A
 ‰  A
 ˆ$ ?  ).    ).050, D- D
 ¬ ;5-









 




  

 







«   E C52A 
).05,  ,0@ 50,0405-(" A 5 50  C '-, 6* 

 )
-,0@-,E  52( 
)%050,  ,%-, (§ 5)')@ ¨L5,405-(F ( 5 G
  

 

ÛaÜAÝÞ ÜAÝ<ßAàáIâHã äå‡àNåWæàNäPçIÜè™éSê7ãAàIç
ê)â
ëAà@ì_â ä¢áIâHãWÞ#âê ÝIáNíé î ÝAï è Ýä_è ç|à<í

Ù× G
526 F
,ØH



5Q ‹K„

=1Q   )D 

 

G -,

 ).   ;

Š
ŠHŠ GJI  KMRQ;ÚN"!@FC0

'

I—  ”

Y•5š –P”|š –Q• ”O”
YPœOš ›



š –™” I—PœP–Y› P”<œP–P—P• —™œOš ”P• › ˜ š › œ¦—™˜
 P”O˜ š ›
_ 

'

Chapter 7. pQ2 Diagram Calculations
6=95; I  <’6 ;A ;


   '     
  &







5Q ‹
‹

@,
   N-,.).050, @6=  ).    I 
   #   Q  ,@).N’)') 6=!-,  ¡0 
 ! ).050,   &  Á  !-,@  )%   ;  4( G  G +,@ @ 
 
 Q  Q   
;5)')@ ;

(2-
 %-,C6
522 >A -, H4(%5;50  M=-,@ 5   D!9-, ).N’)')/!N-,'6= Q 0
 
 
'! )Á  !  -,@  ! 
)
 (
&  G -,C4
 6=& Š Q 
   #   G 
I  -,2,0
,
 @  

 5Q 
 =; 
;5-A 
   Q .  )%  52C-,0@-, % 1L % I 
-, 52 60 I    C!-,CE '52A 
).05,   = 4 
2 !+-,  4( Q  , 
;  C-,03-, 
 ) I 3  ;   I ;5;     -, A)@ )'6
)@ ;(D! -, -,?   ; 
 -,
   I 52 I 
6 !" ).;  -, %).05,  G  0 -,
  . ? ;;(?)@D-,
   I (   
).050,    Q

†‹



%

vxw y

‹


 %  "  ( 
 5+6 i 6'-" ?
$
 "   "

 

(77 '(

 

vxw

‹




'(7



@

$&%



%('

696



S@A1 ,F &<


1
1

5

. ,

+6 i 6  P
"#- ?  "  " 
'G' N
6  '"    6 " N#-
 
6 :i  "  
"#-N 6$ :i Ai "  +" " = 6  
"   

$5



!#" 
" 

-"

@

$&%


 
k  0k     !    
   
  
  


k !
  

 

!
 
 


   0 

  

' '

'

%



 DA<, FG1E<


1

./1

5

. ,

%= 0 5 A- 05- 
 ?6>-,' 50A- 

 I 
  -,C   C!+-,D((()
-,).
  -0D 0     I 
 !"
C ;( - 52   5-(

"$#&%

  52)'6
2   I    

Q

')(+*-,/.1032546178(+*
*

B+
    -,?-,;A 6 ;522'!% ;!" ).  ,  L2 
 L-, 6
E5;A:9   ((() Q 2-

 
 2  .C 5; 52)'60 ;C,3( )@3-,0M, 5; .4   <; 5=  -, 2 
 !"-,D)@ 
  (A @E 
-,C?> 6"). (C ; ,
( -, 6 E5('   
=1QA@ 1 G -, )C6 A 
6  ,    I  ,
 ); 
5 = C2
2. M( -   2 >)%050,  I %4-,M,); 5=  2
52 6
E05 L
EB
 ;0     6
E05-D  ,
  50,; 6 D   -   504 6L6   I   0 ). 1 > 
52A 
).050, C
 Q F  % +-,%)@(&)C6 A 9!F05( -,%6
E05- 
Q  , +2-
 D6
522 = 
  
 -,0 
 (+4   
.-,.    0' >
D
 ;
2&A)@
 =E = QGF+
 = G
  
@-,%6
05- 
E 
 D)'050, )@
%!F((= )@AM5;A2  0 50,; 6 ( ;A 2 
 C ? 0; 
 '504 6C   2A

HIH&JLKMK+ NO P:QGR/SUTVRXWY&Z U+ O WY[N\Y[P]RIK_^DP8R/S[Y\`[a T?NGbUO P[Q8c^UW`&YdO KXNeY&Y&R&f
h g G  iiiGJI LKMRQAjN"!@FC0
562F
,5H

kml Un opl nUq r$s[tuvxwGrDw+yCrDvz[lC{|B}~u r[z
}t€ d
r ‚tvs[tu+oƒt„}n[sD…†|‡ n?ˆ„{ nCv‰{ z[w8…



XW

Section 7.6. The Intensification Consideration
U>6F)@ ;(U9(A  
52(] x
Q F+ 05 G !"+
E  E '
;)@2-  G "!  5 0E     05--0 1  -,
C 
)@
C
 @ 2; ( &






 



5Q
~
5Q
~

-, 0
5   )C6 
!"
52 G  0   (!4C-,6=
D; )@ (Q
0=-,2 L50F (F ?-, ; 
 @, ( 50,;5= -,   32-
 ( A2  !
(  E5  ? 
  0 -, 
;52)')@ ; 4 
 Q 6A- I  D  =,0M( 5).@! 
) $ 0 5  5 - 
   G
  05 = 
% @-, I - ;A!$E @5;( 
D( ).~=- )@  QGF+ 05 G -, 6)' )   )@2(N -,
  @, 50,  152A>-,C ( F-,)D )' )/52(] Q F  G -, G 2 -,6 1 
 - D2( )D 
5( J   ,0 I 2 2,
 . -, 61 
=E  )@( ,  0 1
 @,
 )%D>)' )
(  5  ? 
50
;( Q
   
E  )@2( 
D ;
2     
E  52A 
).050, P
  ( 6 ,- 52 -   
-, =
,>! -, 61 
I Q !  G  ,03( 5,A  $
(M 6 6
C
 >)%  -,  
2A@6 1 
N
 ). 1 ;(ME  52A 
?).05, 
 Q 3 -,$!F05(=,3( I DA~
 =-  ( 5 - 
  C M-,  5
 6
50
;(L -,D2,  ; Q I  2  G -,   ; ?)@A  -,D ;,M( I D-, (.6 052@(
A   !4 Q , %
D
 ;
23-, I  50 >( I  !@ ( -,  )@%-, „
5 = ;A33-,  R Q



5Q

    !    






,
!"
 G -,D 5
 6'1 )@D,  

"# % $  '(     

&

   &  

 k   
k ' '   ‚ 0 ‚  '  ƒ‰ [  
 I‰ [  



I 

"# ) $ *   

&



5Q



@:, -, 504 6 '-,D2,  ; I ;5)@23-
  52  G 52)'60 (504 6'!+-,  

"#  $ *   

&





 *   

,  G -,6 1 
9  )@2(,03(

#  O
"
"$#/.

&



5Q 



5Q ,+

i

I   -,4 
 !



021 (43?065
(<0 *-,'7$79865
,ƒ6p0;:56p0 *-,=< (<4865
,ƒ6p0

 ;( - 52  M   6
E5;A+ ., 5,@6
2     & 5 A; ).~= 
3-,   ; D)@A ?> N " 
3-,
A   5;  6
E5;A(' 2
.52)'6   !"-, A   5;  
, F =
 !$-,'  ;  )@2A 



k l ?n o1l nUq r$s[tuv<wGrDw+yCrDvz[lC{|B}~u r[z
}t€ 8
r ‚tvLs[tu+oƒt„}n[sD…†|‡ n ˆ{ nCv‚{ z!rU…

h g G  iiiGJI 
526 F
,5H

-

 '

: ƒ  k  '  
   U ƒ      

.‰
  0[  ‚ 

k '  ' ?  
!‰. ' [
] 0


KMA@ jN"!@FC0

Chapter 7. pQ2 Diagram Calculations

'

'


/ E

 
[
   
‰    
 
  
0  ‚  

  
    

 6@( i %@ ,. ;( - 52  @ = 6 6   ; I . =)@2-,EN  I . 6 6  
'0E   0 6 )C6 G
 = I  5   
-,  C!9-,'05--0( -, )C 6   )@2-,E G $-, 6  $1)@2-,E  @
@  ,G
 $
(=)@2-,ED ;= & 050
; >-,@ ;( - 52  >!"45 (
 
 I  )'050, @dF+=2 G
-,  ;52 0L).-, G 5)')@   A;(E  C-,C 0(-  G 5;  5 A 5 - 
 I  D-, 4  @

'      ! -,L!"45; )@ A-
(; -,0  $
(C 6 6
C>).  L-, 6 1 
ME  )@2(
2% M52 -" I (D  0     !"
52.(>4L6 , 
-,   
;  ?)@A  @

$5

' '




  0 
 ! ‚





''





/ 
&
 ] 

  !
ƒ
  :‚ [ 



@

 C)% 161 
NE  )@(N50
;(2M!FA(NA   5;  G  0-, 2!" .-,D05- !"
52' 

 05 @ N     G D   
C61 
$E  )@( 5 (2 % ')% 1E6 ;A2
 !"$F  
C-,
  ; ?)@2A  @
8 4



"$#V"

 -,  5, 6(C  , I 2 2,. -,0 -,
5)')@  E 
4 )    0   : H6
052
 
;   ( 5 -
 0 -,
!"
 ,0  0 1 .,A  "! @  , 
!" )@; 6  E 
4 ) >

 ;-
E05 @  , ).-,). 52 $-,2 9 6
2  A  I A  ;(A I   ,;  5  ; 5 6" 056  2
>C ;-
E05 @  , ? ;5-(D!>0F C)'6 A C60
 )@2(
>%E  5 A;@  , ).-,?!
; 
  
-,E  5;( 
6
E5;A >.E  50A ;@  ,L6 1 
&E  )@2(3,D 0 1 !"@, 50,
-,L
(  E5   ,0C ).D>)' ) @ 0 # 
(  E5   G
@, # 
-,
  )@ ,0 66  
@  , G -,  ).D>)C)
 (  5   ( )D 2 @ ,-,=  050
;A 

-,L61 
&  ).(  1 
2  %  L 050
;A  -,'
(' 5   >  @ 3   ( 0  >
, I ; 6
6A( ( )  %-, 61 
9E  )@(= @

!

!

!

! #

%& (+*5-,ƒ6p0<*

"$#$#

')( *,+9
 -,0&-,').D>)C) > 4( G.-
    05C 0 -,0 -
/02143 5 #76 $
@ ~ @> ! 
/0   5 AA ;
')( 89(;:/K&F  D;   @++@=< A 
')( 89(;:



 -, )%050,  50,0
05(F ( 5%D; 

 0 -,    ,6 I  =
 2

')( 89(;: $ 0-, 
   2,6 I  =
 2
')( 89(;: 6 .,=-,+60
 )@2(
>-,0

MN 9M$O

 

.

?>  0 92= )
 
V

 >

6CB
6DE$FGH6 B

@+C

I N-,0  (!4CC;0 

6

 

 2 E
  

@ +A@

 

6  @, 50,'  6
 @-,'6A  I    JILK



HQP&J P[^:RIY+c^UW
R/S[Y<NT?'P +]cT[`!R + WYVKRO c?SV^ +UT ^ + a V a O WƒY+RI^ :S TYX[Y/S]^ +?W_KQS:KIRIY[NZV Y&KM`[WO [UYV$S[Y[WYT-O R/SO RIKdT\VXUT?P]RMT[QUY&KR
b?a Y]T]KEY]VCW^DbN\Y+T<a O P[Y+T?P\V_^T-O a aVDO KM`!+[KEK`T-O R/SaSV^ + 0T [U^ +]Rd/R S[Y N\T]RIY[WO TUa~R/S:T]R]^ P:Y&YV„f7^CT-O a a P[^:R`[S:T:WQUYbSV^ + T?PYS
Ne^DP[YS]f
Hdc0e~Y&K/O V?Y\R/S[Y8S?O KIRI^?WO `VT?aXUT?a +[Y
h g G  iiiGJI LKMA@AjN"!@FC0
562F
,5H

kml Un opl nUq r$s[tuvxwGrDw+yCrDvz[lC{|B}~u r[z
}t€ d
r ‚tvs[tu+oƒt„}n[sD…†|‡ n?ˆ„{ nCv‰{ z[w8…

Af



















  "!$#% & #'()
* ,+

-/.10325460798;:;7=<?>A@;46@CB3DE.;BD;F GIHJ85@;46</KL.MGN:E8OB.E2;< 4NBP8RQO034=@;F 7MB(.A:
A. 767=4SQTBP.E2;< 4VUW.E<?>A4VX?8Y0Z760PF?B3F 79.E<TU=46< 8576F?B [,X\8Y0Z];< <;Q/460P764=:OBP.=^_4SGN< 8AK
460B`DE.E:
aOb_ced6dMd
fIgih5jTk?lnmLoprqLk?s

tvuNwxOyzwxO{
|T}~ €‚;ƒ9„P…T†n‡5ˆMƒW‰ …nC}Š}‹}Š}‹}Š}‹}Š}‹}Š}Š}‹}‹}Š}Š}‹}‹}Š}Š}‹}‹}Š}Š}Š}R}Š}Š}Š}R}Š}Š}Š}Œ5|
|T} Ž’‘O“•”=ˆ1…n–C–—…nO˜™–—…T†O“;š ›œ}‹}Š}Š}‹}‹}Š}Š}‹}‹}Š}Š}‹}‹}Š}Š}Š}R}Š}Š}Š}R}Š}Š}Š}Œ5|
5ž ŸOž\ ¡J¢1£S¤¦¥=£M§ ¨ª©C«O¬n¥6­®žJžVžVžNžVžVžVžJžVžVžVžJžVžVžVžJžVžVžJžVžVžVžNžVžVžVž ¯Y
5ž ŸOž Ÿ °£S¥6±O²\³9´¦§ ¨Iµ¶«O¬n¥6­žVžVžNžVžVžVžJžVžVžVžJžVžVžVžJžVžVžJžVžVžVžNžVžVžVž· 6¸5 
¹zº ¥V¨S»;¼T¢½£S¥J¨ º «1¾I¨¿­\¥6¥=±A¥ÀžVžVžVžJžVžVžVžJžVžVžVžJžVžVžJžVžVžVžNžVžVžVž· 6¸5 
5ž ŸOž Á °£S¥6±O²\³9´¦§ ¨’³6²?£S³6¼_­‚¢1£I©C«O¬n¥=­™žVžVžJžVžVžVžJžVžVžVžJžVžVžJžVžVžVžNžVžVžVž· 6¸AŸ
5ž ŸOž  µ¶²‚­\­\¥=£M§ ¨N¨S»;¼_¢1£S¥J©C«O¬5¥6­ÃžVžVžVžJžVžVžVžJžVžVžVžJžVžVžJžVžVžVžNžVžVžVž· 6¸AŸ
|T} Џ’‘O“CÅ1ÆOš ‰ †5‰ ƒÈÇC…OɃ9‘O“À”=ˆ1…n–C–—…nO˜™–—…T†O“;š ›}‹}Š}Š}‹}‹}Š}Š}Š}R}Š}Š}Š}R}Š}Š}Š}~YÊ5Ä
5ž Á5ž\ ¡J¢1£S¤¦¥=£M§ ¨ª©C«O¬n¥6­®žJžVžVžNžVžVžVžJžVžVžVžJžVžVžVžJžVžVžJžVžVžVžNžVžVžVž· 6¸EÁ
5ž Á5ž Ÿ °£S¥6±O²\³9´¦§ ¨’©C«O¬n¥6­\¨žVžVžNžVžVžVžJžVžVžVžJžVžVžVžJžVžVžJžVžVžVžNžVžVžVž· 6¸EÁ
¨S»O¼_¢1£S¥J©C«O¬5¥6­ËžVžJžVžVžNžVžVžVžJžVžVžVžJžVžVžVžJžVžVžJžVžVžVžNžVžVžVž· 6¸EÁ
Ì ©CÍn£S«½±A¥6¬,¡J¢½£S¤¦¥=£M§ ¨I©C«O¬5¥6­ÎžVžJžVžVžVžJžVžVžVžJžVžVžJžVžVžVžNžVžVžVž· 6¸EÁ
5ž Á5ž Á µ¶²‚­\­\¥=£M§ ¨N©C«O¬5¥6­žJžVžVžNžVžVžVžJžVžVžVžJžVžVžVžJžVžVžJžVžVžVžNžVžVžVž· 6¸EÁ
5ž Á5ž  ÏÐVЮ§ ¨’©C«O¬n¥6­ÒÑÔÓO¼_©C¥9£S²‚³6¢Y­/©C«O¬n¥6­ÕžVžJžVžVžVžJžVžVžJžVžVžVžNžVžVžVž· 6¸YÂ
|T} Ö ’‘O“Ø×*“YÉP…O„`–—“A† Ù,…T†O“;šÚ}Š}‹}Š}Š}‹}‹}Š}Š}‹}‹}Š}Š}‹}‹}Š}Š}Š}R}Š}Š}Š}R}Š}Š}Š}~YÊOÖ
5ž Ânž\  ¹zº ¥J£S¥=ÛÜ«Y£S©C¥M¬v©C«O¬n¥6­ËžNžVžVžVžJžVžVžVžJžVžVžVžJžVžVžJžVžVžVžNžVžVžVž· 6¸YÂ
5ž Ânž Ÿ ÝJ¥6¨¿²\ÞEәÍ5£S«;³6¥6¨¿¨ßžJžVžVžNžVžVžVžJžVžVžVžJžVžVžVžJžVžVžJžVžVžVžNžVžVžVž· 6¸Eà
|T} á âL‡5–C–—ÆE„3Çã}‹}Š}‹}Š}‹}Š}‹}Š}‹}Š}Š}‹}‹}Š}Š}‹}‹}Š}Š}‹}‹}Š}Š}Š}R}Š}Š}Š}R}Š}Š}Š}~YÊ5ä
|T} å æJ‡O“Y›WƒW‰ …_;›Î}‹}Š}‹}Š}‹}Š}‹}Š}‹}Š}Š}‹}‹}Š}Š}‹}‹}Š}Š}‹}‹}Š}Š}Š}R}Š}Š}Š}R}Š}Š}Š}~YÊ5ä
ç5è

Chapter 8. Critical Slow Plunger Velocity



3?065X46
< <75-,ƒ6p0

#




  !"# $ %
'&)(*+,.-0/123 (4-5.-5
,26(4 72
8:9;8<
2.-',.-= 2
76 .> 8=(  ?@) (AU>BC8
D>.8:D8E
.M9'&
' :*F#(48E5 '(  66G @ +4(B#( H 1?I )
J8<
0/1(B
#(BKD23 (4->(K9 8L.-M< 2)
.M9'&
' $(B#(  N?)2(4-' 3 D6 ;
5
#&!(B>3 (4- @PO!.-.8$ 6
3 (K-:(*RQ.
ST-U
.-8=-R.-<a<T( <V 6G' Q;S < <4@ R
##D;KD H +*W(BX#KD2.-'&:
.I9&
' +(B#( H 1? @Y R26
9M
2 G'Z9?8=(G.-'&!'[\D-'&Y

2 K2$ 66,
 %( =-'('=-M
' +'M2W 3 2
 6 (']\D-&
G (^2 1? @`_ ;
-' R
R  % 6DP =#
:(M ?K#
D  2 /3D8:^a= 2C
' C^ 02D 0 %[.-
#G (4D' ;
b
>

22 - ? Oc?6(4DP'(4D'&4de@ @
'7
2(48M8=(4- $8=(^.a
 %( =-'('=-+
' bfY
N9hg `8=(^.a <  YU >'-' H (4-' R8
<9x? j >6G „2 ='ia
O!.\ #ja
-MS"k`k`g b8<(B6
#;#6 0-="> %b> @X';9
' H 2b*FD-
8<-%
1>(B# X(*^ %;8<(B
##6 %- @Cl
Fa''<#*W(B18=P
-'
h .8:  P8<(B Y6 32m.9 @C_ X*W(K\ ('R:9?`U
-  -
-'7((BX6  &4-PnV2  @ Q *UoC
# aK
' $D 6D'
 ;4D'6 %3 (4-' `
>$&^ G-M
'$-[(*p:2'
A @
%q

0 1$rtsXu`v7wv!x<y

#

wv
<MrzN{


_.-, $ 023 (K-'
F2(K8:8=(K- I8=(^ P
#6 02W.9 @ <K.-'26!
H(4D
dI8<(B"
 %(A|-'('=
' =fY
19Fg :8=(^4-6G}R(B1| 6G-9?)  +('=-:2>
(BU@ ! a^ %6G#
('b8=(^ '
G':

> @
'6 08=(^ <
#)6 32m.9~> (Z
G')
2 
>+ 2D#M(*R=
;C
' $.-)'#5}
o€VO '.Fg
8=(^ @5B.# 6aX
, 02W.3 (4-[(*;fY
19Fg !8=(^" $&B G'-7
; >6G 2|g 1R(I8<(B P
 (K-&, 
O!.\ hg 8=(^ ‚<
>:6 32m.959m % >^? @+l
'  ?a'S"kk`g =-D8<m 26
K8<(BK  02W.9 @
ƒ+„W…+„h†

‡!ˆp‰Š y ‰‹ {Œ u+Ž yp
1
vp
vw

2

H
h1
v1
P1

h2
P2

L(t)

^ &4D>: @ +YQ‘ 32'8<
3 2<(*YC
G*W(B18<
3 (4-).-: %%
3 (4-
>?M2(B(BUB.-
6
' 6 32m.3 (K-.-)  %23 (K-[ 9'
' 0,(4-!(4-' (*b,8=( %=2 I
.-)!^  26
' %3.-&
> %
U2 fY
19=+ ç ’@%@`fY
19Fg P8<(BB
 (4- ?: )
\D& >4('“.-
)2.U2D
Y2#( % € 023 (K- @
Y” ^ \• V'–3—W˜1™>š ›œX›•\VS3—m˜Wž3Ÿ —: •3¡6š •3žž3™>š •H¡c¢ ^  £=¤¥™o›\V–H›0˜Wž!˜1–\Vš ž%—$¦4§H›š ™dR ^   Vž3¨H›H™e˜1Ÿ ž3•0˜$›0˜+©}§3ž!ªp§š «6˜m›0˜Wž
¬ •š XHž3™.—1š ˜ S
­F©}§3žR®3§›Hš ™^«H¯9^  :°¥ž3¨0˜±¥›0˜Xª} ¬
P ^
˜ [žRY› V VžV<š •C˜1§3ž`•3žh²H˜}›\V0Vš ˜Nš «•
c^ATK«\• VžH™Vš ¯¥¤4›H;™ [ž3™K›\• Vœ ›%˜WžH)
™ e4™ež Xš \® W§$› XHžb"ž XHž3™4®«•3—1š Vž3™.ž V=˜1§H›0˜"˜1§3ž0š ™^˜1§3ž`Ÿb« VžHœ —9TKžH™ežb—hš Ÿ¨œ SR˜W«H˜m›œ œ SR¯#›œ —mž±
³ ©}§š — Ÿ « V6ž3œ T¥›3?— Vž X3ž3œ «¨$ž V=›0˜}ªY§š «˜m›0˜Wž ¬ •š XHž3™.—1š ˜ S]["S´`š œ œ žH™Uµ —X¤T™.«–¨+š •C˜1§3žCž%›3™#œ S¶3··¸µ —%±

2(46?m &4J¹º a4’»»»Ka¥9?¼`A@}
.€"OM.

½A¾6¿À!¾6¿Á6ÂÃ3ÄÅÆPÇÂÇ;ÈÂÆ.É3¾ÊeË5ÌÅ6Â3É
Ì'ÄÍ6ÂCÎ#ÄÆTÃ3ÄÅ;ÀhÄÌ¿3ÃÏ,ËÐ ¿ÑÊ ¿ÆUÊ É3Ç`Ï
ÒÓ

Section 8.2. The “common” models

_o-; 023 (K-BaR_
0.8:#(G' <'<8<(B( .-'2\D'
-?<&6(K8=>?=2#( 0 %23 (4-; =
-?;G' (^2' N?
 #("  @

}(4-' H C
54D2
-?52>( % P %23 (K-@= 5
Z  KD 7
) G'
-'I
Z\D-'&8=(G.-'&c*F>(K8
'  6*U()'!W &K6a^
' + 6('<-M.-,B &4D#$ @ + @YQb % D8$.-'&[
KD'
' B $ 
? >4('  +6 %%
9  6!
*U
)G'>? '(BoPW (^,(*R3.8=aV
5D- 4D''' &K6aa"
-,
5D- KD':C
G':G' (^2 1?a 
+aT*W(Bb
!&B G'2(K- %%
-!\D-'&G' (^2' N? a 
I
#,2>
 @~;7  KD A.-5, D9 %#
5

I(*C
G5
3.\.aV  :'' &K6a  aV =N8P.-79? [.- 3
"\ @<-2P''' &K6a aK? >266 '[ &4+(*
'M '(; 6 66Ga  aT>M.\"9) 
' .-& @='M 6
' 6.-'&(^262D# 926
D' %-(, KD. .9W.D8 26
9,
2 6G %6IB &4D#, @ ’
@ @ (B ) 8
\ `'

- Ja
A> >423.-'&cC
G'[*F>(K8 '(4(  
C
\K

> > D 3.-&Z.-
-[-'
-25
.b-U
.-8<- 065B &4D#) @ ’49@ @:D a¥,#*W1#
H D
3 (4-P ='-    .-$2'.#2D
K 6'
   @C.-=< 2<26
' 0P-'(P 
' .-&P(B¥
#% >423.-'&
C
G' #6 6D  @

¢U›£

initial height

¢ [£
B &4D#$ @ ’ Y Q‘ 32'8<
3 2(*`#%>423.-& C
G'<*W(B18<
3 (K-).-: D9
-'! 6DY2m 3 26
G' (^2' N?
_ $ =
' H  (I8=(^4MC
G  [2(B(BUB.-
6 ='
M8=(G'
;' C
GMG (B2' N?a"
' = '('=.-^ &4D>: @ @ @   M'!8=(G.-&[26((BU^.-'
aB$C
G'   %
3 (K-'
>?aB'!\D-&R8<(G'6 $9
2|:

 ©}§š —V\› V0Vš ˜Nš «•C˜W«C˜1§3ž «™>š ¡6š •H›œ'¤4›H™;[ž3™Wµ —X¨H›¨ž3™4š —HV6ž3™>š XHžV§Hž3™.ž±?^›3—N—h–ŸbžVC˜1§›%˜}š •R˜1§š —V®%›3—mžR—m«Ÿ žRŸb›0˜1§3žHŸb›0˜Nš ®—
}š œ œ•H«H˜Y§–™e˜"˜1§3ž`¨H™.ž—mžH•0˜m›0˜Nš «•±

T

ç5ç

½~¾6¿À[¾6¿Á6ÂÃ3ÄÅÆ$ÇÂÇ;ÈÂÆ.É3¾ÊeË5ÌÅ6Â3É
Ì'ÄÍ6Â`Î#ÄÆ¥Ã3ÄÅ;ÀhÄÌ¿3ÃÏ,ËÐ ¿6ÑÊ ¿Æ#Ê ÉFÂÏ

26(4?m &4J¹º a^’»»»Ka¥9?,¼`A@+}
.€"OM.

Chapter 8. Critical Slow Plunger Velocity

!G' (^2 1? 
 
aV
-''  KD Z8=(G'6 =*F>(K8 'm &4(' 6*U @ ¼b
' 6Z .-'M 6('` +
%
3 (K-'
o?M26(4->(KG'(4\D8=@
1
vw-vp
v=0

2

2R
h1

v1
vw
P1

h2
P2

L(t)

++')  ! 4$$&#")% %.' /!$&% '' +6/ (*$0)$' $7 1 ('$0'$&24*',2 $&+'$&-'2 % $ 8
3'9  (: ( )A1@:8 BA' 3 \+-)5,A  :( '';+&<$=2 $ 3 '>2$&1" C'-&?$ ?

' $2 % D

B  &KD#: @ @ YQ 02'8
3 2<(*X'$C
G; [8=(G.-&[26((BU^.-'

O
' 0 2(4-' %oG
3 (4-P(*p')  4D .-P:26(4->(KG'(4\D8=)>
 A



      


 @@
B
='# ` }'< (B2
HG (B2' N? @C-' 4D
' H h 
?2(K-'^ 3 (4-' a6'2(B1#6 (K-'^.-'&=
G#
'&CG' (^2' N?
KD'
 `'!\D-'&"G' (^2' N.? 
3 
 @ ’@
 B  
     
Qb % 6D8$.-'&
b
"#
-' *WB2
-<9=-&4 2:92
D 0R(*^'C 6(B> >(^266 % p4D#
3 (K- @Y'#*W(B#a
  4D c8=6%
^-' H 1? = 2[ <
M*FD-23 (4- (* 8:#
D#@2
-9M
' 0 D8=(c9M2(K- %%
- @
R-}':
9(G'$
' 0 D8:3 (4-' a KD'
3 (K-  @'@2
-[9P H.8:  4 (

   

E 
!  F
G  AH>  JILK
N
 @ @@
M
‘'#PO+.-P 26
' 0:26
-P%
|G
\DP(*$(Bp’ @ ;D' a


 @ U@
RQ TS  L
XXWW

E 

='# Q VS  F  II BZYY  =
!^.8=-' H (K-  % +*FD-'23 (4- @$S4D
3 (4-  @ U@2
-9M#
-' *W(B18=c.-(
^.8=-  (4- 6 % C*W(BN8 
^]._&`#a
Q VS  L  \  [ 3
Q VS [  L
^]._&`VcA
6b  
[ Q   S   XZ
 3
='#  [ edLdhfg @7Qb % 6D8$.-'&7-'#&?I M26(4-' %>G' cfY
19Fg 8=(^}
' % D8:3 (4-@aY
-'JD-
2(K-'^ 3 (4-' P(*P-'6&K  &B.9 7
$#
-' *Wha '->&?c26(4-' %oG
3 (4-5KD'
3 (K-*W(B'Z  KD  .-,
2(K-#(4G(K\D8= %6[^ &4D>P @ @@;#
 
k lon qp 
 
  
E 
!
N  
u l 
 


 X m
v 0w x@

r
ur
Bji
its
y —Nžž¦4§H›¨0˜Wž3™Az¯o«™^›{žF˜m›š œ ž|{}{š —m®H–3—m—hš «•
2(46?m &4J¹º a4’»»»Ka¥9?¼`Zw}
.€"OM.

½A¾6¿À[¾6¿Á6Â[ÃHÄÅÆ$ÇÂÇ;È'Â6ÆoÉ0¾ÊeËcÌÅ6Â0É
Ì'ÄÍ6Â`Î>ÄÆKÃHÄÅ;ÀhÄÌ¿3ÃÏ5ËÐ ¿ÑÊ ¿Æ#Ê É3Ç`Ï
~€T

Section 8.2. The “common” models

='#

  
 L 
N 
   \   
N
q
p
v 0w è @

 
 
 
  j[    [ 

n
'= 6'
=*m
2(BFa qpa4 +.-#(BKD2M(
22(KD-b*W(Bp( % .9 =G
3 (4-' C(*"<G' (^2 1? >(" =

%23 (K- *F#(48
7n D#\D'& 4(' w
Y( '
:.-[^ !26
' 3.-'&¥aT' 4('] D' '~9?['5\D-'&
-)2
-!9$26(4-' H #)
' `
- .- 
4(' .-(!
:KD'2Fw '=1? 26
  -D8M9Y a^
-' *W(BV
G
\D=<-o?! -'&: C&K>
T'
- » Aa= 2: ;
>&T'
-P
-?$ '(R 6 66GP96 ?$
; 
'  1R(
(BU> +(*`8<
'&K- DNw
' > % 6D#P.-P'$&
' <
' %P2
-)9P
' 0 D8=)(,9P2(4-' %
-Fw 'M?4#( %%
3 2M> % D#P.'!  4D 26
-9[>#6 %-$9?   v 
0/F
U
-'
8\ ç x @6a='#    ':2-p(*Y':2#( %
%23 (K-M
#
w`(BX
)2(4-' %
-=  KD )-' H 1?: KD
3 (4- v Aw x@`26
-9)#=m F-)
' 



 
#


qp

 
!  L 

  
     l
    l
v 0w @

 r
r
n
i
i
fY
N9 v
-A
 >6G 2|@ D;  KD'
3 (K-,\D  %6G#
T&(48=6W 2
">
3 (4-' . 
' <') %(#
\D3 (4-!w Y#$R:2(4-3.-D([(49%
.-M
-
-
 ?3 2
 0(4\D3 (4-w¼ "-.-&[
)B.8<-' H (4- 6 0 =
#
8=6
"$#
'
%
v 0w ç @
"$#
 S



}3.  &'.-&["- 3 (4- v 0w ç @+
-5#
NU
-&^.-&!4D
3 (4- v Aw @?  
p (    l n qpt j[     '"$# p*(    l  [ 
'"$# )
v 0w»@
+ (K G.-'&!
 KD'
3 (K- v 0w»@R*W(B "$#Tp !
Fp26
-[9$*FD>R>
1U
-&)(!?  ,
W    W    L
"$#Tp 
-. 021 W
v 0w!'@
/ .
43 6Y 5 I 87 I Y 
qp
5 I  7 I :Y 9 
n
fb G'-+ D9 %#
<'' &46a KD'
3 (K- v 0w!@X26
-96G'
\D
=*W(BB "$# pa
-'='`26(BN#6 6(4-B.-'&
\D-'&XG' (^2 1?ca 
.w;= 2 <"-'Z9?) 4D
3 (4- v Aw ç @tw=; = %(4\D3 (4-M.\"9#*WN#~'#'.
' `<
 ;F-'#&?: 0(4\D3 (4>- =0w
ƒ ?W…*?W… @‰ y2ACBEDGF ‹ {IH u`Ž’yp
*
JRq¦h KML,NPO5gihQKYq¦sSR$KUT hnh5j5h
+ .-2fY
19Fg M8=(^}-'G' R(B1| #G 2|)
-c2(€R(B1|H> &((K-[
V;14 .-'&U>B^ 3 (4->=,.-!
"D 58=2'
- 2 $  #
D>$(!"-!
 KD
3 (4-' (6 32m.9$$C
G'wC'?:*W(KD-,.-l
8:9^g $9((K|
%6G#
' KD
3 (4-' #
3.-'&+C
G'`G (^2 1?;(+C
G'$ &4X*W(B¥
6P  KD  v C
U@ WVw + .-2
'6 %  KD'
3 (K- <
#M*W(Bb
!1R(^.8=-' H (K-'
426
' 0ap >6G 2|)
-,26(€R(BN|# $9D.  ;*W(Bb
[ 4D
#
§H›[Hžb®3§3ž®8\Fž|{;˜1§Hž`™.žF¯ož3™.ž3•H®ž›•C{$Y'—W˜Nš œ œ¨–^]]3œ ž,{%_`˜1§3žbža–›%˜Nš «•3—p˜1§3ž`C¯>«–•C{b

XZY

»0

½A¾6¿À!¾6¿Á6ÂÃ3ÄÅÆPÇÂÇ;È'Â6ÆoÉ0¾ÊeËcÌÅ6Â0É
Ì'ÄÍ6ÂÎ>ÄÆTÃHÄÅ;ÀhÄÌ¿3ÃÏ,ËÐ ¿ÑÊ ¿Æ#Ê ÉhÂÏ

26(4?m &4J¹º a^’»»»Ka¥9?,¼`Zw+}
.€"OM.

Chapter 8. Critical Slow Plunger Velocity

'(: 6 6G'w Y>5
#'5KD'
3 (K- P
:'? D' % w 'I;0.- %%
-%
-'6(KD 8=A &4MB nV#-2
v       ;@  +&B G'-M
'


 
l
i     r
; +4D
3 (4- v Aw’@6a [  F )>
1U
-&^.-&TaB(49%
.-[
[-' W* (BN8
  



 





  




 

v 0w’@
v 0w @




;C
G'G (B2' N?) &^ G-[9?







  

l

 
 







v 0wFU@

 >6G 2|!.->(^KD'266 'M(K3.8<
V\D-'&Y
22 #
3 (K-)26(4-2F
w ;HV?c (F3.-'&! &4;
-'
 (  3 (4-<(*}
2P.-2#8=-%
C
G' <3.8=a''.Y8=(^ C
9 =([#^ 2b' %
9.  N?^g(*V
> D 3.-&5C
G')*F>(K-='-[')(4(*`' *F#(4-)'
' U
G 5'c -'&[(*`! 6(<  G'w =w
'?:'-[o*W(B18=[U>Bm.8=- +(4-: ;38$.U
2 P
22 #
3 (K- i#w =
ƒ*?W…*? @[‰ y2ACBEDGF ‹ { D B ‰ D  ˆp‰ Œ u+Ž yp
X#(49
9 ?a+92
D 07 MC
' 2 
`(~c
D'(B# :
P~#G (4D' 8=(^}C
' (4- ?5&((^I*W(B;
KD'
# 6(;  66G ii w:;6?) 3
?c 6:>D 0[fY
19Fg )8=(^4*W(BbG'>? '(B>3.8= %' 
-, 
B nV#-`G (B2' N? v
2626 U
3 (4-@tw
ƒ*?W…*? H BWUÜy ‰'‹ {Î{ ˆp‰ y Œ u+Ž yp
O!.\ p
-5 + D-<9(B1>('R!
:1R()^.8=-  (4-
48=(^KD-'Y
' % D8:3 (4-:(*XDN9D -)4(' w
'?
' 0 D8=['
`$ 4('“
;%.-"-  = D19D -'26$
-!'#*W(BR ; ;
\D' & 4('ihjw + .-'26
%(K\D3 (K- C
' =*W(BC’K¼'?7-
DU
\ ?c9D. ~8=(^^*W(BC
[ KD'
# 6(;  66G!i Vw:;8<
' % 9'

-2
*W(BX KD
#$ '( 6 66G

 

 
  
v 0w @
O (48<-D8 9'

-2$(4-P'P 0
8<$26(4->(KG'(4\D8=?  
k l 
 
  
E 
   u l 
 
 
v 0wLx@
e

r
ur
is
is
"!#§H›0˜"›•+š •0˜Wž3™.ž—W˜Nš •3¡<š {ž%Z› bb%$V• `+¨6§ `3—hš ®:— b
”'&($¥—V˜W«`—1›`b˜1§š —pš —p•H«H˜V¡««F{ž3•H«–3¡§+›b¯W–•+š {6ž%› )˜1§3ž`›œ —m«*Wš •8[3ž3•3˜Wž|{ +<›+•3ž,5›3®®%ž3œ ž3™o›0˜Nš «•=–•š ˜W—-*#®3Ÿ/.3—Nž®!06®3Ÿ1+±
”W8” Y ˜Xš —p•H«H˜}®3œ ž%›H2™ ,X§3žF˜1§Hž3™K˜1§3ž `!\3•H3« ,5˜1§H›0˜"˜1§š —pž a–H›0˜Nš «•3—p›H™ež•H«H˜X›¨6¨œ š ®%M› _œ žRž [3ž3•C¯>«™K›R4— a–H›H™ežC—h§3«H˜}—Fœ žž [Hž±
”# ­ 4 5« ,˜1§3ž ``®«Ÿb!ž 06«–06˜ ,}š ˜1§C˜1§š —}®«•3®Hœ –3—hš «Z• b
”'7 #§ `R›3™.žX˜1§Hž—mžY8˜ ,K«C¡™.«–¨3—V¯W™.«Ÿc˜1§3žY—N›Ÿbž –•š [3žH™e—hš ˜ `C›•C{C˜1§HžY—1›Ÿ ž6{žH¨H›3™e˜1Ÿ žH•0˜p•3«H˜K¯#›ŸCš œ š ›39™ ,}š ˜1§Rž%›3®3§C«H˜1§3ž3™.—
,K«™ \6±

2(46?m &4J¹º a4’»»»Ka¥9?¼`Zw}
.€"OM.

½A¾6¿À[¾6¿Á6Â[ÃHÄÅÆ$ÇÂÇ;È'Â6ÆoÉ0¾ÊeËcÌÅ6Â0É
Ì'ÄÍ6Â`Î>ÄÆKÃHÄÅ;ÀhÄÌ¿3ÃÏ5ËÐ ¿ÑÊ ¿Æ#Ê É3Ç`Ï
~€;:

Section 8.3. The validity of the “common” models

-')'$ %(4\D3 (4-P(*p'6 0<1R()KD'
3 (K- =
    
"$# H  
l 
 
  



r

Pz


 

v $rtsXu`v

v 0w è @
wv!x<y"wv#Mr$zN{

!

ƒ*?*?h† ‡[ˆX‰Š y ‰‹ {‘Œ u+Ž yp
ST-'#&? `|-'('=-+(PB 0 H.
;.-=
M?'K#
D  2X/0D8:$.-< 2=26
' %`'+KD'
 H &4-.-;4D
3 (4- v 0w!'@
( -(`
 ?
-)'$2W W (K-:*W(BX
-(K- 6
' 6.-'&M(KU
3 (4-PR(4D ,>

p $ "$#'&
)(*H ,+-
"$# %
v 0w@
Q 2(K-  #
9 [
8=(4D-$(*$> %
U2R(B1|5'
' [9-c26
Nm I(4D$(K- PC
Ga}< 27 [|-('<.-'! 02 -3 K2,  #
D>
' 'c?K#
D  2</0D8:w['c?4U
D  2;/3D8MZ'-'(48<-'(4-c'
' !9 D^ A*W(B;' '
' %!’»»~?6
# LwoC-*W(B>D-'
 ?a+fY
19Fa v
-'
<(P> %
U2'# ,.-~B 
26
' %3.-&€Z D2
' ! >6G 2|!
-A  %D'- <*F>(K8 < ( + %
R- G>  N? v  >6G 2|a}Q+18=-#(4D
-I
DN ç5ç U@a v '(48=[
-  #G 2|! ç5ç @%@3i .a  &4-'(B>,c#G (4D' )> %
U2w! : 'c>

#
' %(K-P'
.R8=(^K-'G'XR(BN|6 Tw
ƒ*?*?W… @‰ y2ACBEDGF ‹ { Œeu`Ž’ypÜ{
KML,NPO5gih0/ s21/h T
'#$
#NR(9'
'  2:8$ %%
|6 ;.- <8=(^.a"> %0@R' 9'
'  2=4D
3 (4-' `
#M-'(
  26
9 =( 
'(<  66G) H D
3 (4-^aT %2(4-B@+') 4D
>)&(48=6o? )-(*W(4D-'Z.-['[.-4D' >?Lw:V(Z.\\D' U

=?='= 4D
3 (4-'  #G 2|<2( %;
>M-(YG
  Ta%
|+'<26
' 0='# 3  4   365 487 wC(BK

26
' 0 
 <( H 3 G'P
-'!?C'!?'K#
D  2C/0D8:M(K( H <(,#
  1? v   $   @tw

_g¿s¦jnh=1?>*OngA@*h_g-B KC/ s21/h T
+ .-2fY
19Fg !8=(^V < 32 -3 K2M1>(K-(4D' 
-?W G
3 G' 
$ 9'
' 0c(K- M-(~9Fb'
  `*W(4D-'
3 (4-i1‚Vw
ƒ*?*? H BWUÜy ‰‹ { Œeu`Ž yY
' 4(' .-['! '(= 6 6G'.-c-(=DN9D -3i Tw)'  4('] P
7\D'
& 4('L92
D 0 ->?Z -'&
#(49 8$iZTw
"6   C
\ a<&(48=6o?$(*"'= 6(R  66GP 2'.#2D
;w ; =8$ %
| `B 32D' % %).-
2(K8:
m %(K-M.-P':^ 02D' %  (4-P %23 (K-$(*p 2
;w
9:/<;

*” D  [3žH• ,"š ˜1§˜1§3ž—Nž+Ÿb› EU«™KŸRš —W˜mM› \hž%G
— F $}°T¦ $c–•C{ž3™4˜1§3ž+œ ž%›C{ž3™.—F§š ¨«H¯T¤4›H™ `IH™oš _`œ'›•C{;˜Wžž {Z[›3™{Z`®%«•0˜Nš •–Hž—
˜W«›,¥›H™{P´+™m±KJ^™.ž[š ®^\1,}š ˜1§+›C{t{š ˜Nš «•›œ¡™o›•€{—"˜W«®«•0˜Nš •–3žC˜1§š —Y™.ž—Nž%›3™.®3§<–•0˜Nš œ•3«5, ) #[§8`Zb ¬
” ³ Y;,K«•C{6ž3™"§35« ,7ŸC–H®3L§ F $}°T¦ $,¨›Hš M{ J^™.ž [š 8® \R¯>«™B˜1§š —b™ež%—mž%›H™e®HZ§ b
”  ¬ •œ ž—m—p—m«Ÿ ž%«•3žb®%›•žh²¨œ ›š •`›•C;{ .3«™V¨H™.^« [3žb«H˜1§3žH™ ,}š —Nž±
” y —NžžC¦4§H›¨0˜Wž3™ z'±

»

½A¾6¿À!¾6¿Á6ÂÃ3ÄÅÆPÇÂÇ;È'Â6ÆoÉ0¾ÊeËcÌÅ6Â0É
Ì'ÄÍ6ÂÎ>ÄÆTÃHÄÅ;ÀhÄÌ¿3ÃÏ,ËÐ ¿ÑÊ ¿Æ#Ê ÉhÂÏ

26(4?m &4J¹º a^’»»»Ka¥9?,¼`Zw+}
.€"OM.

Chapter 8. Critical Slow Plunger Velocity

ƒ ?*? 7‹ {‘Œ u+Ž yp5w/RŒey ‰ BED ˆ Œ u+Ž yp
*
 =8<(BK9'
' 0!(4-!-D8<m 26
 .8:D
3 (K- =9'
' 0)(4-$'*W(4\ ('.-'&M
' 0 D8:3 (K- '@C%4(' 
D19D -6a}’@=D19D -2)C
' $
' % 6D8= (A9 %-#(4 2'(48=(&-(4D' ;G'>?='# v |> )8=(^ @a
@:D-€ 62' 479(KD-
>?2(4-^ 3 (4-' =
;'M*F#6.-o*m
26 v ('“6?[ %(4 G'! = ! M|'.-(*
2(K-'^ 3 (4
- '@a4
- UB@D-2 
C(' '?!
 `; :' ;F26(BN-'R(^.- =.- = 2\D-&R#8P 
.-!= 2! 8<
oC
6?, :# KD.#,(5
^  &#(G' (^2' N?[(*b')  66G)
-'~|-'('=- G (^2 1?)(*
\D-'&Zw
+ G'U
('"
' % 6D8M3 (K- `.8M  2'  ?
>:.-<
bR(B1| :i W D2P
' ;-'('
bU
- %*WFa
P26(4-' %
-
#6 % 6D# .-P'P  66G$6%2!w
QR2626(B#^.-&Z(Z''.26
 2D
3 (4-c
/16MU > : 0(48=6='#5.-c
 4(' 4  wI;6?~D' %I|^ 
8=(^*W(B"
$4 M $ &#( G (B2' N?Kdb;6?:2
.8 
R'?*W(4D-' 
b$2m 3 26
G' (^2 1?$(9
 0
8=
' .-fY
19Fg M8=(^w;'[#6 %
U2'# P
GM*W(4D-' 0
8=> D  :#6&
K 6 0 +8=(^
D 0Ta"DN9D -
-A
8$.-'
 4('PdNd <-'26
-(K- ?[R(K-' *`cD' 0
'& (*<|>  [8=(^ v 6G-*W(B
&#()G (^2 1?P4 B@bC
' +-'(4D'&4(5#(BKD2< %$1>(K-(4D' =#6 6D  +(BbN
 `')>(K9 8 
6?
 .-P:26(^M  % * i w





$r
Ar,v w
 r v#Mrz


'J?'KU
D  2[/0D8:J

# c.- 
?€ %%
I
-' D- %
?6€B %
Z  D'
3 (K- Tw ' ?'KU
D  2
/0D8:
 0(:

# ='- D .-&:^ nV#-b2>( % € %23 (K- a' D2<
' R 4D
>a2.U2D
ha
-':#
&(B 


6 Tw='?4U
D  2+/0D8:!2
-,98=(G.-'&(Bp %%
3 (4-
>?Lw<' ;1C
G' =,.-)': '(; 6 6G'! <
8=(G.-'&7?K#
D  2+/3D8:.-[
[2.U2D
 2#( % € 023 (K-w$(BY =
-'
 ?' H aV =(B6 M-(8
FC *b
/0D8:! 8=(G.-'&!(Bb-(FwY;)8=( ;.8:(Bo%
-C.-'& (5D-'# %
- `'

[
#&)(Bo3 (K-:(*p
-'#&?c ) ( 
-c
= :26
--(M95-'6&4 2Aw)Q+\T "D A8=2'
- 2 9(B(4|6 3j M 6(' 

fY
19Fg P*W(BN8MD
3 (K- )-'($
262%
9 [
-'7
,B nV#-P
#(
27'
' (A9[8M ('?6Aw)V(^
6?a
P 0(4\D3 (4-  
G'
.
9 ([B P26
' %# <.-M
:*W(B18 (*b
26(48:Db#(&4U
8 €~¼C  4>*W2  w
ƒ*? ?h†  y ‰ y=u ‰ ŒeyXŽ Œeu`Ž yY
_.- C %23 (K-=':8=(K8=-D8 26(4-' %oG
3 (4- W.-2.  `
  M(4-='<26(4->(K'G(K\D8=P.- ^ &4D>
0w 0w(BX
>& $ v   @Y'C
\' '
¥ #6 0 R26
- 9P-&4 2M2(48M'
>$($'.-o3
18=
v '$C
GM ;
' 0 D8= (c
GP
-&4  &B.9 : -&@Fwb')8=(48=-D8 9

-2)>
 
 k l   
 
 "!
  
 l 
 !

v 0w ç @
n
 s
s
='#
  
EE L 
 
   j   
N
  
v 0w ’»@
 # 
E 
  
 # \[     [ 

n
” X©}§š — ¨H›¨ž3™Tš —X›R¡««F{;žh²›ŸC¨œ ž «H¯T¨««™V™.ž—mž0›3™.®3§;™.ž3œ ›%˜Wž,{˜W«›+¨«6«™¥¨H™.ž—Nž3•0˜m›0˜Nš «•=›•C{+˜Wžh²H˜Y¨3™.«®ž—m—hš •3¡±
'” "—Nžž`™.ž3Ÿb›H™ \ «•¨H›¨žz¸
­ &0š •C˜1§3ž`œ ›3—m˜X¶3¸¸ `%ž0›3™.—
2(46?m &4J¹º a4’»»»Ka¥9?¼`Zw}
.€"OM.

½A¾6¿À[¾6¿Á6Â[ÃHÄÅÆ$ÇÂÇ;È'Â6ÆoÉ0¾ÊeËcÌÅ6Â0É
Ì'ÄÍ6Â`Î>ÄÆKÃHÄÅ;ÀhÄÌ¿3ÃÏ5ËÐ ¿ÑÊ ¿Æ#Ê É3Ç`Ï
~€$#

Section 8.4. The Reformed Model

fb G'-P'=G' (^2 1?!#("   a'< 6'
<*m
2(B   2
-!9(K9%
.-'[.-P18= `(*  wb;<U>B> |
H (K- ;*W(B n   *W(BC
8P.-'
Y
-D19D -+G (B2' n N?,#(" 6 ;
; 023 (4-  
' H. ?!26
-,[ 9 26
 2D
Aw
}
' %[(4-P'P
' % 6D8:3 (4-' <D 0.-:')>6G (KD + 023 (K-BaB4D
3 (4- v 0w ç @=#
 

 !

     l
v 0w ’.'@
n  E 
E 
  F        l 
  L
 4D
3 (4- v 0w ’.@+.-(!
)^.8=-' H (K-  % R*W(B18 ?   
 
NU
-'&B.-'& 
Q   S      ^"$# l n   \[       U"$# l  [ 
v 0w ’’@

}(48:9.-.-'&) KD'
3 (KW - v A w @+
-' v 0w ’’@C?  
W
W

W


 5 I 87 I Y 
 n   Q S  T  5 5 I I 7 ^I 7 I :Y 9 Y   
5 I  7 I :Y 9 
"$# 

v 0w ’ @
 Q VS  L      

='# "$#   , "$# -D8M9$= 2 G'(4 G'6 ,*F#(48 '‘8=(48=-D8 26(4-' %oG
3 (4-  KD'
3 (K-w
S KD'
3 (K- v Aw ’ @: P'
-
 (&4D'!(* KD
3 (4- v 0w!@:
-'Z.\Y97>6*W1>‘>.-5
' P'V

 ;H}
o€
O '.Fg + %(K\D3 (K- =Aw
16.00
14.40

momentum

12.80

energy
..........

11.20
9.60

Fr

Miller



Karni

8.00

Garber

6.40


4.80


3.20
1.60
. .. . ..



..... .... .... .... .... .... .... .... .. . ..

0.00
0.00

0.17

0.33

0.49

...
. ....

0.99

1.16

...

........
. .. . .. . .. . . ..

0.66

0.83





..

.
..
...
.
..
...
..
...
.

..
...
.
..
...
..

..
.

..
..
.. .
..
..
.
.
..
...
...

1.32

1.49

1.65

h2
R

^  &4D>P0w U  ;!B#(4D)-D8:9p
' 
:*FD-23 (4-:(*p')>
3 G!'' &K
_ Z'
' ~96- *W(4D-'‘
'~ 0(4\D3 (4-' (*M ;H}
o€VO '.Fg , %(4\D3 (4->= j3ic
-'‘' ;h-'#&?
%(K\D3 (K- =A26
- 9 #6 %-‘.-~
~ H.8: c*W(B18\w O (B>(G'Fa %7 %(K\D3 (K- !26
- 9I
  A(
­N”h©}§š —YŸ «L{ž3œ ,¥›3—"®«•H—W˜1™#–3®F˜Wž|{ }, š ˜1§`›C®«6«¨ž3™o›0˜Nš «•;«H¯K›C›•3«H˜1§3ž3™"™.ž—Nž%›3™.®3§Hž3™m±

»

½A¾6¿À!¾6¿Á6ÂÃ3ÄÅÆPÇÂÇ;È'Â6ÆoÉ0¾ÊeËcÌÅ6Â0É
Ì'ÄÍ6ÂÎ>ÄÆTÃHÄÅ;ÀhÄÌ¿3ÃÏ,ËÐ ¿ÑÊ ¿Æ#Ê ÉhÂÏ

26(4?m &4J¹º a^’»»»Ka¥9?,¼`Zw+}
.€"OM.

Chapter 8. Critical Slow Plunger Velocity


-?)2#( % + 023 (K-$*W(B"$U
-  3 (4-P(*p$*F#6P 6D>*m
24('(5> % 6Dm & 4(' wp;P^ 02D 0 H (4>*W(^2D' % (K-$$2.U2D
}2>( % ` %23 (4-^a H.-2: + C'$(4- ?P(4-'MD' %96?P^ 2
' > Tw + (4\D3 (4-'
*W(B;('+G' (^2 1?~>(" 6 aR D27
' 
8$.-
)4(' v 4(^ %D.\ I'
#
9(K (B B@ab
>c^ 02D' % 0 .-c
Q+-'^ >5jjVw
Y( 
='5B#(4D,-D8:9` )9
' %c(K-[5\D-'& G (B2' N?
-A-'(<(K-!
D' #
8 G' (^2 1?M2(K8:8=(K- ?!D' %5.-P1R(€B^.8=-  (4-
^?4U
D  2R/3D8Mw
' ? >W.8<-%
¥
%
(49%
.-Z9?5fY
19 v fY
19; ç ’@6a"
-' kY
1- v kY
1- ç5ç @
-,
#
-' H 3 (K-[*F>(K8 )*F#6[ D>*m
2 4(' ( > % 6Dm & 4('L##6 0-A9? 4D
3 (4-' v 0w!'@
-'
& 4(' wA'AO[.\ Fg
v Aw ’ @:*W(B
I2.U2D
;2#( 0 M 023 (K-c
#I#6 0-J.- B &KD#5Aw UI*W(B;
\D'<
8=(^ v 1R(IB.8<-' H (4-
 @(*+'7?'K#
D  2$/3D8M7 M
 0( #6 %-A.-AB &4D#0w UAw7; [^ &4D>
'(' C2 
N ?$
b ;H}
o€VO '.Fg R 0(4\D3 (4>- =  +.-P
'&4#68=-b [kY
1->g C? >W.8<-%
4> D  Lw
'
'&K>8=-96NR-MfY
19Fg `? >W.8<-%
4> D  
-  ;H}
.€"OM.hg C 0(4\D3 (4-^a =P 
U >23 (K-:(* (4-' (^.- v
     @a¥ +&(B(^ w
' ? >W.8<-%
}> D  <(K9%
.-'I9?ZkY
1-TR#M%
|-!<- '[2m 3 26
4G' (^2 1?!C
' =(K9L
%
.- v   4D ,>
2'M .<2#('=-@ <. =U >Bm.8=-%
^#6 6D  *F>(K8]fY
N9}
#P.-1#t
%
3 (4- v |'.-[(*b
G#
'&@+(*Y 6D92W 3 2
G' (^2' 3 6 
-' DU2m 3 26
BG (^2 3 6 `; :P? >263 (4(*)(4-'(^.-=
   4     v < 2 G'>?2 ( %(, ;H}
.€"OM.hg  %(4\D3 (4>- =@Fw p-'26a
  P#
' %(K-'
9 P(5
' % D8=P
+)
262DU
2?!(*;kY
1->g P#6 6D  P P9FY
-[fY
19Fg > D  Lw
Y('RG'FaV %[
%
c(B.- )'
G')(~9)%
|-[; [ %(48<!2
D3 (K-'3j Tw
Y(4-[(*C')? >W.8<-%


%
 0 bR>=22|) *X
< %
?< %%
C
' R
2 G'
-'! C ;-(b2 
X'(' :8=
' 6D#8=-
26
Nm (4DFw
_ [ M;  ?c
22I
!.-c,NR(AB.8<-' H (4-
 ?K#
D  2P/3D8Mc 68<
\X
- 
#&^ 6
#$2#
 < 2P
#M#6 6(4-' H.9 ;*W(BV 
>&=-'#&?:^ % .'
3 (K- v p-'# %(K-N ç xx@twp'#*W(B#a
-'#&? 26(4-' %oG
3 (4-M2
--'(9!D 0!([6 32m.9$!?'KU
D  2/3D8:, &4 Lwb;$ 0
8<:26
-9
0
 )*W(B}')?K#
D  2C/0D8:!.-M^ nT>-+&(48=6W  L w * 26(4D> 0a'$ 0
8=)
' +(9P 3
 )*W(B"
2.U2D
R2>( % = 023 (4-w<;D' a¥'\D-'&pG' (^2' N?5'
' <(Z9)&4#
 '
-))(4-'M(K9%
.-'Z9?
fY
19Fg 8=(^.ap= 2,2
-I9,(49' %>G'A.-AB &KD#0w UAwc;ZB#(4D7-D8:9C*W(BC'cfY
19Fg
8=(^4 :
#&}'
- [B#(4D[-D8:9p(49%
.-'.-M'PU >Bm.8=-%
V#6 D  Lw<B#(4D!-D8M9
.-G'# % ?c>(K(Bo3 (K-'
( 4D
#M(*b\D-'&pG (^2 1?a "$#  4 

-'I-'26P':G' (^2 1?
8<
\ ;wb;MfY
N9hg $8=(^'#*W(B#!D-'#6 %3.8<
6 `' \D-&"G' (^2 1?Lw
ƒ ? ?W…  yÒ{BJw ‰ u)D
yÒ{n{
*
V(!(49%
.-PP2m 3 26
  (' \D-'&"G (B2' N?aB(4-' 
' `()*W(4\ ('  #(^24D>
Nw
X
 2D
  6 %3.8<
='R' &KC(*p')  4D 58=6%
w
’Aw
X
 2D
R'RG'(4\D8=`(*^'=  KD :8=6%
 v 8<
| D>'
X?6(4DD 0C';  KD :'
' 0;#(4o1?
-5-'(C'P %(K  ,
' %'@tw
| H
(
Aw
X
 2D
)#26-%
'&$(*Y"\ .-&.-P'P '( 6 66Ga I  I w
U w<^.-')' "$# -D8:9}*F#(48 ^ &4D>P0w UAw
Aw p %' "$# -D8:9}*W(4D-)(!2
 2D
!\D-'&"G (^2 1?[9?[D .-&!
 4D
3 (4- v Aw ç @tw
­W­©«+›¨¨ž%›H™¥š •C˜1§3ž`•3žF²3˜}›C{t{š ˜Nš «•±
­7
ž%—h–œ ˜W—X«H¯4¡«6«L{;žh²¨žH™oš Ÿ ž3•3˜W—Y¨žH™\¯>«™#Ÿbž|{_`C—mžH™oš «–3— ™.ž—Nž%›3™.®3§Hž3™.—p›3™.ž1,KžHœ ®«Ÿbž±
2(46?m &4J¹º a4’»»»Ka¥9?¼`Zw}
.€"OM.

½A¾6¿À[¾6¿Á6Â[ÃHÄÅÆ$ÇÂÇ;È'Â6ÆoÉ0¾ÊeËcÌÅ6Â0É
Ì'ÄÍ6Â`Î>ÄÆKÃHÄÅ;ÀhÄÌ¿3ÃÏ5ËÐ ¿ÑÊ ¿Æ#Ê É3Ç`Ï
~€

Section 8.5. Summary

 



!






_o-M 

XR:
-
 ? & 4('“.- : 6(` 6 66GM
-G' (K
)? >  2 +U >B#6 %  (4-:(
62
 2D
<$#KD.#)\D-&^G' (^2 1?Lw_ '
' `96-= '('=-+
bfY
N9hg +8=(^ Y(%
\ ?=#(4-'&
-M'#*W(B#) >6G 2|g <8=(^B <-2 % 0
m. ?N#(4-'6(KD +
' CR\wp; 0
8<2
-)9 0
  ()
\
('Y8=(^ C^ 02D 0 %!.-< `
b'
Zw '<26(4--23 (4-M91R6-< ;1C
G'=P
-:':?4U
D  2
/0D8:A'
' 96-5? >
.-Aw~'Z8=6(^Z*W(B2
 2D
3.-&c',2W 3 2
}  (' \D-&`G (B2' N?~'
'
96-#(G Aw
r={ Khv!x${


 '
= p/0D' 3 K2
3 (4-$*W(BXKD
3 (4-:0w ’



I+ '(' '
     
*W(B  


 D-'o€B26(4-' 1D'23 (4

I+ '(' '5>
3 G)1#(BC2#
~9?5fY
19Fg )8=(^4<-)') D9 %#
, &4
G
>?.-'&5'
U
8=;w
 

» è



½A¾6¿À!¾6¿Á6ÂÃ3ÄÅÆPÇÂÇ;È'Â6ÆoÉ0¾ÊeËcÌÅ6Â0É
Ì'ÄÍ6ÂÎ>ÄÆTÃHÄÅ;ÀhÄÌ¿3ÃÏ,ËÐ ¿ÑÊ ¿Æ#Ê ÉhÂÏ

 

 <

26(4?m &4J¹º a^’»»»Ka¥9?,¼`Zw+}
.€"OM.

Chapter 8. Critical Slow Plunger Velocity

2(46?m &4J¹º a4’»»»Ka¥9?¼`Zw}
.€"OM.

½A¾6¿À[¾6¿Á6Â[ÃHÄÅÆ$ÇÂÇ;È'Â6ÆoÉ0¾ÊeËcÌÅ6Â0É
Ì'ÄÍ6Â`Î>ÄÆKÃHÄÅ;ÀhÄÌ¿3ÃÏ5ËÐ ¿ÑÊ ¿Æ#Ê É3Ç`Ï
~€Ó

   

6

x

I

v# $ uG h v!x




Ú+ •# 

& #%· 
"!






# 


(!Ú

D;.A4VB`HJ@;81F
TGÈQ_460PD;4646:;0P76F 7I4J.E25H‹4MB32;K
F 4646:O46:rB7WB38;D;:;4Š@;B`F?KLB3F 8®8;:1F GNGNBÔ48r1QOB303DE4¿81GiG9G94V46@v4;29F[rG=B`76F :MDE^,.E:MF ^_:rF :MB`D;^C4VG=UWBÔ.A.A:;7M@E>;.1>A0PH @
BP.E:
 k hTg /h Ao 
TT

-B K KZRUN1

SR

;




p>(KC6 H &K-)(*R'MG'-3.-&, ?' 8  (4-'M(*C,>4D.#8=- <*W(B+>4D2.-'&5
. '&
' :(B#(  N?Lw
4(B#(  N?<KD'(:-U
.-8=-R(*"&
' % C2(K- %3 D R

#&P(B>3 (4-(*V'(%
B(B#( H 1?a6 2
\ ?
='-2
' $C
\ P
#[G'>?.- v 06Z^ &4D> ç w'@tw5',8
.-526
D' % P(*
. &
' !(B#(  N?
>
.-' D !2' -G'-
>
^a`\D9W 2
-:6G'
(BU
3 (4- v #
23 (K-~>(^2 % 06 3@6aC.-'26(BN#2[
268=-:(*
G'- aK
-!'[8$ >.-&c>(^2 % 06 Lw'!#6 %-;2'
p26(4-' H # +!.- "D'-2$(* '$G-;
>
v .-!
8=( 6'm 2P
-[G
2DD8]G'-3.-&B@+(4-M[#6  4D
^&
' v .- 'M^ @
+':-[(*b'$"\ .-'&
#(^26 0 Lw


maximum
porosity

shrinkage
porosity

wall thickness

^ &4D> ç wb'M#
3 G'P W.-|
'& (B>( H 1?M
' 
:*FD-'23 (4-:(*X':26
' 3.-'&  2|- %

» ç

Chapter 9. Venting System Design

QX8<( 'm 2[G'-3.-&TaY~8=( %P  ? D' %A26
' %3.-& 8='(^¥a` M(4-'Z.-,< 25',G-!
(4-I(~'5
8=( >5
-'J ,>6*W1> '#'.-Z
' )
.+G'-3.-& w <- ?~.-c?>#8<c2
' %
>
('} 0(4\D3 (4-' =# KD.#TaB D2M
' `G
2DD8 G'-3.-&Ta 4(B>!B#6PV2- KD v .- &'.-'2$
-[
\D8$.-D8
26
' %3.-&B@$
-'7 4D'6 &26
' %3.-& wb
2DD8  M
  5(7U>'U
2:
. &
' $*F#(48 'c8=(4  9*W(B#, 
'
' )'c(4(BoD- 1?c(8$ >Z c'~  KD 8=%

-'J [ [2
\XG
2DD8EG-3.-'&Aw' 4(B>
B>2- 4D'$ +
PG
m
3 (4-$(*p<G
2DD8“G-3.-'&[.-$< 2<'$C( >?'&-: ;.-#(^4D2.-(M
26
G N?+(M>
26C'
.4
-=(M>
2}; '<  4D :8<%
.a
-;'#*W(B#`2>
6
`G'
2DD8 v }
:
OM.> ç5ç ^9@tw + KDU &M2
' 3.-'&, <
!^ nT>-=
#(
2[.- < 2: Do*m
26P-' H (K-[ .-2#
' 0
( >4D2)'c( 0 H.9 ,8P >.-'&A>(^266 % 06 v 68<
\   5-D8M9
' $R\ @tw['!&
' 06 M.-[[ 6(
 G'$
-2
G 1?M
#)8<
 8<(  ?:(*Y
.p
-)'#*W(B#<'$18 ;F
.E =[ D' %5>
*UZwb'6 %
#6 ;h %(K\D3 (K-8 =
#M2D8:9# %(K8=:
-2#
:
*m
C8=(B#:? >-  G!#(^2 % Lw<_o-M ;2
ha¥
4D
  %
3 G'^ 02D 0 H (4-(4-$='-'6 % %(K\D3 (K- C '(4D 9 D 0!
-M<-<'?M
#M-'(-'6[
#6 %-Aw
<9G (KD 6 ?aY~96 %:G'-3.
3 (4-7 !
2 G'I='-7
#
3 G' ? 
>&G'-
#
I !6 H &K-Aw
Y('RG'Fa4(I8$.-.8P &:'M 02(K-'
o?,8<
2.-.-'& v D2[
' ;m.8:8$.-'&@a¥(,-' D>M*F>U &.-'&; .G'-3.-& ?' 8 a
-'<(-' D><9#
|
'&(4D H R'`2
' R8<(4 Ta6G'- `'
G'(M9Go?P-
N#(' w
Q 1? 2
 H &6(*XG'-C 2|-'6 0 % =U
-&*F>(K8 €B’  |wY'6 0$26(4- T 23.-'&# KD.#8<- `(K-$
G-;
>
) D'&& +
-M(43.8:D8]
#
wQb $D 6D'
 ;F2(K8:8=(K- =)
>(
2! ;6 32m.9['P1#(B>
#!#6 0-[
-)!#*W(B18=58<(B4 ; 02W.9Aw



%q


$rtsXu`v


wv!x<y w
 v#MrzN{

!

 ?W…*?h† `ˆX‰  EyxD ?  Œeu`Ž yY
*
':"# $8=(^K
 .-'&! ) U>'#
23 (4- (*C
.p*F#(48 )26
G N?)C
' =(4-'[9? +
2' LwM_.-)
8=(^.a +
2 v +
2L  ç ’@`G' (4
,8=(^*W(BpM&
' *4(' *F>(K8
)B M2
G 1?9
' %[(4-M
*W(4\ (';.-&)
' % D8:3 (4-' @'$&
' <D->&(B6 +
-) %-#(4 2M>(^2 % ;.-PP^ P26
G N?aK’@`
KD'
' 

?5 %
? > % a @'[(4- ?I#6  %
-2!(7'&
'$ 4('  M
$'[-#
-2(*+G-6a U@
;38<D
>.8:D8 8<
' 0 4(' U
! :> %- =Ka¥
-' @  4D 78<%
"
' P-(, Do*m
26:-  (4-^a4D
58=6%
}#6 0 D> < 4D
4(,)&
' #6 0 D>N w +
2' $
 %(cB nV#-3
~91R6-!NR(526
' % 
2'(4| 4('
-,D-€B2(K| 4(' v 9D +^ nT>-3
3 (K-P^ ,-(2(K8=$.-(,
6? .-) <8=(^ t@ w
Qb % 6D8:3 (4%- [# KD.> C
b*W(B}2'(4| 4('JM#6 % 6D# #
3 (9
9(KDb1R([91R6-<'<2
G 1?
-'[G-`U > F w
Q+\8=( %:'5 3
8=~8=(^XC
' ,>
96?Z %G'U
C#6 0
#2> Ti wJQ+\p %A8=(^ a ; c
U >23 (K- (* '.-.| v '.-.!|  ç x!x@a}-&4 2':*Fm 23 (K-.-)'PG-3.-'& %? %\
8 w='PG-=6  &4.-A
A2(K8:8=U2
 ?' 8 .-'2\D'6 
5 
' %!
-AU > 6a 0G'U
R4D2 a`
- 0G'U

91D[U >B
L- 
H (K-
2(K-U
23 (K- <.-!< 2 '#6  %
-2 26(B [2 - v
5
06 v + 
.#0(  ç  ¥a}
'& Lx @%@=26
9 6G'
\D
(Z9,
#&X
- ,
-'5
)1? 26
^G
\D (*
5
 <
9(KD è (BC8=(B# w _.-) <26
' 0a
I#6 % 6D#7U
3 (7*W(BC',2(K|'.-'&c26(4-B 3 (K-c M
[ 
'  Z
-7'7#6 % 6D#7U
3 ( #
2'6 M
G'
\D'$(4- ?M
*UX
9(KD’  (*p) (4-$ #(4|: +
' % w`_ +26
-!9$ '('=-$
C='-$' 4('
 P2'(4|,',> % D#[.-['[26
G N?(B6 )-(:#8<
.-26(4-' %
-<
' P
' % D8=7.-['58=(^ M9D
.-'2>
' % `? >(K--3
\ T? w

”$"¨¨H›3™.ž3•3˜1œ `3)•H«;œ š ˜Wž3™o›0˜1–™.žC—F–™#™ ` ¥, ›3—p™.ža–š ™.ž|{ .H›[H›š œ ›M_œ ž .•3žž|{ž,{$›0˜V˜1§H›0˜"˜Nš Ÿbž±
2(46?m &4J¹º a4’»»»Ka¥9?¼`Zw}
.€"OM.

½A¾6¿À[¾6¿Á6Â[ÃHÄÅÆ$ÇÂÇ;È'Â6ÆoÉ0¾ÊeËcÌÅ6Â0É
Ì'ÄÍ6Â`Î>ÄÆKÃHÄÅ;ÀhÄÌ¿3ÃÏ5ËÐ ¿ÑÊ ¿Æ#Ê É3Ç`Ï
~L~h

Section 9.2. The “common” models

*?W…*?W… H BWUÜy ‰‹ { Œeu`Ž yY
O[.\ "
-', C D-6a^.-'<
1 ? ç »Kg aB2(K- %D'2
!8=(^(
22(4D-b*W(BT';*Fm.-23 (4- .-
G'-3.-&! ?' \8 wb'?[9
' %).R8=(^(K-P*W(K\ ('.-'&)
' 0 D8:3 (K- 
Nw
p(5'
#
-' *W
A’ w$_ 0('18<
 4(' v 2(4-' %
-Y8:#
D>'@C.-='-U
-'26($G- v
262(BU^.-&($'=
D'(B#
.-P)#6 0-%
3 (4-@
Aw$
--'( 4('“.-P')> `G-
U w+Q. &
' +(496? `': 
&
' 8=(^
O[.\ }
-'5 ` D-+ 02m.9)'P26
 2D
3 (K- #(^24D> `*W(B"1R( 26
' 0P
' +2(K|)
-'
D-'2(K|H26(4-B 3 (K-T w<;)26
 2D
3 (4-' ;*W(BY')2(K|H,2
' %)
# %%
-'
#5
-'c2
-59 *W(4D-c.
-?9(B(4|P
9(4D<
-- ( 4(' 9DC; M
-!.-> 3.-'&M1 %F w '$26(4-B 3 (K- ;.-P'!8=(4 [
-)
 G'M
>M2
 2D
,
262(BU^.-&!'M
8:9 -;2(4-^ 3 (4- v %6:: 68<
o KD(:(*b 
b'
W@Vj w
'$26
 2D
3 (4-' 
9(KD=D-2'(4| 26
' 0$
#=G'>?).-> 3.-'&)
- .\49P^ 02D 0 %'#:.-:
  F 
8=(B#P6%
. L w 'P26
 2D
3 (4-' <>(^26KD#*W(B})D-'2(K|!
' +*W(K\ ('.-'& 

Qb % D8= HJ-D8M9 v -U
-27O
2c-D8:9b(5')G-0@M ('R 
- HI*W(BC2'(4|
2(4-^ 3 (4
}
 2D
['c2(B1> (4-^.-&Z %%
 v 2(K|A2(4-^ 3 (4-' 3@
5
a I#6 % 6D#ZU
3 (¥aC
-'I
8:#
D>!U
3 ()*W(B":
' 0 D8= HZ-D8M9

}
 2D
<:^ nV#-2!91R6-$:2
 2D

5

-'[P
2D

5
w
X % '!^ nV#-2
5
(c2
 2D
:'[(KD9  %%
# v '6(B#3 26
¥U > 0@$2(4-^ 3 (4-' P9'
' 0
(4-P'$
8M9 -+2(4-^  3 (4-' Lw

}
 2D
M':2(K-'^ 3 (4-' +.-MP^ !9'
' 0!(4-P'P(KD9 $ %
X2(K-'^ 3 (4-' Lw

Y('‘'!8<
' 0 4(' (4D ;N8P.-59?[8<
' % 26(4-' %>G
3 (4-w
*R2(KD# %aB'6 %:2
 2D
3 (4-' `
#:1>(K-(4D' Lw_o-)2(K|
 4('a':2(K-'^ 3 (4-' 
#:18$.-'
s  T  O 1 s  T  9?~D€ %
8
-'J-6G=9?,('=-, 
8 Vw,;2
 2D
3 (4-' <*W(B<D-2'(4|
4('
#!8<
'8<
3 2
=#(4-'&Aw ;P
' % 6D8M3 (K-)8
 .-P'$"> % %-'G'}C
' 22| wYQ+-'
8<
'8<
3 2
\ ? 6
|'.-'&¥a' Y } KD G
 -V( /0D' "&KD % H.-'& %(K\D3 (K-wX'6 %bN#(B# p
>R(K- ?*F#
23 (4(*X('"('Y.-$
;8=(^< 2:.-2\D$
8=(K-& ('V<*W(4\ (';.-,& }(K-'@C
' 0 D8:3 (K-(*
2(K- %%
-C8:#
D>M.-P'^ M `=#(4-'&¥aNR(B@(B(B}
' % 6D8M3 (K-$(*}': 0('18<
' 4('$a#6@
(B(Bb8=
' 6D#8<- `6%2!w <-M(4:(*p'
`C
' = `P2m m (4-M*W(Bb> 4D.>!G'-+
>
w
­ ©}§š —YŸ «L{ž3œ™.ž—F–œ ˜W—pš ••3ž¡›0˜Nš [Hžb˜Wž3Ÿ¨žH™.›0˜1–™.žš •C˜1§3žR—F§3«H˜}—hœ žžžCš •C˜ `¨š ®%›œ™o›•3¡ž±
7 4 «5,7«H˜1§3ž3™ ,}š —mž )®%›•<š ˜ _žb Y ˜Yš —Rœ š \hž›3—N—h–ŸCš •3¡•Hž¡›0˜Nš [HžC˜Wž3Ÿ¨žH™.›0˜1–™.ž;š •+˜1§3ž {š ž`®%›[š ˜ ` {–™>š •3¡;˜1§3žš •E#ž%®F˜Nš «•±
Y —Xš ˜p™.ž%›œ š —W˜Nš ®b

!

½A¾6¿À!¾6¿Á6ÂÃ3ÄÅÆPÇÂÇ;È'Â6ÆoÉ0¾ÊeËcÌÅ6Â0É
Ì'ÄÍ6ÂÎ>ÄÆTÃHÄÅ;ÀhÄÌ¿3ÃÏ,ËÐ ¿ÑÊ ¿Æ#Ê ÉhÂÏ

26(4?m &4J¹º a^’»»»Ka¥9?,¼`Zw+}
.€"OM.



A

rPxr :z h {"u  {"{ h v[x

Chapter 9. Venting System Design

‘'-7
A-'(4-2(48M> % .9 c  KD I D2c
' :C
; D 6¥ap' 0
8<,
8=(KD-!>(K\  9?,
\D-'&`.\ 4(' (KD:(*`' %? %8\w Y('RG'Fap
.< M
726(48:#6 0 H.9 [ D9 %%
-'26
-ZD :
9(G' %%
8=-;2
--'(P9)
   w<; 4(']#
)(4D=- =(4-)'#6 H %%
-'26:( 4('
\D' +'[ %(4-PG' (^2 1? v  %(4-
>

' +R\ @tw'#:2(4D 59P>: H D
3 (4-' @'$ 4(' #

(4D T h KZK+
-='G'(4\D8=PD 6!9?: %(4-^a’@  4(' U
;(KD % / s_g¿hP'
-<;G(K\D8=
D' '9?P (K-Ba(B @Y'! 4(' U
=(4D ’h L NSOST(P';G'(4\D8=PD 6[9?'P %(4-wp;

' 26
' 0: 2
\ )'$2W 3 2
B6  &4-^aB
-', ; 
' % %(^2'
) P'P2m 3 26
^
#
w
Q.S 4(' b.-`'G-3.-'&< %? %8 26
-P#
2+G'>?P
#&G' (^2 3  CD+(
9(KD »   4  |wX;
.K26
--(}U >2< pG' (^2 1?; (KD}&(B.-'&;>(KD&K+
; 2'
\ ?;2(4-4&4D#=26(4-4D  v 26(4-G>&^.-&
B G'#&B.-'&72(K-'KD 0@Fw[ )'-'(48=-'
5 !|-('<-c9?',-
8=[( * ;2'(4|
 4(') =Aw); )?' H 2

'-'(48<-'(4- b'P|?;(!D-> %%
-'^.-&$'G'-3.-&:6  &4-:>(^2 % TwR_o-
.KG'-3.-'&¥a'G'-3.-&
?' 8w'
' :( 96 H &K-7 %(Z'
:
.`G (B2' N?c(B [-(!>
2' 66I(*; 0(4D-', ).-c('
R(B# a R1qTh 
s k K ¦Ss RVlnq/s*mEh 1 w_.-;G
2DD8 G-3.-'&¥a''=
.¥G (B2' N?M>
2'6 ' 6:(*T 0(4D-'
\8=( %R.-' %
-%
-'6(4D'  ?a
-'P;6  &4-= 6(KD )9; 6D'2;
C  -' D#6 
p'=
.X> % D#;(B6
-(? >266[P
8=( W 2 #6 0 D>Nw
Xm (B;8=(^ *W(B;#^ 23.-'&5[(K3.8MD8LG-P
>
,^  -'(26(4-' H b'c> H %%
-'26,.-[
G-3.-'&P ?' 8 v #6 0 D>$U
3 ($(*Y 6 % 
-<’@twY'G'-b H &4-.-
<26(48:8=#2'
 %? %8“.-'2\D'6
: 
' %;
-!? > 6aT 0G'U
K4D2 aT
-, %G'U
¥
91D;? >
-  (4-' 2(4-U
23 (4-' =.- < 2 '#6  |
%
-'26<26( !2' -6a
5
a4 C(*"(B#V(* € è (B 8=(B#wYD' a #6 % 6D#:U
3 ( 2>
3.-&)2'(4|
4('L M
! 
' % Aw -(*+^ nV#-26 91R6-G'
2DD8
G-3.-'&Z
-I
8=( W 2)G'-3.-&
(^262D# R4DW.-'&$' %
oh€TD3.8=NwC(BKG'
2DD8 G-3.-'&¥a
2'(4|.-&$2(K-'^ 3 (4- 6 %%
9  6P
\8=( %
.- %%
-%
-'6(KD 6 ? v  <- <(K-)'!
.bG(K\D8=[.-!)G'-3.-&54D20@6aV=. !.-!')
8=( W 2
26
' 0[!G'(4\D8=(*'
.<'
' $( 9Z>4D2c( 8=(B#!'
-~'
 * v -B.-'&7(4-'7#6 0 D>
#
3 (B@9*W(B#'52(K|'.-'&~2(K-'^ 3 (4-c6G (4' j :
-I !26
- '
-7(K- ?c='- 8=(B#,'
’ 9 ,(B=8=(B>[(*'c (4- %>(K| P
 0 wZO (B>(G'FaV 4('  !-'()-2 % 0
m. ?2'(4|Z.
8=( 6'm 2)G'-3.-& w -'26! 4('L :2(K|Ta}'#5 !-'(IB nV#-2c.-526
 2D
3.-'&5  4('
91R6-,'6 01R(~26
' 06 Tw‘_ PDN-' (KDP
:'I8
8<
3 2 [.-~9(72
' %
>, H.8$.
haC
-'
>6*W(B>!9(M26
' 06 
#!#6 0-.-P' > %-2
;w
'M#(4 (*X$2'8$ 2
4#
23 (K- CC
'  6('<-<(,9:.-  &4- K26
-FwX'$B nV#-2M.-$&
'
%(K\D9.  N? v 8<(  ?c?'K#(&-@.-c  4D c
-'5 %(K  ,2
-c9 6('<- (I9[.-' H &K- K2
- v Q + O  ç  è @tw
(BRU >
8: aV'58<D
>.8MD8E?K>(&-c# 
' %[4Dm.-&c %(K  B K2
3 (4-)(*`
Z|'. (&K#
8L(*+
\D8$.-D8
 
9(KD è   
=
8=( W 2:8:#
D>!
-Z#6 0 D>Nw$  :  % ;
- (*b' G(K\D8=
-$(9;B 6
26Ta
-:26
- 9P-&4 2 w + (48=(*T'C( >'?&-$ R :4Dm.-&$'"\ .-'&
3.8= v }
:HO '.; çnç 49@Fw`;
' +NR([6nT2 -'(26
-2^
2)('Y(4D6a¥
-['[-'nV2
 $8$.-.8<
w
'I-D8=m 26
X .8:D
3 (4-' #(^4D2AD-#
  %3 2Z#6 6D  !
-'A'#I -'(A(' KD'
-3 %
3 G
(B(4 *W(BT"-^.-&MG'-; (^26
3 (4-' v )
' %;
26 v 3@C(9<"\ B@
-'   0 D'P ` 3.\
-:(K4D'6 %3 (4- (B
6?Lw;'#
#aX('R6Gh
a 4D
  %
3 G':U >B
-
3 (4-' =
-7#
' 0(4-
9 :&KD % 06 
=26
D' ['[
262DU
2?(*C'5
' M
2 v 'c  KD ~8=6%
X#
2'6 H@<6 3.8
 (A9) .-[',
' %

» $€ 
» (*Kb"\ .-'&P#(^2 % Lwp Y.-*W(BN8<
3 (K-.-2#
' 06 "'C  &4- K26
-2R(*^=D-> %%
-'^.-'&
(*+=
  P'c> 4D.>ZG'-:
#
w + .-2c8<( P(*`'
.'
' $( 9G-IKDm.-&c'5.- 3

%
'&6 +(*p$"\ .-'&>(^2 % aK.-P= 2P'$G-< (B2
3 (4-' (5-'(=
6?M
#(4 Nw
Q. G-3.-'&7 =!2'
 :8<'(B,(*(4U
3 (4-^aV
-'Z = 6(KD Z95D 0ID- 6 0 <
2626%
9 


2(46?m &4J¹º a4’»»»Ka¥9?¼`Zw}
.€"OM.

½A¾6¿À[¾6¿Á6Â[ÃHÄÅÆ$ÇÂÇ;È'Â6ÆoÉ0¾ÊeËcÌÅ6Â0É
Ì'ÄÍ6Â`Î>ÄÆKÃHÄÅ;ÀhÄÌ¿3ÃÏ5ËÐ ¿ÑÊ ¿Æ#Ê É3Ç`Ï
~L~ :

Section 9.4. The Analysis

# 6 D  [26
--(97(K9%
.-'D' H.-'&  Fw QR22%
9  > D  [
#ZB [2D :( (K9%
.- @ <-7
#6 H %%
-'26(Ic
.*4(' .-cI8=(4 J 8<(B>, H &4- K26
-$'
-c'Z#6  %
-2c.-c'G'-3.-'&
?' 8 a}
-7’@=='-['58$ >.-&~#(B266 0 %6 $
>[
D'&48=-I96?[! 2 K2,8=(K ,&6(K8=>?Lw,_.'6 %2
' %6 a''`? >U
23 (K-=(*¥
.}W (B^('+"\ .-&$26
-P#KD'26`;
."(B#(  N?< 2P> 4D.>
' D' %P(*p(}2- 4D'6 Tw
Q+-7
^ 3 (4-
"(490/123 G7 M( #(G 5
5((K"( ;2(48M9.-' =c',
2D'
"G'-
>
5 5
#6 H %%
-'26 v .-[)G'-3.-&c %? %8@=(,[
. 4(' "D' a" .8$.-
3.-&5-'65*W(BC2
 2D
3 (4-'
(*'&
' 4('L.-,'[G'-).-,(BU(J8$.-.8P &['Z-D8=W 2
}26
 2D
3 (4-' Lw D,6M
w v D
$
w ç5ç ’@<
-'c(> )
G[ 6('<-)
='[
.;#6 0 D> )U
23 26
\ ?7D- *W(BN8 .-[! %? %8\w
Y-2a +
-'
 ?' H +26
-:
 %(,#(G <'
G'U
'&P
. #6 % 6D#'
 '(4D 9)D' %.-!-D8=W 2

H.8MD
3 (K- Tw



r]xMPz{ h{
'c8=(^p [#6 0- '#[ c
~8$.-.8
T(*8
8<
3 26
"6%
. Lw Y('RG'FaX8:
' H 
&B G'-<(
\'P?' H 2
^D-> %%
-'^.-'&:(*"'P-(K8=-
wp;$.-> #
"26
-"-'8=(B>
%
.  B 32D' %  (4-' .- 0G'U
('V %(4DU26 v }
OM.> ç5ç 
@twXQb ;96*W(B>a'$.-6&K#

#(
2
 M8: ('?6 w7Q+\"',
' % 6D8M3 (K- $< 25
>ID 0 .-, 8=(^}
>, %
~ %(Z'
P'?726
97U >
8$.-'J
- ^ 02D' % 0
)Z26(4-2\D' H (K-c(*=' #6 %-[2
Zw p>~ 
  )(*
' % 6D8M3 (K- = 2M
>)D' %,.-M6G (4.-&  <8<(B 
Nw' 8
.-[> H %
-2()'$
.C 4('  ;
' 0 D8= (c9M.-:'<G'-3.-'&) %? %8\w
’Aw'$
.2 4(' .-:'P2? .-'  
' 0 D8=!(K-€B^.8=-' H (K-'
w
Aw'$
.Y.-MP2? .-RD-#&(B6 +
-! %-#(4 2M>(^266 % Tw
U w'$
.}(K9?' +M 
&
' 8=(^.a   w
Aw'<&6(48<>?:(*YG'-3.-&! ?' 8 s (B6 -'(+2
-&KDm.-'& '"\ .-&,#(^26 0 v :w w>aB
&
[91R6-$!
6 ( -(.-2#
' %PKDm.-'& '"\ .-&5#(^2 % 3@Fw
xAw'M\D-'& 8=(G'6 +
`
2(4-' %
-RG' (^2 1?MKDm.-& '<"\ .-'&>(^2 % a
-  +18$.-'
9?P!  j B
'&K#
8]26
 2D
3 (K- Tw
è w'<G'(4\D8=$(*p$G'-3.-'&) %? %8  -&4  &B.9 $2(48M'
>)()P2? .-}G(K\D8<w
Aw'<G'-3.-'& %? %8 26
-[9!##6 0-59? (4-'  (K-&Ta U
 &4`2(K-'KD Fw
ç w'!> H %
-2:('[  4D 78<%
 4('a
5
aT(B6 :-(=2
-&:4DW.-'&[':"\ .-'&c#(B266 0
v KD():2'
-'&:.-:'  aB(BO)
2[-D8:9# 3@Fw





»Aw+'%4(' .-P'<G'-3.-'&) %? %8  
-
^
9'
3 2 4(' v 
--( 4('+@Fw
!Nw+' #6  %
-2()4('$a
5
aK $-'(`
nV259?MP2
-'&M.-:'<G'-
#
w
  [[
9(G'[
' % 6D8:3 (4-' aT')*W(4\ (';.-&I8=(^T
' $ '('=-,.-ZB &KD# ç w ’c )#(4( %Aw Q
\D-'&D' '6 $'c  4D A8=6%
.aX
- 9((*'8 v -(' 26
\ Z
' $'c %(4-@:>(KT
.
>(KD&KM
[ (4-'&¥aB %#
 &K+2(K-'KD Fw
!;

½A¾6¿À!¾6¿Á6ÂÃ3ÄÅÆPÇÂÇ;È'Â6ÆoÉ0¾ÊeËcÌÅ6Â0É
Ì'ÄÍ6ÂÎ>ÄÆTÃHÄÅ;ÀhÄÌ¿3ÃÏ,ËÐ ¿ÑÊ ¿Æ#Ê ÉhÂÏ

26(4?m &4J¹º a^’»»»Ka¥9?,¼`Zw+}
.€"OM.

Chapter 9. Venting System Design

^ &4D> ç w ’  Q H.8M  48<(B*W(B"$G'-3.-'&) %? %8
')8<
' % 9

-'26(*X':
. .-P':2? .-'"?  
 
v ç w@
 l   & (  
 p 4D
3 (4- v ç w'@Y p`(4- ? KD'
3 (K-
b-'6<( 9 0(4 G' wXV(< %(4 G'+ 6a<?' H 26
>(KL
>3 6 (*X'$
.C-)(,9!>
)()$&6(48<>?M
-')')>(^266 % Tw QR2626(B#^.-& ([
' % 6D8:3 (4U¥aB'P
.R8<
' 0 +2
-[9PU >B#6 % 0[
'



v ç w ’@
s
;G'(4\D8=$(*YP2? .-RD-'X
' 0 D8:3 (K- x[26
-[9$=m F-M
'

   
v ç w @
,+2



;D' a'"> %N8 .-: 4D
3 (4- v ç w'@; >> %-59?
(
 
      (
 
v ç w U@


s


'"\ .-'& #(^26 0 M(^262D#  .-c
cG'>?Z '(B>[m (B~3.8=   O =O 6

 aY
-I>6*W(B>
 
!#
-' *W: 5.-' H &K- K2
- 0w]; c|'.-J(*$4('E 7>6*W1>‘(J
' I
--( 4('%.w];
.- %%
-%
-'6(KD 4('L#
Z'
' $(A9?>#6 0 %~.-[18= :(*'c> H %%
-'26 (c' 4('a
5
a}
#6 % 6D#!U
3 (¥a4
-!'$2'
U
2m 3 26 +(*+
--'( 4(' v + 
.#(0 ç  @tw+kC-('< &(*+
--'( 4('
 $> 4D.#)*W(BX? >#6 0 H.-'&)$ %2(K-')N8 .-: KD
3 (4- v ç w'@tw

')8<
' %) 4(' #
:2
-[9$=m F-M
'
 H   M      Q   H 
  & ( 



,+


v ç w @
M 
 ,+ s M     M  
s
s
='#
"

Q   H
  l    H
q  r !  #"
v ç w x@
i
 
D$ ›••3
« %5« ,5§H›3C— _ž%ž3•C—W˜1–C{š ž|{žh²H˜Wž3•3—hš [Hž3œ `5)›•C{=•–Ÿbž3™.«–3G— _«« \%—
{ž—m®H™oš _š •H¡˜1§š &— %'3« ,®%›)• _žY¯>«–•C{± F^ž [3ž3™e˜1§3(ž '
œ ž—N(— ))› _H™>š ž¯K—h–ŸŸb›H™ `R«• $ ›••3)« %'3« ,7š —p¨H™.^« [š {ž|{<š • $V¨¨ž3•C{š ²$°X±
2(46?m &4J¹º a4’»»»Ka¥9?¼`Zw}
.€"OM.

½A¾6¿À[¾6¿Á6Â[ÃHÄÅÆ$ÇÂÇ;È'Â6ÆoÉ0¾ÊeËcÌÅ6Â0É
Ì'ÄÍ6Â`Î>ÄÆKÃHÄÅ;ÀhÄÌ¿3ÃÏ5ËÐ ¿ÑÊ ¿Æ#Ê É3Ç`Ï
~L~ #

Section 9.5. Results and Discussion

' O)
2)-D8:9}
R<-#
-2=(M'<26(4-4D 6a  H
aK `26
 2D
9?[
--( 4('‘2
U
2h
 m 3 26 R*W(BV';G'-3.-& ?' 8 > H %%
-'26a
5
aB
-:'M> % D#:U
3 (Aw  ,+) ':8<
D>.8:D8
G
\D(*  H6 FwC_o-;G
2DD8 G'-3.-&Ta''-#
-2PO)
2P-D8:9ha  H
a^ b2(K- %%
-
-'$4D

(  ,+ w
+ D9 %3 D3.-'&)
 KD'
3 (K- v ç w UB@
- v ç w @.-(! 4D
3 (4- v ç w@a^
-5#
NU
-&^.-&Ta?   

   (
  Q  H.
(




v ç wè @
s   G


s
'P %(K\D3 (K-:([ KD
3 (4- v ç w è @2
-9:(K9%
s.-'c96?-Ds 8=W 2
¥.-&4U
3 (4-:*W(B w+;!#6  4D

8<
' 0 *FU
23 (K- .-Z'726
G N?~
' [
I*FD-23 (K-Z(*3.8=~ )-~18$.-'D' H.-'&A ;% 
Y&
'8 =
' % 6D8M3 (K-wb_ b b.8:(B>%
-}( (B.-}(4D}'  &4- K26
-2R(*4' (
(  wY R
U
s 8=6V>#6 %-
'#
3 ($96NR-R'b"\ .-'&`3.8=C
-'bG
2D
3 (4-R3.8=Nw   "'  3.8=b= 2CR(4D $9# KD.#
(cG
2D
)[2? .-b*W(BC
2(K- %%
-M8<
' % 4('L#
[
='58<D
>.8:D8 O)
27-D8:9b='')&
' =8:U
D>
-~> % 6D#5>8<
.-
=''.`.- 3
4G
\D a D-'b'[2(K-'^ 3 (4-)'
<
4('  $2(K|Ta v '5#6 % 6D#!B nV#-2c96NR-!58=(K 726
G N?
-5')(KD  )-c(*
2(K-'KD  
#&$-(KD&K([2>
:
M2'(4| 4(' w @
-[U >B#6 % 059?


W
 
v ç w @

  ,+ M     M Y
s

bW 3 2
¥2(K-'^ 3 (4-!(^262D# =<-   ,+0w_.-[G
2DD8 G'-3.-&TaT)G'(4\D8=D' '~9?!
 (4- = 4D
B(' 4(']U
aV
-',-' D#6 
#6 % 6D#!.-)'M26
G N?[( :-'(<.-2#
' %
v
9(G)')
8<( 'm 2#6 0 D>'@tw_.-
.bG'-3.-&TaT[2W 3 2
¥2(K-'^ 3 (4-!-' D> =
=' 4('
 $-'(2'(4| w;(B} $#
' %(K-Ba4:2W 3 2
B
#
%   =6"-[
' ':
#

<8<
| +$3.8=
U
3 ( ,+ 4  4D
(!(4-'w ; +26
-[9P(4-' 96?[ ((K|'.-'&
 4D
3 (4- v ç w @aT.-P= 2$G
\D
(*  2
-[9$G'
W cD-3.4   KD
( ,+
-'[ 0()P2m 3 26
B
#
[


W

 
%
v ç wç @
,+  ,+ M
    M Y
+ D9 %3 D3.-'&P
 KD'
3 (K-  v s ç w ’@C.-(P KD'
3 (K- v ç w ç @a
-'D .-&$'*m
2 
 ; 0(4D-'PG (B2' N?$26
9PU >B#6 0 %[
'     a?   
    ,+    +
v ç w»@
='#   b'; 66M(*" %(KD-:
b'.- 3
'26(4-B 3 (K- .-' H +<2? .-' v
8:9 -R2(4-^ 3 (4-' 3@tw
' ,+ '(4D 59PU >B> % 059?S^2|Ho ^}
o€VO '." 4D
3 (4-w





Ar;{ :
 z "{
M x


 h {"u  {"{ h v!x

 ') > D  (*
-D8<m 26
BG
\D'
3 (K-$(*p'PKD
3 (4-' .-:'!#(^26B.-'&) %23 (4-M
>!> %-
.-:B  &K
D# ç w Ka< 2;U>B.9  Y`"-
#6 % 6D#`='- ç » “(*¥+ %>(K|H<
' Y
 0P
'
;*FD-23 (4(* w

! 

½A¾6¿À!¾6¿Á6ÂÃ3ÄÅÆPÇÂÇ;È'Â6ÆoÉ0¾ÊeËcÌÅ6Â0É
Ì'ÄÍ6ÂÎ>ÄÆTÃHÄÅ;ÀhÄÌ¿3ÃÏ,ËÐ ¿ÑÊ ¿Æ#Ê ÉhÂÏ

26(4?m &4J¹º a^’»»»Ka¥9?,¼`Zw+}
.€"OM.




Chapter 9. Venting System Design

K
#
8=6# 5.- "D-'2'.-& 'J>(^2 % 
#Z'~
>
#
3 (Ta
a=
-' I*FW 23 (4-‘'
#
8<Fa

5
w<B#(48](' 6%
. 2
 2D
3 (4-' v }
:OM.> ç5ç 
@ C
' +*W(KD-!
`' .- "D-'26P(*Y
'
U
8=
5
(4-,I> % 6D#G' (48=- .-552? .-'; KD  68<
\wI;c.-"D'-25
8<
\V(4-,c#6  4D
"
.= 8<

' 0 .-'2? .-'FaR9D)
#&(4-'IO)
2Z-D8M9Fa  (LH(tw,;
nV2 (*X':
>
[U
3 (¥a a4
>$ D^ 5'#P H.-2M  +'P(K8$.-'
-=
#
8=6Zw

Y(5'

,.-I
.;G'-3.-'&J ! 6  &4 ?IB nV#- *F#(48

[.-ZG
2DD8 G'-3.-& v }
:HO '.Fa
S^2|>)
-‘fp(K 
%'.-  ç5ç x@[9?~
I*m
2(B=(* Q  ,+!tw  !*m
2(BP
' [ H &4- K26
-2,*W(B= 68<
\

5

-: 68<
\ <-='MO
2M-D8M9X 
#&a
' bC
' C '('=-$.-('T%
. M2
 2D
3 (4-'
v }
 O '.;  ç5ç 
F@ wX'+6"- 3 (K-+2( %-$'#= 9
' %(4-'*m
2X
}*W(BK
; 68<
\O)
2$-D8M9
$*m
2(B Q  ,++26
-9M &4-'(B# w_o-:')8<
0/1(Bm N ?:
(*p'P26
' 06  ,+ + 8<
\ w
(B}G
\D (*Y:
>
U
3 ([&4#
X
- w ’Ka 3  aB'!#6 0 D> .-2#
' 06 +'$G(K\D8=
4(' U
=(*X
.pD-3.
KD
' H 
?€ %%
 ;#
2A
 w`_o-P
.TG'-3.-&Ta KD'
'  
?€ %

 
2 G')='-P'G(K\D8<m 2<
. 4('“#
P(KD;  4 D
()'G(K\D8=)D 6, 9?P) (K- w
'[#6 0 D>M
-['8
' % 4 (']U
M
>8<
.-%
.-' 2(4
-' %
-
*U  = %
) P
#
2A w;
#6 % 6D#5.-5 4D
' HX 
 ?
€ %%
, M
,*FD-23 (K-,(* w (B` 8<
\VG
\D :(*
>7 [-(
 ;&4#
}
- (4-'$'[#6 % 6D#) ;26(4-26
G'!DC
U a4
-'='   

?€ %%
P %
'&N w '  6 % 
-:(4-'='M> % D#: +2(K-'2
GP('=-C
UL wX; % > D  `
#:.-M^.#2+2(K-U
' R(
#G (4D' <8<(4  <96? +
2' v +
2L  ç ’@6aV¼`#
 v ¼`U
;  ç x è @a '.-.| v Y.-.!|  ç x’@R
-7l.- 0?
-' ~
\
2 v l.- %?5
-'
 A
\
2!  ç5è ’@aT<>c8<(B P
' 0 D8=5
<'5#6 % 6D#
- 8<
' %
4('“U
!#8<
.- 26(4-' %
-
-
#P
F%
.-.- %%
-%
-'6(KD 6 ?$*W(Bp
.}G'-3.-& w

^ &4D> ç w Y;)#6 0 D>!U
3 ( `*W(BX
.p
-!G
2DD8 G'-3.-&[
 ç » (*p') %(4-: %>(K|H
V([#*W"(M< #(4|=26(48: 3 (K- v »»
(*"< #(4|@` ;8=
-.-'&4  % R .-'26j'@+-'(M&
' =8<
' %
 c *U.-Z'Z2? .-'FaD' 5-( #6 0 D>Z2
- 9 8=
' D>¥a`
-' ’@ 'cG-[26
-J9 9 (^2|
'
>3
\ ?(Bb(%
\ ?
='!-c(*[ %>(K|HNwM;D' aV' ;F26(48: 3 (K- = v -c(*5#(^2 % 3@<(*
"\ .-'&#(^2 % ; `6 32m.9)  =
'- ç » (*X$ #(4|P `
 0 wC^ &4D> ç w #6 %- '="-

*W(B
5   `.wA'"-
b#6 % 6D# v >
\ ?cI> % 6D#ZU
3 (@
#6 % 6D#~#
3 (A
'
5*FD -'
23 (4
' P6 02W.9~.-Z 
B &KD# ç w 0w!'5#6 % 6D#.-'!^ [26
G N?7.-'2>
' %6
- $ %>(K-&K ?(49?
9(4D<
( *+
  :.- 3
^G
\D'M<*W(BR
. G-3.-'&AwP;,#6 % 6D##8
.- $
\8=( %



2(K- %%
  -

*U >
2'6 <G'
\D'$(*Nw ’A w
 +.8:  6 '
C<G-`
#
!  6D [2 - ?)
#&
='*W(BpG'
2DD8 G'-3.-& w + .8$.
C#6 6D  =2
-9

 *W(B
.pG-3.-'&
-[<
(49' %oG'!<-P)#6  4D
K8<
' 0 `*F#
23 (4-!  (F w
 =^ 02D' %  (4-
-['6 0#6 6D  =
#>*W2 ?!26(BN#2.-)
[2
' %P<>)
\'
' 0 D8:3 (4-'
#) 0
3 4A w Y('RG'Fa4',>
^R(BN 7 <^ nT>-
-','
' % 6D8M3 (K- P
G'M(,U >
8$.-c
-'
%(K8=$(*Y8
> 
NwQb 0 D8:3 (4- 7 5-'(
J> m 23 (K-7(I'A8=(^.a9DU
'=&KD 7.-c'7 H &4-w ;
-&^.-p'
' b(M-' D>='
 'P> H %%
-'26.-<'P8=(K P(M
., 4(' v
-8=%
 4('+@
' R(
9)
' < 68<
\4
' :( % H.9 w ;&KD M^ 2%
6 ='
;-&^.-b H &K- '
)*W(Bb
. v
-
')  4D 58=6%
 @+
' +
'  6(B>
' $( % H.9 w
’AwQb 0 D8:3 (4-' ¥aU¥a4
-»)
#$G'>?>
  3 2$
' % 6D8M3 (K- TwC(BX? >
8M a$1#(B .-[D .-&
' 0 D8:3 (4-PU $ 6 % `
-M»0w  w
2(46?m &4J¹º a4’»»»Ka¥9?¼`Zw}
.€"OM.

½A¾6¿À[¾6¿Á6Â[ÃHÄÅÆ$ÇÂÇ;È'Â6ÆoÉ0¾ÊeËcÌÅ6Â0É
Ì'ÄÍ6Â`Î>ÄÆKÃHÄÅ;ÀhÄÌ¿3ÃÏ5ËÐ ¿ÑÊ ¿Æ#Ê É3Ç`Ï
~L~


Section 9.5. Results and Discussion

Aw 8=(^  !
-~.-'^ 26
3 (K-,<-7
' 0 D8:3 (4-   )&(B(^Aw _.-c'7.- 3
X %
'&6 v (*<
"\ .-&!#(^2 % 3@ M> % 6D# RG'>?$ 8<
\
-).- 26
' %;M> % 6D# v *W(BU2'@ ( (4-<

 : $ 68<
\.a}
-c>6*W(B>)'[&
5 P
\8=( % &6#(Aw!Qb $' "\ .-'&~>(^266 % )#(&K> % 06 a
M> % 6D#$.-2#
' 06 a
-:' #*W(B#;'=&
: .-'2>
' % wpQJ H &K- K2
- &
)> 4D.#6 RG'>?
H &4- K26
-$#6 % 6D# = 2[(^262 D
# <(K- ?
;'M"-
4 %
'&6 (*R' "\ .-&I>(^266 % 
-'5(K- ?
='-P'$
#
#
3 ( + 8<
\.a $ wbD a ;
' % 6D8M3 (K-M `G'>?#
' 0(4-
9 Nw
U w+Qb % D8:3 (4- x ;
' % 0(B2'
  M
' 0 D8:3 (4- ç aT9D $8=(B#$ %-' H 3 G'w ;P2
-'&M.-P
> H %
-2 v
72
-'&5.-c
' % D8:3 (4-Z.- ç 2>
6 M26(4-' % 4D'- ?5
72'
-'&,.-5I\D-'&
G (B2' N?Tw ' \D-'& #
2 '~26(4-' %
-)G' (^2' N?AGo? *m
' %6a$('R6Gha [G' (^2' N?
2#
' %,4DW.-'&c',KDU
3 (4-(*"\ .-& #(^2 % Lw7;2'
-'&,
'&
.-,-' :(4-,
> H %
-2.-!58=(K AwM 2
-595D' %7
' 
&4D ,9?!!-&^.-R
-'5-
-'266 <
.8:(Bo%
-2(*b2#
3.-'&[
[
: M
8$.-.8:D8L#6 H %%
-'26(! 4(' w
Aw+Q+-(p&4D $*W(Bp'PG'-3.-& %? %8 6  &4- v .- G
2DD8]G'-3.-'&@= =
' 0 D8:3 (4- è w'
-'&B.-'6M'
' !( #KD'267'7G-!G'(4\D8=7 %( 
c 6 0 [&
' c
' !( 9ZG
2D
 w 
> m 23 (4-,'
' =(Z9) H &4-!26
>6*FD\ ?5|6.-'&,.-,8P.-''
'#6  %
-2M
 0(7
' ;(Z9
8$.-.8P & v %(48<<<'
`(4(   #6 %W 23 (4-@tw`_o-
.}G'-3.-&Ta='-P ;
' % D8:3 (4-  $-'(
G'
  Ta'
;B nV#-R8=(^66 32m.96 }'C  D'
3 (K-w Y('RG'Fa-'("*FD "\ .-'&`
' % 6D8:3 (4-+26
.8:#(G'M'[26
' 3.-'&~926
D' %,
>&(B>3 (4-[(*,  4D A8=6%
4= 27D-'#&(B M8$ >.-'&
 P'$
.b `? >
D' )([(KD  <' 8<(4  w
xAw+Qb % D8:3 (4-M (4-'P(*Y'!9'

' 0 D8:3 (4-' .-: $8=(^w_o-8<
-? 26
' 06 `'#) 8=(B>
'
-(K-!G'-6ap
-c'[-#
-2ZO)
2I-D8:9C*W(BB nV#-$G- :26(4D A9
5B nV#-
G'
\D'w[;D' aV'[ D'&&6 %~8='(^c(*2(K-G'# H (K-5 -'(<G'
  TaX
-c'#*W(B#)!G
\D
(*',2m 3 26
X
#
I -'(P? >
2FwIQ 96FFa+8=(B#2(K8:  26
J8=(^Y # KD.# wA
' % D8:3 (4-Z26
--'(59 D 0J
' 
A&4D ,*W(B=Z6  &4-I .-'26c
' c96F<G-3.-'&J26
-J9
2 G' v
-)D -
-'2'.-& ' KD
  N?@ '(4DC-' Dm.-&)' 3
8=O)
2[-D8:9;w
è w+Qb % D8:3 (4- ç  <

o3
\ ?!
#(4W
:
' 0 D8:3 (K-w`'!#6 H %%
-'5
26 ).-MG'-3.-'&[ ?' 8L
M*FD-23 (4- (* $
-IO)
2-D8:9# Lw V6aX>P'[#6  %
-2a
a" ;26
 2D
c9'
' 0
(4-:'
' 0 D8:3 (K-:
`'O)
2,-D8:9C =
[26(4-' %
-+
- 4D
B(  ,+ w;;M1>(B
4D'(I )
' % D8:3 (4-Z 
>&5.-,'Z.- 3
" %
'&6 M='# $
-'O
2~-D8:9#
>
8<
\w,Qb P'["\ .-& >(&4#6 % !>(&4#6 % 06 a" :1>(B; [#KD'26 w~_o-G
2DD8 G-3.-'&c
O
2<-D8M9T>
2'6 p=8<D
>.8MD8 .- %%
- ?
-'='#*W(B#R Y
' 0 D8:3 (K- pU >
2FwY'
-#
-2:O)
2:-   D
8:9V G'>?$ 8<
\ v '* 4('‘ bG'-M-'(b2'(4|) 4('+@b.-<
.¥G-3.-'&='!
#
Z#
3 (Ta 33  <Go?Z
#&!
-'5'#*W(B#M'[
' % 6D8:3 (4- )(B(B;Q
w p('R6Gha
>&
#K 6 0 +M
22D#
2? (*b[8<(B.a4  H &4-)
2 G'6   =
.8
-['P#- =(* 
8=(^T
>5-'(
nV2A9? $1#(B;w7O (B>(G'FaV 8<(BV26
-79,.8:>(GA9?[%
|'.-'&
.-(!2(K-  #
3 (K-':2
-'&(*Y)#6 H %%
-'26w
Aw':2
-&:(* 'PG-=
#
!(B =
nT2+'[> H %%
-'26w Y('RG'FaK
!%
. ,26
 2D
3 (K26
-< 6(' 
R
'  (4-'&:
' R'G'-R
#
: 
9(G:'
 *"(*"'1? 26
2>( % b %23 (K-Ba<1>(B
 =8$.-.8<
w_ *p<G'-
#
PD1- +(KDb(,9)9 (' 
 *X(*}<1? 26
G'-2>( % ` %23 (4-P
.8:#(G'8=-+ $-'6Aw


! è

½A¾6¿À!¾6¿Á6ÂÃ3ÄÅÆPÇÂÇ;È'Â6ÆoÉ0¾ÊeËcÌÅ6Â0É
Ì'ÄÍ6ÂÎ>ÄÆTÃHÄÅ;ÀhÄÌ¿3ÃÏ,ËÐ ¿ÑÊ ¿Æ#Ê ÉhÂÏ

26(4?m &4J¹º a^’»»»Ka¥9?,¼`Zw+}
.€"OM.



Chapter 9. Venting System Design




C!






 
-'
 ?' H v G'-I; Z'71>(B# 3@.-B 2
6 !'#~ 
~2W 3 2
pG'-
#
9 (' < 27
G-3.
3 (K-7 [(B(B+
-'A
9(G'[= 2,Z> H %
-2(I
. 4('L 8$.-.8<
w7 :2m 3 26
}
>
- 5(4-A'I&(48=6o?
-J'I"\ .-'& 3.8=Nw '~2m 3 26
C
#

 %( #(G  ,
8=
-A(
;F26(48:9.- =<
2D
G-R
>
 =';G'-+> H %%
-'26*W(Bp-D8=m 26
 H.8MD
3 (K- b(*"=2
G 1?
"\ .-&Ta4%
|.-&7.-(5
262(KD-')26(48:#6 0 H.9.  N? (*R' &
'! 4(' wM_o8:(B>%
-'26M(*C) H &4-[
 %(
C
' + '('=-w



r;{  hv!x${
R-p2(K- %ND23 (K



2(46?m &4J¹º a4’»»»Ka¥9?¼`Zw}
.€"OM.

½A¾6¿À[¾6¿Á6Â[ÃHÄÅÆ$ÇÂÇ;È'Â6ÆoÉ0¾ÊeËcÌÅ6Â0É
Ì'ÄÍ6Â`Î>ÄÆKÃHÄÅ;ÀhÄÌ¿3ÃÏ5ËÐ ¿ÑÊ ¿Æ#Ê É3Ç`Ï
~L~Ó

   





  
 
  
! 
#"%$'&)(*,+-"/.102(43/*5076 +-"

98

Chapter 10. Clamping Force Calculations

*5+'( 6  0J¹º  ’»»»   ¼ (Zw
( &%6 (

½A¾6¿À[¾6¿Á6Â[ÃHÄÅÆ$ÇÂÇ;È'Â6ÆoÉ0¾ÊeËcÌÅ6Â0É
Ì'ÄÍ6Â`Î>ÄÆKÃHÄÅ;ÀhÄÌ¿3ÃÏ5ËÐ ¿ÑÊ ¿Æ#Ê É3Ç`Ï
~ :T

 



 
  

"!#

  








  
 
       
 

 "!#%$&('")+*-,/.&01!3254++614+ 7589!:; <>=? ; @A8B!C !ED
F
H
J
G
K
I
M
G
H
L
O
N
Q
I
M
P
R
S " 0  6 . . &9*2076 + " &?>  6  6 01. 0 /& &,. 0 (T 6 .(U &)" 0WV &U> )&)( 01.YX ( & %*2076 +-" 0  & )+ .26 076 +-" 0  0 0 /&ZV1*5+JU[U +-"X
]\_^ $ 6 -( `U 6 . 6aU )( +)& (cbed  &%6 ( *5+fUgU & "901. ( & ( &9. )+ " . &,. 01+ 0 /& 3 0  + (ih . )& (cjOVid  &kU 0 -l
&/x +-U 3 ( 07" 6 * T T +]0m / &,+ ( " 3-+]m %m *50 02/3'& ( 6 " /\z5y ^*/6 &)$ "%6 *5-& ( ` Un"%$|Xp{ o .2" 6a U 6 " 6 T&9 &)(#( 6 01" +rQb q  901& (Bs`tYu-bWd  & )&)(wv /. .,3  U 6 0 01&9$01+
d  6 . ( 0 6 .Bm + (0 /&%} . . + * 6 01&~d & *  ")6 * T { $ 6 01+ (w (ibe€b#{‚bJyQU & T . & (cb
ƒ FJN„R-PJ…c†ˆ‡Š‰HF`‡nLIKP|F]…c†Œ‹(…+IKPHŒIHŽB‡Š‰M†…c†/Žc†`…i†]†]R‡Š‰HF`‡nLIKP‰HF`]†’‘(‰HIHR>†HGFJGHr‡A‰JF`‡5LIKP|KI
GHIH‡[‰JF((†WFJGMLWIQ“A”Y†(‘‡A•–IQGˆ—1‰JF(‡9RAIQ†](†`…˜—%•–‡A‰‹fPK“Jƒ ™š• R-‰f•aGM›‡Š‰J•–R[•aG`ŽiI`…YNOF`‡A•–IKG‚œ%ž™ †`F(R>†ˆR>†MGJrF
‘]IK‹]LWIMŽŸ‡A‰f• RgFJ‹f‹K†HGHK•– z‡9IŒ‡A‰H†ˆ…c†]ŽE†M…c†]†(Rœ —%•š™a™¡“K†W›Q™–FM|‡>I‰M†`F]…BŽ+…iIKN¢‡Š‰H†MNŒœ
d  6 . *5+ "/* T 3/$'&,. *5+fUgU &)" 01. 01+ 0  &z{ $ 6 01+ (cb
6¤4.+ 3'*,(4+ S " (  ( &9&T *5T (6 0 &Š&A££ + &6 (¡&Av0 v   &,0 ( 0 + , *5+ & &93 ( .  . 0 0  /&¦0 & /&V ( &U& > / %)&.$'. )&)+ ((01*/.Y.6 X 01+ & )+3 T&9$5.2$ 6 077¤ 6 0163/+-+ $ "(  .& 6 .& 6 "9m ( 0& 0 //0 . &¥/+ & "U ` 0 T )&&(&]b(U %§ 01 + +©07(6 *0V /( &T & %0 $/( & &,& %+( .ª$'( XZ&)( +/1o (3m &A"-0m m&) `(& &,U &9]\6 .ªT 6t~ )^ (¨v v $ 666 * 0 - ( 0 `  (U &&
"/+-" (U + 3 . 01+ 0  & 3 0  + ( .-b¥
d /&  *,+JUgU & "90 +-" 0  & )&)( "%$ %*,*,+ ( $ 6 "  01+0  &9. & &U> )&)( 01. 0  &
)&)( %*,*5& 90 "%*5& 6 . $ &,01&)(EU 6 "/&9$Qb¦S  £ &* /+ . &)" 0 /& 3 "'3/.53 T .101& 01+ 3 (T 6 . 0  &%6 ( *,+JUgU &)" 01.
 &9* 3 . &ZS  & T 6 &A/£ &0  0 +)0 /&)(~U +)076 £ 076 +-"/. ( &6 " £ + T £ & $ 6 " 0  &%6 ( ( &9. )+ " . &,.-b«
(01&,+ . 0)+)6 " "`. ¬ & 0 01 + 0 0  0 &  & 3 (&9.1T 6 0w* v 07 6 +- " 01++/m ( &/U .53`+]Ug£ & U 0 /(&  6 +]"-mm + 0 (E)U 6 . 076 +-)&" )`( T +6 " *¬ 0   &W&  6 . 6 &01+q /+ .1)&07)6 " " |6 0 { q01" + +-63 0 "  &9&T &)& ($r 3 v `( 6T6 06" *] b 0 U  &&
¯Á-Yµ3¸ÜµE³A¶ è­c®#Ë Ì>ÝدªÌY¼A°±
ÍQ¸`ÍQ»+°iÍÏÙ¨²>Î"Í#³ªÐ ´iÞ¸Þµ·½ µ:ÆE½ ½–ºªÐ ¶9ȊÁw³AÃwµÂ¶A¼º °ªÐ¸µE°+¯ªÑ"°¨È>´¹³AÌAÇ/º„
¶AÈAÈA¶A»A°ª»>Ò¸a½ ´+°±
´¹¼-³Yص:¼-½ ¼-¶A»ªºªÈYµCƹ³9µ:Ð ½ ½¯Yº9º¿µEÁ5Ã˜É ¾3Ò(ºª¸aÆC°+¸aµ:°ª°À½ ¶AµEÈY¼AµÂ¼9¸–µ¡°A¾©Ê(ºAßfȊ´ªÃwº>¯9½³ªà9»A¸a°ª°ªÁ>¸a¸H°ÀÆE½Ó>µÜفÓA¾Â̪¸a¼9¼-ÔA¾KÃÅ
ÕkğÖ×½®#ºAÄBº9¯ª°+°w½ ºŠÆCºª¼9Þ°+µC³Y³-ÆCµE¼9ʯªµC᪰ª³¢Î>ÃØÕ>³¹ÕžÇ/µ:ÈAâ[½ ´¹¶A³A¶A³YÒAÆi°ªµE¯>¸a¯ª´+½ º9°+¼-¼AÁ9ظ–µÂ٘¼-¶AºžÈY¼9µ:¾`ãf½ º9µEàªÁ
¯9°ª°˜ºŠÈª¶>É °¡ºªÚ ÆCÇ ^µ:½¼-µEÈYÈYÑ-µEµÂ½ ³Y¯-°>Û ÊÊ
ÄB½ ºAºª°¹³A¶A¼-Ò ½ Æ+ÊHÄ5ä¥å>å>Ô-áYå9Û:áªÎ>Î>æ

"!]ç

Chapter A. What The Establishment’s Scientists Say

0  & )& / ).&)(. ( +& 6 "*/ 6 0 0  01&&9&1$ (m &Š3 &9m 02$ &)3'6( 01(&,+& &9(c. %b[$ * S $ m#6" 070 6/+ ( & & " %. ( *5&Ab˜0 m &SJ01(v + &9&6 0T–%T  . /6 . & * T /( & +  0 + /39. 0&/& 0 U 01+T / .%( "%&,U$.)+3%. -0* "%  $ /01 .1+ "/S +-0 * " / (& " U ( 01&+ +  3 3._. 0 /£)0 +" 6 vT *,00 + //( &/&/( &,66 ((.)++*5+f-Ug"%6 ")$ 6U &+ "/&" *,."9&~b˜01.eSv v `6 0 U6 T–T
.5 3  (. & + T0 3  01 & 0 T  0   )+& . 6 07( 6 &£/& )(T  +-.,3%3'$ ( & +]m0  0 /0&/6 0 ( /*%& (  6 076 * ( 6 & .AU . + )("/$ +-3% $( & +/.1m 0 0 "% $&%66 ("  *%(  6 07& 6 * 6 6 .Š"%U $ 60 0  &  T %b˜$ § 0 3  ( 0 0 /&)6 0 (EU + )&( &  S( . `U6 "
'3 `T 6 * 076 +-" .,3/*  /. 0 )6 .  + +J¬(b







 !"#%$&('*),+-).0/1'

T
5v bg} T–T Am
T–T
Am
Hh "v ¥{ T ~U `¬ eo
MtAbŸd
Šm
JU kv
1o Ev
T ~o _m
v "t
`UgU
/m
’V JUgU X
T /Ub
/\5^ `U Ÿv Mt
T JU wm JU
`U
ij
d#231H3G;q7 Z\D(U!5KQ4 3 ;Y;`7 ;j4 QXD;q7 HT3!5K3GH(=FD=!5B9žOm Q5\9A23r6stW7 T–T 7 QXDGsHTQ T–T =5XH7 3[4G=;R9:7EDZ@7ED6HXV;R9A5BM-bd 23
U]\5^Ha7 =ZX5l=`Uu7 ;(9A23Œ[
U QT;R94 QJUg[U Q\DN4G= T 46V T =9:7 QXDavb7 1m =FDGM9A26=9= T–T vb=!5K3wV;?3HxW<MZ[U QT;R9(Ha7 3
4G=;R9:7EDZy3DZa7ED3G3!5K;-bpd 23S7a(
U U!Q5B9?=FD64<3fQ]#m 9A2!7 ;@H7 =Z\5K=`u
U 4 =FDW!3NHT3/U QXD;R9A5l=9R3GHcW<Mg9A23’m8=64A9
9A26=919R3!D;Q/m%"
U 7 T–T 7 QXD;Q]_m HTQ T–T =5K;e26= £ 3W!3 3!DN7ED £ 3 ;R9R3HzW<M|{¨}_wq##} vh{žyÏt§ vm=FDHSQ9A235_U =Y.¤ Q5
7ED;R9:7 9AV9R3 ;123!5K3(=FDH0=FW5BQF=6HC7ED0U/\5o
^ Ha7 =ZX5l=`

U 5K3 ;Y3G=5K4!2Mb
SEDeQ5KHT3!5-9RQf4 Q5,5K3G4<9z.V Z\5K=`U[U =!53\X vT9A23&5B3ŠOm 3!5K3 3(4!2=FDZ319RQKj
d 23@U]\_}^ Ha7 =ZX5l=`~
#
U 7 ;`9A23[[U QT;R9j4 QJUgU QXD(4 = T 4!V T =9:7 Q\DeV;?3HNW<M(H7 34 =;?9:7EDZe3!DZ7ED3 35B;j9RQ0H3Šl
9R35:
U 7ED39A235B3 T =9:7 QXD;<27EUW!3 9:hv 3G3!D[9A23Ha7 34G=;R9:7EDZzU =64!2!7ED3[=FD6HZF=9:7EDZHT3 ;A7 ZXDeU=5K=`U 3<9R3!5K;Gv
=FD6H&9A23@5B3G;<V T 9:7EDZˆ[
U 3 9?= T  Q"€
v 5K=9R3`b
S 9_;?3G3/[U ;vF9A23&5K3AOm 35B3G31hv QXV T HgDQ9 T 7aA¬ 3";?QJU 3n8m =64<9R;`9RQgW!31v 5O7 9>9R3D!M!¬ DQ"[v DHb
 PfNˆNWF]…cLzIMŽŸ‡A‰H†ˆ…c†]ŽE†M…c†]†(Rk‹QIHRŠ•–‡>•šIKGM6

ƒ †]ŽE†M…c†]z
† „†… 3 T–T vT9AU 23(QXDU6gX =FU!U/3!\ 5Ï^ Lv ==!;#5K3(UFVFQXW D T T7 M&; 27E3D@Hf3AW!ˆ3Š9AOm5B3]Q[U5B3¥3Yo 4 {¨=}_;Y3 w; q#b_†} § VFHa5P79A323!4 =5E[U ;?9:Q7ED5K3TZevd3!7 9#DZ=67E4<D9A3 V3= 53LtT–T M=FD; HeVTUF9AU!2Q3[5B9R3!;_5‡5K9AQ25B3;
7ED9A23pRV 4<QfUg[
RV 4<QfUg[
U QXDXzU QHT3 T b
ƒ †]ŽE†M…c†]y
† ‰‹Š 35PM1=FDZ\5O7 T M\]8]`nQ"Œv HT=5B3`9A23 =FVG9A2Q5B;k;:=<M 9A26=9*9A23ORV 4<QfUg[U QXDX~U QHT3 T 7 ;¨[v 5KQXDZKb … 23!D
7ED~m8=64<9 vX=64 4 Q5KHa7EDZ9RQN27aUevt7 9 7 ;Ÿ£3!5BMfV;?3Šm>V T b
ƒ †]ŽE†M…c†]†y d 230W7 Ž<Ž =5,5KQC=FUFU!5BQF=6462\]5b
q 2=FDZ3H09A23z[U 3=FD!7EDZ0Q/mžv 2=9_9A23=FVG9A2Q5K;Ÿ[v 5KQ!9R3O,o ;?3 3(9A23
>V Q/6
£ = T 3GHgW!Qˆ63GH`@X 4 QJUgU 3!D9ØOm Q5m3Aˆ!=`(U U T 3 tŠbžd 27 ;[U!5KQaHXV64<3H0=fD3A}v 9‡MTU!3 T QTZ7 45[v 27 462@7 ; = T [U Q;?9
=FW;<VF5lHK
b {k=`[U 3 T MGvX9A23Ha7 ;Y4!2=5BZT3(4<Q3<047 3DG9 vÏ*q dv-7 ;[4<Q\D;?9?=FDG9BOm Q5n=N5‡VTDFD3!5kQ5n4 =FD@QXD T M[6£ =!5BM
v 7 9A2"9:7a[U 3(bd 23#9A27E5lHNU!Q;?;A7EW!7 T 7 9‡MGv][v 27 462e7 ;j9A239RQXU7 4#Q]*m 9A23eU6=FU!3!5>vF9A23n8m =64A9j9A2=9Ÿmq &4 =FDFDQ9
#
W!3#=;Y;q7 Z\D3H1=5‡VTDFD35\;RM;R9R3]p
U WTV9L26= £ 3_9RQ(4G= T 46V T =9R3GHnOm Q5\3Š£ 35PM1;?3<9nQ/nm 5,VFDFD35t=FDHH7 3 4 =;?9:7EDZ
U =64627ED34 =FD0DQ!9`3AˆT7 ;R91U!Q;Y;q7EW7 T 7 9,MGv=FD6H@9A235B3ŠOm Q5B3"9A23%[v 2Q T 3@U6=FU!3!5k7 ;[7E5‡5B3 T 3A6£ =FDG9Šb
1
‘ 3!D7 4&
¬ ’*=!5PsJ“e37E5ih ;#=FD;¹hv 3!5ij
d


`UgU Ød

T

23046587 9:7 4<;"=9>9?=64 @9A23&=!5B9:7 4 3C7ED09A2F5B3G30H7 IJ3!5K3!D9 L= M;
9A23N5K3 O3!5K3 3G;"9A5PM09RQSHT3!DMSUTVFW 7 4 =9:7 QXD
W=;Y3GHQXD[Z\5K= 1=!5?]8] 23_^-5B;?9`5K3 O35B3G3[Ha7 HXD 9b; 2Q c=FDM dDZ 7 ; 2 "7 ;R9?= A3 ; 89A2Q\VZ\2(23[= 3 ZT3GH19A26=9
23eH7 H
23(;Y3G4<Q\DHS5B3 O3!5K3 3f26=6H0;YQ [3026=FD6H [587 9>9R3!DgDQ9R3 ; QXDe9A23fU!5B3U!587EDG9 O9 hQfH7 IJ3!5K3!D926=FDH
[587 9:7EDZi 0WFVG9j7 9j7 ;_DQ!9k9A23[ZX5l= =5mWFVG9k9A23#4<QXD9R3!D9bQ J9A23[=!5B9:7 4 3 89A23 8=64A9b9A26=9n9A23 >4 Q QXD
U oHa7 =ZX5l= 7 ; 5BQ\DZ 7 ;j9A23@U!5KQXW 3
n3!5K3e7 ;_=FD(Q587 Z7ED6= ;Y3 Z 3!D9 >5KQ p9A23"; VTW "7 9>9R3GHNU6=FU!3!5

!

W ib

4<QXU MT587 ZX29x• ” v T vtW<M `5

’*=5Es-“367E5

–— ˜A™0— ˜<š ›0œqž6Ÿ" j›G #¡› ŸP¢Y—£¥¤¦Fž ›Y¢
¦T§ ›`¨B!Ÿ\œqž#™.!¦6˜:œG©N¤6ª ˜<«!£ ˜ŸK£ ¢: `©

¬q­G®

Section A.2. Referee 1 (from hand written notes)

 

          !"#$#%
&'()+*,- . /0#00  .)$12 .34356 7&8 
$9;:8<  =&>   =)8 ?)6@A=6B?

 
@C
$98@BD E6 6 #:
FT

T

OU

Am nU (bd

Am ˜£


T m

T

3G=;?35B3=6H [M@5K3!WFV9>9?= 9RQ(9A23(U!Q7ED9R;h9A23(5K3 O35B3G3 ; =6HT3
23(5K3 O35B3G3 ; 35B;A7 QXD=!5K3 A3!U9L=;j4 Q;Y3
=;U!QT;?;q7EW 319RQ09A23Q5O7 Za7ED=
*UFVG9 ;?Q [3(4<Q5‡5K3G4A9:7 Q\D;7ED@=e; XV6=5B30W5K=64 q3 9 n9RQC4 =5O7 lMe9A23&5K3 O35B3G3 ;
U!Q7ED9

T

T b5S

HG
/¬ ?I J
Šb
KMLON,LQPRLQLTS@U"VWVWX@YQZH[.\^]_]`X4\"acbdYaeUfVT\^YhgiU"YQZjkbdl"XZemnbd[ [eX@YQZHX@YnS@X"o
p"qsrutsv"wOxsyOyspsz_{p"|Q|nvOpft~}q€p ”" xst‚}Rvftuƒ  qsy„p_{…yQ†‚}Q{u{"v"qsy_v^q ” vˆ‡
Š‰





!fä

fU

Am

Œ‹& "(/Ž‘ T),+t+-"/ /1"+-#'’
b “ U"VWX\•”lO”c\"aH–T—faH\"VWVW\"a™˜ “ X@Xm_bd—"m_jdbd—"mQZeX–M]`U"aeZebdU"Yn[
š †nvftsvs›
! b ¦ “ U"bkŸ_VWaHbdYnjd\"\^aej§bkZ\"œžaŠZHU"bdS@g1jkXTZemn¨ªX©«[Š\•Ÿ_œ_ n¬^V)­"ŸnbkZŠY_ZHX4XW–®4¯"VT¯f\^°fYO±ˆŸnbd[H[ S“aHbdZe]saHZbklOZebdU)Y_—nZe²m_X\^ZŠZ¡\"S¡m_X–h¢?bkX£c\f[ZHbkYn—W¤ˆY_—"bdY_X4X@a¥1a¡\"–_X
³ †nvupftOy`} ” zQv´}q¶µ‚}^v¸·sp_{Ry‚}qs¹¸ºfqs¹‚}qnvQvft€}Q{»p~{x"¼O¼‚pftQ½  ƒ„yf†nv…|st_vn{"v^qsy
p"tOy‚} ”” zfvˆ‡-¾y¿}Q{À¼‚v"qOy‚}  qnvfr…yQ†nvfts” v…yQ†npfyÁ }•yÂ}Q{»p~{•x^¼O¼‚pftO½  ƒu” yf†nv¸ |Ot_vn{"v"qOy
p"tOy‚} zfvˆ‡ ³ †n”^vf t_v€ }Q{q yQ †‚}qs¹´{"v t_ vfy„p"w xsyÁ }•yc‡ ³ †‚}Q{…pftOy‚} zQvÃ
| }qOy`{ xsy
³ †‚}Q{„}Q{ ƒ ” v"qsyOt_pOz
yf†npfy¸
Q
y
n
†
Å
v
O
Ä
Ä
O
¼
¼
ˆ
q
O
Æ

Æ
¼
s
r
s
v
´
z
Q
}
Ã
{
y
_
y
s
p
Q
z
"
z
…
½
s
Ç
t
s
q
c
¹
‡
}ȼn|  tOysp"q ” vɁ y ” rÊ}^v ” pn{Ry‚}4qs¹„v"qs¹‚}4qnvOvft`{‡ ³ †_v»|QxOwÊzn} ” pfy‚\”}  q  ƒuyQ†§}Q{
}4q_ƒ t^¼`pfy‚} q p"qOq y»wnv¸rsvszQp"½_vQr…xOqsy`}"z…yQ†nv»t_vf˂}Rv"Ǹ|st vn{O{u}Q{…ƒ`}q§}f{•†nvQr™‡
ç bÌ ZbÍ[Y_U"Z.SjdX4\"a™ZHUWZem_XaHX4\f–sX@a”mOœTZHm_X(ÎeS@U"Yn[ŠZH\"YfZ]_aHX4[H[ŠŸnaeXÏ\"Yn–…ÎeSUfYn[ŠZH\^YQZ]ÊUR”cX@a¡Ï
[ŠbkZeŸn\^ZebdU"Yn[”cX@aHX[Š]`X4S@bÑÐÊS4\^jdjkœ;S¡m_Uf[eX@YMZeUž–sX4VWU"Yn[ŠZea¡\RZHX.ZHm_X\^ŸsZHm_U"aÒ []ÊUfbkYQZ4²$Ó¸mnbdS¡m
[ŠbkZeŸn\^ZebdU"Y;bd[VWUQ[Z jdbklfXZemn\^ZgiU"Ÿ_Yn–ÀÔ jkbdl"X4jkœžgiU"Ÿ_Yn–sÕ1bkY(\W–sbdXS@\f[ZHbkY_—WVT\"S¡mnbkY_X•Ö¢.UOX[Zem_X
ÎeSUfYn[ŠZH\^YQZ]_aHX4[H[ŠŸ_aHX4Ï)SUfaeaHX4[e]`U"Yn–hSjdUf[eX@jdœWZeUTU"j͖sX4a [ZœOjdXVT\fS¡m_bkYnX4[”m_X4YhbdYQZeX@YÊ[Šbkgiœ"X4a
Ô bdYQZeX@YÊ[ŠbkÐnX@aeÕA `U^ZŠZHjkX]naeX[e[eŸ_aHX?”\"[\"]_]_jdbkX–žZHUWZem_XbdY ¦ X4SZebdU"Y([eœO[ŠZeX4Vן_YQZemnaeU"ZŠZejdX4–ÊÖ(¢.UOX[
Zem_X(ÎHSU"YÊ[Z¡\^YQZc]`UR”cX@a¡Ï[ebÑZHŸn\RZHbkUfYn[\"[H[eŸ_VWX\)Y_X4”™X4aVT\"S¡m_bdY_X4[4o_[eŸnS¡m;\f[ØcŸ_m_X@a “ S^osZHmn\RZ
—"X@YnX@a¡\RZeX[6ZemnX?]_aHX4[H[eŸ_aeXaHX4ÙQŸ_bdaHX4–)ZeU)\"S¡m_bdX@ÚfX.\#–_X4[ebkaHX4–W—Q\RZeX?Ú"X4jkUsSbkZœ_Ö “ U"VWX.X@Ûs]_jd\"Yn\RZHbkUfY
U^g1ZHm_XjdU"—"bÍSU^g6[ŠX4jkXSÈZebdY_—WZHm_X4[eXZ”™UT[ebÑZHŸn\RZHbkUfYn[”™UfŸ_j͖M `Xm_X@jd]sgiŸ_j
bkY;ZHm_XVT\^YOŸn[HSaHbk]sZ²
Ü {Çnpn{u{Ry_pfysvQr€}q¶yQ†nvupftOy‚} ” zQv$ÝhyQ†_vn{"v¶{s}•yfxnpfy‚}  q‚{ÀÇnvftsv ” †  {"v"q¸w_v ” p"x‚{^v
yf†nvf”"½„
pft_ v»wOx§}^zfr`}qs¹ÃwÊz \”RÞ {+wOxsy…¼  t_v´}¼_|  tOy_p^qsynz"½»y  rOv•¼  q‚{•yOt_pfy_vÉyQ†npf”oyu” yQ†_v

ÄQÄ ¼O¼ q™ÆOÆ#¼ rsvsz´}Q{y y_pszOz"½»ÇOt qs¹ß-¾Rƒ~}•y¿}f{ÃÇst qs¹uƒ t„yQÇ wnp_{s} pn{"v_{
}yÁ{†  xÊzfr…w_v¶p"w`{  z^xsysvsz"½… Çst  qs¹~}q€p"qs½ ”"  ¼_w§}qnpfy`}  q‚{  ƒ„yf†nv»yQÇ €” pn{"v_{6‡
à vfË_vftOyf†nvszQvn{Q{
ÝMp^q~pQrQr`}•y‚} qnpszÃv"áQ|ÊzQp"q_pfy‚} q´}Q{ù‚}•Ë_v"qÁ}4q€·f†_p"|sy_vft„âã‡
 !"[



–— ˜A™&— ˜Aš ›fœ:Tž6Ÿ j›G #¡› ŸP¢Y—£¥¤¦Fž ›Y¢
¦T§ ›j¨B6Ÿdœqž#™.!¦6˜:œG©g¤6ª ˜<«!£ ˜ŸK£ ¢.›A©

!

’ ib

4 QXU<MF587 ZX29x• ” v T vtW<M `5 _’*=5Es-“367E5

Chapter A. What The Establishment’s Scientists Say

b ¥mnX\^ŸsZHm_U"aÒ [\"]_]_aHUf\"S¡mhbd[ŸÊ[ŠX@giŸ_jÍÖbkÚfX4[]`X@a¡[Š]`X4SZebdÚ"XZeUT\TS@U"VWVWU"Y_jdœžŸn[eX4–h]_aHUOS@X4[H[

X4Y_—"bdY_X4X@aHbkY_—)VWXZHm_Us– ¨ª]?±cbkY(–sbdXS@\"[ŠZebdY_—ʲ “ U"VWXU^g
Zem_XaHŸ_Y_Y_X4ajkX4Y_—^ZHmn[ S¡m_UQ[ŠX4Y ¨Š®
VWX@ZeX@aȱcVWbk—fmQZ `XSUfYn[ebd–sX4aXÛ_SX4]sZebdU"YÊ\^j§bdY;–sbdXS@\f[ZHbkYn—#˜žœfXZZemnX\^ŸsZHm_U"aŸn[eX4[cZHm_bd[ZeU
[em_UR”¶m_UR”„VŸnS¡mhbdYX@aHaeUfac\"Y»Îe\•Ú"X4aH\"—"XÏÚR\^jdŸ_XgiU"a?£ S4\^Y; ÊXf²ˆ¥m_X\^ŸsZHm_U"aVWbd—"mQZ \^jÍ[ŠU
YnU^ZeXZHmn\RZZHm_
X UfaŠZH m .VWX@aHbdS4\^Y¢.bdX£c\"[ŠZebdY_
— .[H[ŠUsS@bd\^ZebdU"Yh\"Yn–;VT\^YOœž]_a¡\"SZebkZebdU"Y_X4aH[cŸn[eX
\  a¡\RZHbkU)U^g  #\"[\–_X4[ebk—fYžZH\"ae—fXZcgiU"ac—f\^ZebdY_—n²$¥m_X\^Ÿ_Zem_UfaHÏ\^Yn\"jkœs[ebd[™aeX4bkY_giU"a¡SX4[
ZHm_bÍ[ÚR\^jdŸ_ X\"[\)—"UOUs–žZ¡\^aH—"X@Z4o_\^YʖžZHmn\RZ.[ŠZea¡\•œObkY_—gª\^agiaHU"VÅbÑZ VT\•œžaHX4[eŸ_jkZH[bdYh]`UOU"a –sX[Šbd—"Y
]Ê\^aeZcÐÊjkjdbkYn—T]_aeUf _jdX@VT[¨ bk—ʲ "±
³ †nv¸t_vfË`}^v"Çnvft…t_vQƒsvftÊ{Éy  {^vfË_vft_pOz|  }qsyÊ{+ÇO†§} ” †¶p"t_vÁ}ȼn|  tOysp"qsy…y  pQrQrQt_vn{O{‡
Ü zOz…yQ†nvuƒ  xst~{s} svn{¸{•†  Ç~zfpftO¹_v¸vftQt  t`!
{ ŠÇnv¸r  q  y¸qnvQvQr¸y  ys p Þ #
v "%$i¼ &¸y 


³
rsv•¼ ” q`{RyOt_ pfysvyQ†np"(y '‡ †_v qnv´ {s)} sv$Ý;yQ†_” v¸tsvQƒsvft_vQv…t_vQƒsvftQt_vQr…y pn{
vfá v"|Oy‚} qnpO*
z "«¼‚vfy_v"(t '1Ý«}Q{q yuyQ†_v¶p QyQ xnpsz¸zQv^qs¹OyQ†¸
wOxOy„yf†nvutsv"|st_vn{^v"qsy_vQr
zQv"qs¹Oyf+
† et_vOpQr¸yQ†_v„p"tOy‚} ” zfv¸pf¹_pʁ }(q ”'‡ , t„ rsvn{s}•¹fq ” p"quwn v¸t_v"|st_v_{"v"qsy_”vfrws½´p
zQpftO¹_vuzfv"qs¹OyQ†c‡  ³ †§}Q{u{s}yQ”"xn pfy‚} q p^q¶
wnvuƒ xQq_r»yQ†st xs¹Q† xOy»yQ†nv¸r`}^v p_{Ry‚}qs¹
}q_rfx‚{•yOtO½¸rfx_vu y yQ” †_vÄOÄ ¼O¼ q™ÆOƼ  rsvszÃÇO†§} ” †„r  vn{Éq  y ”^ q‚{s}RrOvft¸tQxOqOq_vft
rsvn{s}•¹fq‡ .O½ ƒOƒÊ} v´}Q{…ƒfxÊzOzÃǧ}yQ†„tQxOqOqnv"tursvn{s}•¹fq‚{Àǧ}•yf†¶tsv"|st_vn{^v"qs#
y "«¼‚vfy_v"t
zQv"qs¹Oyf†~{•x ” †´pn{  qnv…ÇO†§} ” †„¹  y à Ü µs· Ü Æ{rsvn{O}•¹Qq¶p"Çnp"tsr ^ ‡
¾q´ tsvf” ¹_pftsrn{+y / 0 yQ†nvupft_vOp»t_p"y‚}  ÝM|ÊzfvOpn{"v ”"  ¼_|npft_vǂ}•yQ†„” yQ†n v  yQ †nv"t¸t_vQƒsvftsvOv
ÇO† €
zQpÊ}ȼ
2143 6‡ 547 3 9‡ 8;:ã‡B¾»p¼~q yÁ{xst_v…ÇO †§} à † Ü ƒ„Ü ½ x¶tsvOpszO” z"½ 
t_v"|st_v_{"v"qsy à Ü µs · Ü ÆÈ{À|  {s}y‚}  +
q 4¾r`}•rfq™ÆŠy„ƒ`}qsr¶p^qs½ ƒ  µs· ÆÈ{À|OxOwÊz_} pfy‚} q
}q´tsvf¹_pftsrn{+y yQ†§”}Q{É| ” }4qs(y '‡-¾…r ” q  y´
pf¹OtsvOvÃǧ}•yQ†uw yQ†„t_vQƒsvftsvOvn{6‡ ³ †§}Q{
Ë_psz^xnvÆ_pn{…y wnv pOz xÊzQp"y_vQr¸p"qsr p"qOq  y»w_v~{•|_v ” xÊzQp"y_vQr»p_{…yQ†_v¸tsvQƒsvft_vQvn{
pn{O{"vftQy_vQr™<
‡ ,nzQvOp_{"v»ƒ`}q_r„p"q€vfáQ|nzQp"qnpfy`} q»y yQ†‚}Q{É| }qsy~}4q´yQ†_v»|_p"|nvft tÂ}q
vfË_v"quwnvfyQy_vft~}q´·f†np"|Oy_vftu∇


¥m_X@aHX\^aHX[ŠX4Ú"X@a¡\^j‚VT\ ¦ UfaSU"YÊSX@aHYn[ Ì mn\•Ú"X\^ `U"Ÿ_ZcZHm_bÍ[]n\^]`X@a²ã¥m_XTÔ V)UQ[ZeÕ1VT\ ¦ UfacUfY_XTÔ U"g
Zem_X[ŠX@Õ1bÍ[Zemn\^ZÔ bkZŠÕbd[Ÿ_YÊSjdX4\^a”mÊ\RZZem_X]Ê\^]`X@a bÍ[\RZeZeX@VW]sZHbkYn—WZeUT\"S4SU"VW]_jdbÍ[ŠmA² Ì [cZHm_X]n\"]ÊX4a
ZeaHœObkY_—)ZHUž[ŠŸ_—f—"X[Z\)Y_X@”´”c\•œTU"g6–_X4[ebk—fY_bkYn—ZHm_XaHbk—f—"bdY_—#giUfa \W–sbkXS4\"[ŠZebdY_—nosUfabd[bkZZeaHœObkYn—ZHU
\"–_–;\^YhbkVW]_aHURÚ"X4VWX@YQZ™ZHU)Zem_XSUfYOÚ"X@YQZHbkUfYn\^j`] „[ŠUfjkŸsZHbkUfYAoOU"abÍ[bÑZZeaHœObkYn—#ZHUW[eU"VWX4m_UR”u[ŠŸn—"—"X[Z
\@? VT\^Zem_X4VW\^ZebÍS@\"j§ n\"[ebd[cgiUfaZem_X(] „–_bd\"—"a¡\^VÒ Ö
³ †nv…|np"|nvft~{•†  ǂ{ÉyQ†np"!
y "A'Ô yQ†_vÅÄQÄ ”" qsËs” v"qsy‚}  qnpsz C|  B;D  {  z^xsy‚}  q™ÆOÆ«}Q{ y  y_pszOz"½
Çst ” qs¹ˆ Ý EC'yQ†nOv
‚
¼
f
p
f
y
n
†
•
v
‚
¼
pfy`} pszÉp"qnpsz^½Oy‚} pOzu{ z^xOy‚} quƒ tuyQ†nv»C| B;D |st ˂}Rrsv_{p"q
vfá vszOzQv^qsy»y  z¸ƒ  t~{RyQx_rQ½`}qs¹¸yQ†nvuvQƒQƒsv ” y  ƒuË_pft`}  x‚{+|np"t_p•¼‚vfysvft`{6‡
¥m_XU^ZHm_X@aVT\ ¦ U"aSUfYnSX4aeY;bd[Zem_X]`UQUfaU"aH—f\"Y_Gb F\RZHbkUfYMU^g
Zem_Xb͖sX\"[”m_bÍS¡m;Zem_X\"ŸsZem_UfaH[Ô \^aHXÕ
ZeaHœObkY_—)ZHUT]_aeX[ŠX4YQZ4² _UfabkYn[ŠZH\"YnSXfosbÑZ bÍ[Ÿ_YÊSjdX4\^amnUR”¶[e]ÊXSbkÐÊSaeX[ŠŸ_jkZH[]naeX[ŠX4YfZHX4–hbkY;ZHm_XaeX[ŠŸnjÑZ¡[
[ŠXSÈZHbkUfY;”mnX@aHXUf sZH\"bkYnX4– ¨ŠÔ giU"abdYn[Z¡\^YnS@XÕ1mnUR”„”[email protected]_XaeX[ŠŸnjÑZ¡[bkHY bk—fŸ_aHX4I[ )\^Yn – 
S@\"jdS@Ÿ_jd\^ZeX–n֕±È²
¾Ãr  q  y¸xOq_rOvft`{Ry_p^q_rÆ  DŽyQ†_v  tO¹_p"q§} spfy‚}  q  ƒuyQ†nv…|np"|_vftut_vszQ”pfysvn”{+y  yQ†nv¸ƒsp ” y
yQ†_pfyuyQ†nv¸t_vQƒsvftsvOv…r  v_{q  y„xQq_rsvft`{•y_p"q_rɆ  K
Ç J‚}•4
¹ :¶p^q_K
r L¸Çnv"t_v psz xnzQpfy_vQrˆ‡ ³ †_v
>=




 !"[

M µÂ¼ŸµE¯ª°˜»A°+ÆCµ#¼9¾ÏèÙBÈAº9ÑA°ª¸aƵC³AºªÑ-½ ºªÁ

!

W ib

4<QXU MT587 ZX29x• ” v T vtW<M `5

’*=5Es-“367E5

–— ˜A™0— ˜<š ›0œqž6Ÿ" j›G #¡› ŸP¢Y—£¥¤¦Fž ›Y¢
¦T§ ›`¨B!Ÿ\œqž#™.!¦6˜:œG©N¤6ª ˜<«!£ ˜ŸK£ ¢: `©

/N

¬q­

Section A.3. Referee 2

 tO¹sp"q§)} sp"y‚}  q  ƒ¸yQ†nv»|np"|nvftur  vn{Éq  yu†npfË_v¸p^qs½OyQ†§}4qs¹ur  ǧ}•yQ†u†§}f{ÃxOqsrsvft`{Rysp"q_r`}qO¹
Qy †nv ”" q ” v"|syʁ {+|st_vn{"v^qsy_vQr™‡2¾q„t_vf¹spftsr¸y  yQ†nv»xOq_rsv"t`{Ry_p"qsr`}qs¹  ƒ¸†  ÇKJ‚}•¹QxOt_v :
p"q_rKL¸Çnvft_v wOy_pÊ}qnvfrãÝMyQ†nv¸t_vQƒOvft_vOv„{† xÊzfr»tsvQƒsvftOtsvQr»y p"q€vszQv•¼‚v^qsy_pftO½»ƒ_z^x§}Rr
¼‚v ” †np"q§} ” {+y_vfáOy¸w QfÞ p"q_r ”" ¼nw‚}qnvQr´}y„ǧ}yQ†„yQ†nvuvfáQ|Êzfp"qnpfy‚}  q…|stsvn{"v"qsysvQr´}q¶yQ†nv
|np"|_vftc‡
“ X4Ú"X@a¡\^j§[e]ÊXSbkÐÊSSUfVWV)X4YQZH[\^aHX”aebkZŠZHX@YU"YhZemnXVW\"YOŸn[eS@aebd]sZbkZH[eX@jkg VWUf[ŠZU"g
ZHm_X4[eX”cX@aHX\"aeX\"[
”m_X4aeXZemnXaeX4ÚQbdX@”cX@a”\"[Ÿ_YÊSjdX4\^aUfY;”mÊ\RZZem_X\"ŸsZemnU"a¡[V)X\^YQZU"a  \"aeX\"[c”m_X@aHXgiŸ_aeZem_X4a
–sbÍ[eS@Ÿn[H[ŠbdU"Y;”c\f[cY_X4S@X4[H[e\"aeœf² ?YnXbÍ[H[ŠŸ_XZHmn\RZ bÍ[]n\^aeZebÍSŸnjd\"aejdœžbdaels[eU"VWX?bÍ[ZHm_X\^ŸsZHm_U"a¡[™ZeX4Yn–sX@YÊSœ
bdY[eX4SZebdU"Yn[®\"Yn– ZHUW”™UfYn–sX@aÔ ”\^Yn–sX4aŠÕ§U «”bÑZHm»ÎŠX4–_bÑZHU"aHbd\"jd[HÏ#\"Yn–;U^ZemnX@aŸ_Yn[eŸ_]_]`U"aeZeX–
SUfVWV)X4YQZH[”m_bÍS¡mmn\•Ú"XY_UW]_jÍ\"SXbdY\)ZeX4S¡mnY_bdS4\^jA\"aŠZHbdS@jkXf²
,nzfvOpn{"v¶{•†  Dž¼‚vuvfË_v"q  qnv»xOq‚{xO|O|  tQy_vQr ”^ ¼O¼‚v"qOyßOß
.ZemnX@a SUfVWV)X4YQZH[ȬRSUfYnSX4aeYÊ[™bdYnS@jkŸn–_ X 

”mn\RZ –sUOX4[cZHm_XZebkZejdXmn\•ÚfX.ZHUž–sUW”bÑZHm;Zem_X]n\"]ÊX4a¡Ö¥mnX]n\^]`X@a –sUOX[Y_U^Z –sX@ÐnY_X”mn\^Z.\
]  #–_bd\"—"a¡\^V×bÍ[\^Yn–MZemnXaeX[ŠŸ_jkZH[–_U"YAÒ Z aeX\^jdjkœžZebdXbkY”bkZem;Zem_XŸÊ[ŠXU^g$[eŸnS¡m;–_bd\"—"a¡\^VT[@²
³ †nv…|np"|_vft¸|st_vn{"v^qsy`{+yQ†_v¶vfásp ” y„p"qnpOz"½Oy‚} ” pszu{  zRxsy‚}  q¸ƒ  tuyQ†nv»C| B;D
rÊ}^pf¹O t_p¼.‡ ³ †nvutsvn{•xÊz"yÊ{+”"y‚ }^v~ }q¶Ë_vftO ½»ÇnvOzOzÃǧ}•yQ”"†„
yQ†nv” ”" tQt_v ” y…| B D r`}^p"¹Ot_p•¼.‡

q_ƒ tOyfxOqnpfy_vOz"½ˆÝ)yQ†nvÅÄOÄ ¼O¼ q™ÆQƼ rOvsz´}Q{„}q tQt_v yup^q_rÁ{ yf†nvutsvn{•xÊz"yÊ{
” p"qOq  y»w_v¸y`}^vQr~}q„ǧ}•yQ†Â}•yc‡
]  ÁbÍ[ \)aHX4[eŸ_jÑZU"g
ZHm_X\^]_]njkbÍS@\^ZebdU"Y;U^gØcX4aeY_UfŸ_jdjkb Ò [XÙQŸn\RZHbkUfY

]A²
T¥m_XaHX@jÍ\RZHbkUfYn[em_bk
[Šœs[ŠZeX@VCjkbdl"XZemÊ\RZ.[em_UR”YhbdHY bk—®"²$Ó¸mÊ\RZ bÍ[cZem_Xa¡\RZHbkUfYn\^j‚U"a Ê\"[ebd[ `X@m_bdYn–;X4ÙQŸn\^ZebdU"Y ® 
X"² —n² ~¨® ± M”bkZemY ®"o§®•¬ so_\"Yn–«®R¬

 vft_v€¾ ¼nx‚{RyuyQ†_p"q Þ yQ†nv»t_vQƒOvft_vOv»ƒ  tu†‚}Q{ ”" ¼O¼‚v^qsyß-¾•ƒ„yQ†_v¸tsvQƒsvft_vQvÆnpQr
{^”^vf t‚}  x`{À|st  wnzQv•¼¶xOq_rOvft`{Ry_p^” q_r`}qs¹yQ†§}f{|  }qsyˆÝ ¾É |st  wnp"wÊz"½€
{†  xÊzfr…†_pfË_v
q‚{s}RrOvft_vQr…pQrOr`}qO¹„p„r`}f{ x‚{O{O} q„p"w xsy¸yQ†§}f{| }qsyˆÝ«{x ” †´pn{¶}q€·"†np"|sy_v"tu∇

]A² )¥m_XaHX@jÍ\RZHbkUfYn[em_bk]h ÊX@Z”™X4X@YX4ÙQŸn\^ZebdU"Y ®f¨ \f±ˆZeU(®Q¨ªS4±c\"Yn–\)–_bkXS4\"[ŠZebdY_—VT\fS¡m_bkYnX\"[
Ί]`UQUfaHÏno6ÎeSUfVWV)UfYnÏ_os\"Yn–ÎeXÛ_SX4jkjdX@YQZ¡Ï]`X@aegiU"aHVT\^YnS@X?bÍ[Y_U"Z SjdX4\^a \"Yn–hY_X@X–_[ZeUW `X
–sX@ÚfX@jdU"]`X4–§osUfa\^Z jkX\"[ŠZ –sXÐnYnX4–§²
{"vOv…|st_v"˂}  x‚{ ”^ ¼O¼‚v"qOy

Ì ZbÍ[”cX@jdj§lQYnUR”YžZemÊ\RZ£  giU"a \)–sbdXS@\f[ZHbkY_—)VT\"S¡m_bdY_X\^Yʖh–sbdXbd[YnU^Z \WSU"YÊ[Z¡\^YQZ4² Ì Yhgª\"SÈZ
bÑZ bÍ[SUfV)VWUfYh]_a¡\"SZebÍSXZeUWX@ÛO]`X@aHbdV)X4YQZH\^jdjdœM–sXZHX@aHVWbkY_X£  giU"aŸn[eXU"Y–sbdX4[”bkZem ? [ebdV)bdjÍ\^aÒ
—f\RZHbkYn—jÍ\•œ"UfŸsZH[cbdYhZHm_XgiŸsZHŸ_aeXf²ãØcŸsZ  ÊXS@\"Ÿn[ŠXVWUQ[Z –sbdX4[mn\•ÚfXYQŸnV)X4aeUfŸn[c—f\^ZeX4[ naH\"YnS¡m_bdY_—
U  U^g6YOŸ_VWX@aHU"Ÿn[caHŸ_Y_Y_X4aH[4oOZeUž–_XZeX4aeVWbdY_X\^jdjAU^g
Zem_XgiaHbÍSÈZebdU"Y;gª\fSÈZeUfaH[\f[\#giŸnYnSÈZHbkUfY;U"g
X@œOY_Ufjd–_[YOŸ_V ÊX4a”™UfŸ_j͖M `XÙQŸ_bÑZHX–s!b TS@Ÿ_jkZ.\^Yn–;ÚObkaeZeŸÊ\^jdjkœžŸnYfZHaH\fSÈZ¡\^ _jdX.giUfa.–sX[Šbd—"Y
]_Ÿ_aH]ÊUQ[ŠX[@² X@YnX@a¡\^jdjkœž–sbdXS@\f[ZHbkYn—)X4Y_—"bdY_X4X@a¡[ˆÐÊYn–SU"YOÚfX@YQZebdU"Yn\"j‚]  )\^]_]_aHUf\fS¡mM”cU"aHls[
ÙfŸnbÑZHX”cX@jdj§giUfa –sX4[ebk—fYh]nŸ_ae]`Uf[eX4[4²
³ †§}Q{ ÄOÄÈ{"vfË_vftspszÉ|  }4qsy`{
Æ ”" ¼O¼‚v"qsy…¹‚}•Ë_vɼ‚v¸yQ†nv  |O|  tOyQxOq‚}•yO½…y  r`}f{ ” x‚{O{^vn{
yf†nv¸ƒ  zOz  ǧ}qs¹…|  }qsy`{#"

!s

–— ˜A™&— ˜Aš ›fœ:Tž6Ÿ j›G #¡› ŸP¢Y—£¥¤¦Fž ›Y¢
¦T§ ›j¨B6Ÿdœqž#™.!¦6˜:œG©g¤6ª ˜<«!£ ˜ŸK£ ¢.›A©

!

’ ib

4 QXU<MF587 ZX29x• ” v T vtW<M `5 _’*=5Es-“367E5

Chapter A. What The Establishment’s Scientists Say

¾ÉÇ  xÊzfr Þ }q_r_z"½„p_{ Þ yf†nv»t_vQƒsvftsvOv$ÝMy  |ÊzQvQpn{"vÃ|st  ˂}Rrsv…yQ†_v»q_p•¼‚vn{  ƒ
p"qs ½ ”" ¼n|n p"q§}Rvn{ÀÇO†  ¼ ÄQÄHvfáQ|nv"t‚}¼‚v"qOy_pszOzR½…rsv"y_vft^¼
}4qnv÷n‡fÆOÆ ,_vftf†n” p"|‚{ÉyQ†_vf½
r  }•y¶
r ÇOquxOqsrsvft Ü x`{RyOt_psz_}^pC' ÇO†_vft_v…yQ†nvCÄOĝt_vf¹QxÊzfpftˆÆOÆW|O†s½`{s} {…zQp"ǂ{
r q  y´ p"|O|nz"½ Š|ÊzQ” vQpn{"v$Ýhƒ  tO¹‚” }•Ësv+ ¼‚v¶p^w  xsy»wnvn}qs¹uyQ†nv ” ½Qq‚} ” psz»p"w  xsy
yQ†§}f{+| }qsy™”"‡B
y yQ†§}Q”"{… p"qO½ yQ†nvft»Çnp"½c‡'‡ ,_zQvOpn{"v6Ý
 ¼_|n¾ p"qsp"½¸qOyQq †_pfy¸y¸tsx‚vOp{"vnyu
{•† ÇÃ
‚
¼

v
p

{
Q
y
†nvCÄOÄ ¼O¼ q™ÆOƞC| B;D r`}^pf¹Qt_p•¼€p"qsrÂ}•y
Ç t Þ {6‡
µQ” xnv»” y  yQ†nv ”" ¼n |Oxsy_v"t»t_vfË   z^xsy‚}  q™Ýž” y  rspf” ½Á}•yÂ}Q{É|  {O{s}4wÊzQv…y  ” r  ” yQ†nv 
psz xÊzQpfy`} q‚{ ƒuyQ†nv¸·  ƒ t¶p~{•|_v }Rƒ`} rsvn{s}¹Qq¸Ç§}•yQ†´p~{•|nv }•ƒ`} ƒ_z Ç
t_pfysv Hr`}^v ” pn{•y‚}qs¹¼‚p ” †§}qnv '‡7¾q¶ƒsp ” yˆÝ;yQ†§}Q{„}Q{…vfás p ” ynz"½»ÇQ†npfyuyQ†§}Q{
|np" |_vft„pszOz¸p"wÞ xsyc‡  . ” t_v ” Ë_v"tˆÝMy  rOpf½¸” yQ†nvftsv~}f{¸p»|st ¹Q” t_p•¼´yQ†np"y´pOz"t_vOpQrf½
r v_{ÉyQ†nvn{"v }4q_r ƒ psz xÊzfpfy‚} q`{
Ý pszOzQvQr»µ`}^v ,_vftOƒsv y s‡
 vftsv…yQ†nv¸t_vQƒsvftsvOv¶}qsyQt  rfx ” v»puqnv^Ç¿}•rsvOp  ƒuyQ†nvCÄOÄeƒsp¼
}"z"½ˆÆQ@
Æ 7;7»yQ†nv
}¼n|Ot  Ë_vQr ”^”" q‚{Rysp"qsy¸·  ‡ ¾4q€v_” {O{"v"q ” v$ÝhyQ†nv€}RrsvQp  ƒ ÄOĊƒsp•¼
}"z^½ˆÆO” Æ }f{ ”
}¼n|Ot Ë_v q‚{Ry_p^qsy¸·  }q¶” ÇQ†§} † q_v„p_{O{s}•¹Q q_vQr»Ë_psz^x_v…y p€” {•|nv }Rƒ`” }
¹Ot  xO|  ƒutQxO qOqnv"” t`{6
‡ n}q v…yQ†‚}Q{„}RrsvOp»Ë‚} zQpfy_v…yQ†_v»w_pn{s} |O†s½Ê{s} {Ãzfp"ǂ{
p"q_r¸yQ†_ v»|Ot rfx ” vn{+yQ†nv  |O|  {s}•y_vy  tsvOpsz"yO½¸yQt_v"q_rÊ{u}y»¼nx`{Ry¸wnv
p"wnp^q_r qnvfr™‡ Ü yQxnpszQz"½ˆÝžyf†nvÁ}•rsvOp ƒÅÄOÄeƒsp¼
}"z"½ˆÆQÆ«}Q{Ãt_pfyQ†nv"t»w§)} spftQt_v$Ý
wnv ” p"x‚{"v»p ” †np^qs ¹_v´}q¶yQ†nvursvn{s}¹Q q ” p"q€zQvOpfruy  p€{s}•¹Qq‚”"}R ƒ`} ” ” p^qsy ” ” †_p"qs¹_v
}q„yQ†nv¸Ë_pszRxnv ƒ„·  ‡ JQxstQyQ†n vft^¼ t_v$ÝTyQ†nvCÄOÄeƒsp¼
}"” z"½ˆÆQ Æ q Ov" |sy p^qÁzQvQpQr
y  p»” | O t„rs vn{O}•¹Q+
q et_vQpQr„p"w xsyuyQ†‚}Q{u}q¶yQ†nv€{"v y‚} qÅÄOĝ| tursvn{O}•¹Qq
vQƒOƒOv y`{
ÆQÆ ƒuyQ†§}Q{Éw QfÞ '‡   Ç  qnv ” p"q´rsv ” }•rsvQrÃÇO †‚} ” †¶rsvnÞ {s}¹QqÁ}Q{
|npftQy  ƒuÇQ†npfy ÄOÄeƒsp¼
” }"z"½ˆ” ÆQÆ¡›ºQË_v"qÂ}Rƒ¸yQ†nvftsv» Ç_vft_”"v… q ¼
}Q” {Ry_p vn{
ÝMyf†nv
p"xsyf† tˆÆ{ ¼‚vfyQ† r psz xÊzQpfy‚}4qs¹…yQ†_vu·  '¶}f{ ƒ xst`{"v †_vOp"|nvft„p^q_r
ƒspn{•y_vft¸yQ†np^q¶yf†nv»t_vQƒsvftsvOv$Æ{»{xs¹O¹_vn{•y‚}  q¸p"w  xsyÄOĊƒsp•¼
}"z^½ˆÆOÆ  ƒ„tQxQqOqnvft
rsvn{O}•¹Qq‡-¾q¿{x"¼O¼‚pftQ½ˆÝMyQ†§}f{¶}•rsvOpupuËsvftO½¸wnpQr~}RrsvQpˆ‡
š †np"y~}Q{»·  1 ”" q`{Ry_p"qsy_› ³ †_v¸tsvQƒsvft_vQv…t_vQƒsvftÊ{Éy  yf†nv ” pn{"v…ÇO†nv"t_v¸·  }f{
”" q`{Ry_p"qsy»ƒ  t~{•|nv ” }Rƒ`} ” tfxOqOqnvft„rsv_{s}•¹Qq¸wOxOyuÇQ†§} ” †Á}Q{q  y„yQ†nv ” p_{"v€}q
t_”"vO pOzn}•yO½c‡  ³ †nvu
·  r  vn{Éq  y¶rOv"|nv"q_r  qÊz"½  q¶yQ†nv»tQxO” qOq_vftˆÝMwOxsy ”  q¶yQ†nv

¼_w§}qnpfy`} q ƒuyf†nvutfxOqOqnvft€{•½`” {Ry_v•¼¶” ǂ}•yQ†„yQ†nv¸r`}^v p_” {Ry‚}qs ¹¼`p †§}q_v…Ë‚}^p
yQ†n

v _v»qOx"¼_wnvftc‡ ³ †Ox‚{
Ýp~{•|nv }Rƒ`} tfxOqOqnvfturOvn{s}•¹Qq p"qOq y»†_pfË_v¸· 
Ĕ"O ÄHp_{O{s}•¹Qq_vQrだÆOÆWy  }•yc‡ ³ †nv¸· (†npn{Ãy  wn” v ” psz ” xÊzQpfy_” vfr»ƒ  t¶p"qs½
¼_w§}qnpfy`} q»tfxOqOqnvft€{•½`{Ry_v•¼¶Ç‚}•yQ†¶r`}^v pn{•y‚}qs¹¼‚p †§}qnvã‡
¾É Ç  xÊzfr„Þz_} Þ v»y  ƒ`}q_r„p"qs½ ” p_{"v…ÇOQ†n vft_v»yQ†_vÅÄQÄ ”" ¼O¼  q™ÆOÆW C| B D r`}Rpf¹Ot_p•¼
r” v_{+ Ç t  ‡ Þ ,_zQvOpn{"v…tsvOpQr¸yQ†nv…|st ƒÊ{u}q´·f†np"|Oy_vftuâ~{•† ǧ}4qs¹…ÇO†s½Â}•y
p"qQq y»Ç t ‡

¢?bÍ[eS@Ÿn[e[ebdU"Y\^Yn–haeX[ŠŸnjÑZ¡[ €—"aHX4\RZ –sX\^j§U"g6–sbÍ[HSŸn[H[ŠbdU"YMgiUsSŸn[eX4[UfYMZHm_XaHX@—"bdU"YÊ[™”mnX@aHX
 /0  ²d®  œfXZ bdY;ZœQ]nbdS4\^jA–sbdXS@\"[ŠZebdY_—T–sbdX4I[  /0  ² °ZeU ² ¯ s²
,nzQvQpn{"v»t_vOpQr¸yQ†_v ”^ ¼O¼‚v"qOy`{+y  yQ†nv…|st_v"˂}  x‚{ÉtsvQƒsvft_vQv
Ì Y(SU"YÊSjdŸn[ŠbdU"Y1osbÑZÒ [ ¦ ŸÊ[Z.\)]_jÍ\^bdY([ŠjdU"]_]OœT]_bdX4S@XU^g6”™Ufael
¾É†  |_v¸yf†npfyut_vQƒsv"t_vOv»r  v_{q  yü
}q_r¸yQ†np"y¾Éǧ}"zQz…x`{"v€}•y€p_{…yQ†_v ” †np"|sy_v"t
fx  y_vˆ‡

!

W ib

4<QXU MT587 ZX29x• ” v T vtW<M `5

’*=5Es-“367E5

–— ˜A™0— ˜<š ›0œqž6Ÿ" j›G #¡› ŸP¢Y—£¥¤¦Fž ›Y¢
¦T§ ›`¨B!Ÿ\œqž#™.!¦6˜:œG©N¤6ª ˜<«!£ ˜ŸK£ ¢: `©

¬q­

Section A.4. Referee 3

¨iZem_X Ÿ_Zem_UfaH[cX@ÚfX@Yhmn\•Ú"X?U"Y_XU^gAZHm_XaeX@giX@aHX@YnS@X4[ˆZeUZem_X4bkaUR”Yh]_Ÿ_ _jdbdS4\RZHbkUfYn[™[ebkZeX4–hbdYnSUfaeaHX4SZejdœ ±È²
,_v"tQ†np"|‚{1ÝMyQ†nv»t_vQƒOvft_vOv¶{•†  xÊzfr„zQvQpftQq„yQ†npfy¼`pf¹_p `}4qnvn{ ” †_p"qs¹_vÃqnp¼‚vn{…p"q_rãÝ;yQ†_pfy
yQ†nv…qnp¼‚vup"|O|nvOp"t`{u}q¶yQ†nv»t_vQƒsv"t_v"q ” v„}Q{…yf†nvɼ‚pf¹_p Ê}qnvqnp¼‚vupfy¶yf†nv»y‚}¼‚v  ƒ
Çst‚}y‚}qs¹¸yQ†_v»|_p"|nvftc‡



 !"[

=

¥m_XgiUfjkjdUR”bkYn—)S@U"VWVWX@YQZH[\"aeXY_U"Z.\^aHaH\"Y_—"X–TbkY(\"YQœM]n\^aeZebÍSŸ_jÍ\^aUfaH–sX4a4²
X@YnX@a¡\^j 6¥mnX?ZHXÛOZ mn\f[\YOŸ_V ÊX4aU^gX@aHaeUfaH[™bkY—faH\"V)VT\"a4oOŸn[H\^—fX\"Yn–h[e]`X@jdjkbdY_—)Zemn\^Z Y_X@X–žZHUT ÊX
\"–n–saeX[e[eX4–M ÊX@giU"aHX]_Ÿ_ _jdbÍS@\RZHbkUfYA²
]H;®  ™]n\^a¡\^—faH\"]_m ˆ¥m_XÐna¡[ŠZH[X@YQZeX4YnSX[H\•œO[™ZHmn\RZZHm_ X
nUR”„a¡\RZHXbd[ \giŸ_YÊSÈZebdU"YU"g
ZeX4VW]ÊX4aH\^ZeŸ_aHX"osœfXZZemnXaeX[ZU^g
Zem_X]Ê\^a¡\^—"a¡\^]nmM[e\•œs[cZHmn\RZbkZ.bd[eYAÒ Z4²
³ †_v¸tsvn{Ry  ƒuyQ†nv…|npft_p"¹Ot_p"|O†´{"pf½uyQ†nvuƒ_z  Çutspfy_v€}Q{»p¸ÇnvQp Þ ƒfxOq ” y`}  q  ƒ¸yQ†nv
y_v•¼_|nvft_pfyfxst_v…”"p^ q_r¸ yQ†npfyÁ
}•y´vfáQ|ÊzfpÊ}q‚{ÀÇQ†s½c‡ ¾É†  |nv»yQ†np"y´v"Ë_vftO½  qnv»pf¹OtsvOvn{+ǧ}•yf†»¼`v
yQ†np"yÂ}” y¿}Q{ ” ¼O¼ q„y  {Ry_p" y_vup ”" ¼O¼  q¶pn{Q{•x"¼n|sy`}  q„p"qsr¶v" áQ|ÊzQpÊ}4q¸
ÇO†s½Á}q¶yQ†npfy
|npftQy‚} xÊzfpft p_{"v€}•y¿}f{Ãq  yÂ}ȼn| tOysp"qsyc‡2¾ǂ}Q{•†„yQ†npfyÃÞ ¼ t_v…|nv  |ÊzfvÃÇ  xʁ zfrur 
x‚{•y„yf†npfyc‡ J`}•t`{RyˆÝ }y„Ç xÊzfruvszn}ȼ
}qnpfysvÀ¼‚p"qs½Ã¼
}f{Ry_p v_{+yQ†npfy¶pftsv~{R½fq qs½^¼ x‚{
ǧp
}•yf†¶tsvn{"vOpft ” †~}q´r`}^v ” pn{•y‚}qs¹ˆÝMw_v ” p"x‚{^v¶}•y¶ƒ  t ” v_{ÉyQ†nvCÄOÄ{@¼`pftOyˆÆOƞt_vn{"vOp"t ” †nvftÊ{
y ” †nv ”•Þ yQ†nv¼‚p  t„p_{O{•x"¼n |Oy‚}  q‚{ yQ†nvf½Ã¼‚p Þ vˆ‡ Ov ”" q_rãÝ }y»¼‚p Þ vn{ ” zQvQpftuy  yQ†nv
t_vOpfrsvft»ÇO†s½uyQ†_v¶pn{Q{•x"¼n|sy`} q…Ç_pn{+¼`pQrsvˆ‡
]  ã\Rg ZHX@a¤ˆÙ   “ m_U"Ÿ_j͖žbdYn–sbÍS@\^ZeXbkVWVWX4–_bd\^ZeX@jdœTZHmn\RZcZem_X[eŸ_ n[HSaHbk]_ZÔ [Õ‚aeX@giX@acZeUZemnX[eX4SZebdU"Yn[cbdY
bk—fŸ_aHX)®f²
¾Éǧ}"zOz ”" q‚{s}Rrsv"t»yQ†§}Q{1Ý
_vfyˆÝ ¾¸p¼€q  yÂ{xst_v»yQ†§}Q{„}Q{…p¸¹ O r~}RrOvOpˆ‡
H]  ˆ\Rg ZeX4a X4ÙQŸn\^ZebdU"Y  ˆ¥m_X@aHXbd[ \)VT\ ¦ Ufa\"[H[ŠŸ_VW]sZHbkUfYhVT\f–sXm_X@aHXZemn\^Z.[ŠmnU"Ÿ_j͖MYnU^Z ]n\f[e[
”bkZem_UfŸsZ.[ŠUfVWXS@U"VWVWX@YQZÔ [ŠÕ M>Î .[H[eŸ_VWbkY_—T[ŠZeX\"–sœM[ŠZH\^ZeXÏ ˆ¥m_bÍ[ \"[H[eŸ_VW]sZebdU"Y;—"UOX4[cZHU)Zem_Xm_X\^aeZ
U^gZemnbd[\"]_]_aHUf\"S¡mMZeUWZHm_XÐnjdjkbdY_—TS@\"jdS@Ÿ_jd\^ZebdU"Y\^Yn–hX4[ŠZH\" _jdbd[em_X4[cZHm_X `U"Ÿ_Yn–n[U^g6bÑZ¡[\^]_]njkbÍS@\" _bkjdbkZœ"²
¥m_X\"ŸsZem_UfaH[[em_U"Ÿnjd––sbÍ[eS@Ÿn[H[cZem_bÍ[]`U"bdYfZ²
š vOzOz6Ý ¾y  y_pszQz"½ur`}Q{"p"¹Ot_vOvǂ}•yQ†„yQ†nv¸t_vQƒsv"t_vOv  q¶yQ†§}f{|  }qsyc‡ ³ †nvɼ‚p  t
fxnv_{Ry‚}  q€}q€rÊ}^v ” pn{Ry‚}4qs¹~}Q{†  DŽy  v"q‚{•xstsv…yQ†nv»t‚}•¹Q†Oy„tsp"qs¹_v  ƒ„ƒ`}"zQzn}qs¹¸y‚}ȼ‚v
 ” psz ” xÊzQpfy_vyQ†nv¸· 
p"q_r¸¹_p"y_v»Ë_vsz \ ” }•yO½c‡ ³ †§}Q{É|np"|_vftˆÆ{«¼`pÊ}q ”" q  ” vftQqÁ}Q{” †  DŽ” y p
p"q_rursv"y_vft^¼
 }4qnv¶}RƒuyQ†nv¸·  wnvC” ÄOÄHpn{O{O}•¹QqnvQr$ÆOƞy p€{•|nv }•ƒ`}  tQxQqOqn” vftc‡ ³ †nv» xOq‚{RysvOpQrQ½
{Ry_p"y_v€}Q{ qÊz"½¶p€{s}RrsvuvQƒOƒOv y„p"q_r¸†npn{Ë_v"tO½´zn}¼
}•ysvQr€}¼n| tOy_p"q vÃrfxnv¸y Ü º  ˆ‡
 ƒ ”" xstÊ{"v…yQ†nv¸ƒ_z  Ç¿}f{Ãq  y ”^ qsy‚}qQx  x‚{ s{Ry_vOpQrf½u{•y_pfy_v¸p"qsrÂ}Q{…pQƒQƒsv ” y_vfr…ws½Ã¼‚p"qs½
|npftsp•¼‚vfy_v"t` {…{•x ” †´pn{…yf†nv… |§}Q{Ry  q„Ç_vÊ}•¹Q†syãÝ;vfy ” Ý(pszQz  ƒ»ÇO†‚} ” †´pft_v»t_vszfpfy_vQr»y  yQ†nv
yOt_p^q‚{s}•y‚ } q…| }qsy¶p"q_r»q y„y yQ†nv»C| B;D r`}^pf¹Otsp•¼„ |nvftÁ{"vˆ‡ ³ †n” v…xO q‚{Ry_vQpQrQ½´{Ryspfy_v
vfá‚}f{Ry`{ qÊz^½Â}4q´yQ†_v~}4q§}•y‚}^pOz»p"q_ruƒ`}qnpOz´{•y_pf¹_vn{ ƒ„yQ†_v~}4q v y` } q” ‡ Ü {»p
¹_v"q_vft_pszÔ tQxnzQv$ÝM†npfË` }qs¹„p»ÇnvszOz»rsvn{O}•¹Qqn\vQ” r…| B D r`}^p"¹Ot_p•¼„Ç‚}"zOzÁ |st r"x v¸ p
{s}•¹fq§}Rƒ`} p"qsy´}ȼn|st Ësv•¼‚v"qsy¶}q¶yQ†nv…|st vn{O{rsvn{O}•¹Qq‡-¾•yÂ{† xÊzfr…w_v¸q y_vQr»yQ†np"y´p
ƒfxÊzQz…|_p"|nvftur`}f{ ” x‚{O{O}qs¹»yQ†_v»xQq‚{Ry_vOpfrQ½€{Ry_pfysv´}Q{Ãw_vÊ}qs¹»|stsv"|npft_vfr¸ƒ  t¸|OxOwÊz_} ” pfy‚}  q
pfy„yQ†nv…|st_v_{"v"qsy¸y‚}ȼ‚vˆ‡


!

É ÆϵE¯9°B¸a°i¾Ü°ª¸a°+°ŸÒ ¼Š¼ª½ ºªÁŸ¾Ü¼A¸M¼-ºª°w¼>¸JÆC°ià9°ª¸Ü³AÒ-°c²-¶AÒ ³Aº9³Yµ:½ ¼-º9Æ
–— ˜A™&— ˜Aš ›fœ:Tž6Ÿ j›G #¡› ŸP¢Y—£¥¤¦Fž ›Y¢
¦T§ ›j¨B6Ÿdœqž#™.!¦6˜:œG©g¤6ª ˜<«!£ ˜ŸK£ ¢.›A©

!

’ ib

4 QXU<MF587 ZX29x• ” v T vtW<M `5 _’*=5Es-“367E5

Chapter A. What The Establishment’s Scientists Say

Ì Y—"X@YnX@a¡\^j`Zem_XUfae—Q\^Y_b F4\^ZebdU"YhU^g1ZHm_X]n\"]ÊX4abd[ [eU"VWX4”mn\RZ”cX4\^l ˆZem_XbdYQZeaHUO–_ŸnSÈZHbkUfYhX[Š]`X4S@bd\"jkjdœ
–sUOX4[YnU^ZÚ"X4aeœž”cX@jdjA[eXZZemnXZeX4S¡mnY_bdS4\^jAS@U"YQZeX@ÛQZgiUfaZem_X]  VWXZHm_Us–\^Yn–;[ŠmnUR”„m_UR”„Zem_X
]_aHX4[eX@YQZ”™UfaelWÐ_Z¡[bdYfZHUTbÑZ²
³ †nv…|st_vn{"v^qsy»Ç  t Þ r  vn{Éq  y„ƒ`}•yÂ}qsy  |_pn{Ry¸Ç  t Þ ß7¾•yÁ{•†  ǂ{yQ†_pfyuyQ†nv…|npn{Ry
Ç  t Þ }Q{ÃÇOt  qs¹ˆÝp^q_r»wOx§}"zfrn{Ãyf†nvɼ‚pfyQ†nv¼‚pfy‚} ” pszÉyQ†_v  tO½»wnv^†§}q_r»yQ†_v»| B D r`}^p"¹Ot_p•¼.‡
¥m_XjÍ\"[ŠZ]Ê\^a¡\^—"a¡\^]nmžU^gZem_XbdYQZeaHUWbd[S@U"YsgiŸn[eX4–ÀÔ SUfYsgiŸn[ebkY_—"Õ ²$¥m_Xb͖sX\bdYQZeaHUs–sŸnSX–;bkYhZem_XjÍ\"[ŠZ
[ŠX4YQZeX@YÊSXU"Y;]n\"—"X bd[cZHmn\RZZHm_X£c¢Á[em_U"Ÿ_j͖;ÚR\^aHœž[ŠUfV)X4m_UR”¶–_Ÿ_aebdY_—)ZemnXS@\^jÍSŸnjd\^ZebdU"YAos\^Yʖ
[ŠŸn n[ŠXÙQŸ_X@YQZejdœžÚR\^aHbÍ\RZebdU"Y;”bkZem X@œOY_Ufjd–n[YQŸnV# `X@abÍ[ –sbÍ[eS@Ÿn[e[eX4–Aos _ŸsZZemnXbkYQZeX4aeÚfX@Y_bdY_—WVT\RZHX@aHbd\"j
\^ `U"ŸsZ—fX@U"VWX@ZeaHœ)X `XSÈZ¡[™bÍ[cbkYÊSU"YÊ[ŠbÍ[ZHX@YQZ”bÑZHm;\)–sbÍ[eS@Ÿn[e[ebdU"YMU"gAZemnbkY_—Q[™Zemn\^ZS4\^Yhڕ\"aeœT–sŸnaebdY_—Zem_X
S@\"jdS@Ÿ_jd\^ZebdU"YA²$¥m_XjÍ\"[ŠZZ”™UT[eX@YQZeX4YnSX[–sUWY_U^ZÐnZZeU"—fXZHm_X@a”cX@jdj§X@bkZem_X4a ΝZHm_X\"[H[ŠŸnV)]_ZebdU"YU^g
SUfYn[Z¡\^YQZ?£c¢~bÍ[Y_U^Z ÚR\^jdb͖_Ï ãU"lR\•œ"oO _ŸsZ bÍ[ZHmn\RZ”mn\^Z œ"U"Ÿ;\^aHX—"U"bdY_—ZeU)ZH\"jkl;\^ `U"ŸsZosU"a \"aeXœ"UfŸ
—"UfbkY_—)ZHUZ¡\^jdlh\" ÊUfŸsZTΊ]n\"aŠZHbdS@Ÿ_jd\"aejdœWZemnX X ‚X4SÈZ¡[U^g
Zem_X—Q\RZHX\"aeX\"ÏQÖ
J`}•t`{Rynz^½ˆÝh·  {•†  xnzfr»q  yuË_pftO½„rfxOt‚}qs¹¸yQ†_v ” psz ” xÊzfpfy‚}  q`{»}•yÂ}Q{…p ”" q‚{Ry_p"qOy¸ƒ  t¶p
{•|_v ” }Rƒ`} ” {"vfy ” ƒutQxOqOqnv"t€{R½`” {Ry_v¼~p"q_rur`}^v ” pn{Ry`}qs¹É¼‚p ”  †§}qnvã
‡ ” Ov ”^”  q_r_z"½ãÝ  q ” vu p"qO½
|np"t_p•¼‚vfysvft€}Q{ †np"qO¹_vQrãÝ {x †´pn{Á ¹_pfy_vupft_vQp$Ý;·  †_pn{y w_vut_v psz xnzQpfy_vQrˆ‡  à ǁ
yQ†_vut_vf ƒsvft_ vOv6Æ{»{Ry_p"y_” v•¼‚v"qOy»
·  {•† xÊz"r»Ë_pftO½ˆÝ }f{•q™ÆŠyut‚}•¹f†sy„p"q_ruyQ†nvftsvQƒ t_vu{ ¼‚v ƒ
yQ†_v„ƒ zOz ǧ}4qs¹¸r`}Q{ x‚{O{s}  q€}Q{Çst  qs¹c‡
à  Ç~p"w  xsy¸yQ†nvuƒ`}•yQy‚}qs¹
"xnvn{Ry‚}  q‡ š †npfy„r  t_vQƒsv"t_vOv+¼‚vOp^q‚{Éws½ÄOÄeƒ`}•y
y  ¹_ vfyQ†nv"tn›6” ÆOÆ'µ  yQ” †nv…|np"|nv"tu†_pn{ y  w_v ”^ ¼n|  {^vQr€}q´p„tQ†O½^¼
}qs¹…Ë_vft`{"vO› ” Ü qs½Q† ”  ǙÝ
¹_v ¼‚” vfyOt`} pszvQƒOƒsv” y`{Á pft_v…|npftQy ƒ _v"½Qq zfrn{ÀqOx"¼nw_vft et_vfË`}^v"DŽƒ_z^x‚}Rr¼‚v †np^q§} { '
‡ 
 v^q v$ÝhyQ†_v¶vQƒQƒsv y`{ ƒ„yf†nvu¹spfy_vupft_vOp¶{† ǂ{yQ†np"y¶·  Ë_p"t‚}^vn{Ãpn{ÇnvszQzup^q_r»†npn{Ãy
”
”

”"

”

 
wnv¸
y ¹_t_vfyQv †npsv"tnz › xÊzfpfy_vQr™‡  ÇO†np"yÂ}f{¶}4q q‚{O}Q{Ry_v"qOyn› Ƕr yQ†nvn{"v´{"v^qsy_v"q vn{Àq y„ƒ`}y
?Y];°non\Rg ZHX@a ¤ˆÙ ®  Ì ZHm_bdY_lžZHmn\RZ bkZ ”™UfŸ_j͖M `X\)—"UOUs–Mb͖sX4\ZHUTbkYn–_bdS4\RZeXbdVWV)X–sbÍ\RZeX4jkœMZemn\^Z
Zem_X[ŠXXÙQŸn\RZHbkUfYn[\^aHX? ]njkU"ZŠZeX–;bkHY bk—fŸ_aHX nosaH\^Zem_X4aZemn\"Y”c\"bÑZHbkY_—ZeUWZHm_XY_X@ÛQZ.[eX4SZebdU"Y; ÊX@giU"aHX
aeX@giX@aHaebdY_—ZeU bd— n²
jÍ[ŠUÊo_VT\^lObdY_—)Zem_X  F ,\^ÛObÍ[™U"Y;Zem_bÍ[—faH\"]_mMjdU"—Q\^aHbÑZHm_VWbdS”cU"Ÿ_j͖MmnX@jd];—faeX\RZHjkœTbdY([Šm_UR”bdY_—Zem_X
–s!b `X4aeX4YnSX[bkYhZemnXZem_aHX@X]_ŸnV)](S¡mn\"aH\fSÈZHX@aHbd[ŠZebÍS@[4²
.sv"qsy‚}  q§}qs¹ÃyQ†nvuƒ`}•¹Qxstsv ”" xÊzfr…w_vu¹ Q r~}RrsvOp…wOxsyÁ¾Ãr  q™Æy´p"¹Ot_vOv…ǧ}•yf†u½  x€p"w  xsy
yQ†_v´z  ¹Á{ ” pszQv$Ý ¾Ãr  q  y~{"vOv„p"qs½¸wnv^qnvQƒ`}•yÊ{6‡
?Y]A²® \Rg ZHX@a.¤™Ù(®"® ™¥m_X[eU"jdŸsZebdU"YU^g6¤ˆÙ(®f®aeXÙfŸnbkaHX4[™giŸ_jdjAbdYsgiU"aHVT\RZebdU"Y;U"Y;ZHm_X–sbdXS4\"[ŠZebdY_—
VT\"S¡m_bdY_ X  .S4SUfaH–sbdY_—ZeUWZHm_bd[ V)Us–sX4j o_Zem_XVT\"S¡mnbkY_XS¡mn\"aH\fSÈZHX@aHGb F4X4–T Oœ ˆVT\RÛ§o ?VW\^Ûh\^YʖMZHm_X
XÛs]`U"Y_X4YfZ bdY(¤ˆÙ(®f²$¥m_X”™UfaH–_bkY_—)U^g
Zem_bÍ[ [eX@YQZeX4YnSXfo_m_UR”cX@ÚfX@aofVWbd—"mQZ  ÊXbdYn–sbÍS@\^ZebdY_—)Zemn\^ZZem_X4aeX
bd[U"VWX?bkYsgiUfaeVT\^ZebdU"YžZHU `Xmn\"–MU"YMZem_XVT\"S¡m_bdY_XU^ZHm_X@acZemÊ\RZcZem_X[ŠXZemnaeX4X?]n\"aH\"VWXZeX4aH[4² Ì –sU)Y_U^Z
Zem_bdY_lMZemn\^ZZemn\^Z bd[”mÊ\RZZem_X\"ŸsZemnU"a¡[bkYQZeX4Yn–§o_ nŸsZZem_bÍ[bÍ[SUfYsgiŸn[ebkY_—ʲ
³ †§}Q{„}Q{»vfá_p ” y_z"½…ÇO†np"y„yf†nv¶p^xsyQ†  tÊ{¸}qsy_v^q_rsvQr™‡ ³ †nvɼ  rOvsz»r  vn{Éq  y ”" q_ƒ`}qnvfr
y  p€{•|nv ” }•ƒ`” } ” vfáQ|  qnv"qs” y  t´ƒ"” xOq ” y‚}  q™ÝTwQxsy¶tspfyQ†nvft¸¹`}•Ë_ vn{…zn}ȼ
}•y‚}qO¹ ”” pn{"vn {‡
ºOËsvftO” ½„r`}^v pn{•y‚}qs¹¼‚p †§}qnv p"q„
Ë_pftO½¸wnvfyfÇnvOv"quyQ†_v¸yfÇ vfáOyOt_v¼‚v»ƒfxOq y‚} q‚{1Ýhpn{
r`}f{ x‚{O{^vQr´}q¶yQ†nv…” |np"|_vftc‡  ” v^q ” v$ÝW¼  t_v€}q_ƒ  tR¼‚pfy‚}  q€}Q{qnvOvQrOvQr¸ƒ  t¶vOp ” †
}qsr`}•Ë‚}Rr"xnpszÃr`}Rv pn{Ry‚}qO¹¼‚p †§}4qnvˆ‡
]À®   Ì ZHX@Yn–hZHUW–_bd[H\^—faeX4X?”bkZem;ZemnX]_aeX4VWbd[eX4[U"g
ZHm_X–sbÍ[eS@Ÿn[e[ebdU"YhgiU"jdjkUR”bdY_—W¤ˆÙ(® s² Ì ZHm_bdY_lžZHmn\RZ
?VT\RÛh–sX4]ÊX4Yn–_[VWUfaeX[ŠZeaHU"Y_—fjkœTUfYMZHm_XVT\"S¡m_bdY_X[eGb F4X?ZHmn\^Y(–sUOX[ ãVT\RÛ§² Ì Y—"X@YnX@a¡\^j o …VT\RÛhbd[
Zem_XbdYQZeX4Yn[ŠbkÐÊS4\RZebdU"Y;]_aHX4[H[ŠŸnaeXZemÊ\RZ U"YnX”\^YQZ¡[cZeUT\"S¡m_bdX@ÚfX–_Ÿ_aebdY_—T[eU"jdbd–sbkÐÊS4\RZebdU"Y1o_\^Yn–hZemnbd[

!

W ib

4<QXU MT587 ZX29x• ” v T vtW<M `5

’*=5Es-“367E5

–— ˜A™0— ˜<š ›0œqž6Ÿ" j›G #¡› ŸP¢Y—£¥¤¦Fž ›Y¢
¦T§ ›`¨B!Ÿ\œqž#™.!¦6˜:œG©N¤6ª ˜<«!£ ˜ŸK£ ¢: `©
¬

 

Section A.4. Referee 3

[em_U"Ÿ_j͖hY_U^Z.S¡mn\"Y_—"XV#ŸÊS¡m;”bkZem;ZHm_XVT\"S¡m_bdY_X[Šb F@Xfos”m_X@aHX4\f[cZem_XS@jd\"VW]_bkYn—giUfaHS@X"oOZHm_X]_aHUO–_ŸnSÈZ
U^g
Zem_bÍ[]_aHX4[H[eŸ_aeX\^Yʖh]njd\^ZŠZeX4Y(\^aHX"oO—"UOX4[Ÿn]A² ?YMZHm_XU^ZHm_X@amÊ\^Yn–§on”m_X@Y;U"Y_Xmn\f[jd\"ae—fX@a\^aHX4\#ZeU
VT\^lfXjÍ\^aH—"X4acS4\"[ŠZebdY_—nosUfY_X”\^YQZH[™ZeUTbdYnS@aeX\"[eX.ZHm_XÚ"UfjkŸ_VWX@ZeaHbdS
nUR”¶aH\^ZeXU^gV)X@ZH\"j1[ŠU)ZHmn\RZ
nUR”
a¡\RZeXU"g
VWXZ¡\^j1[eU)Zemn\^ZÐnjkjAZebdV)X[”bdjkj§Y_U"Z —"UWŸ_]”bkZem;Zem_XVT\fS¡m_bkYnX[eb F@X"²™£™UfVWV)UfY_jdœ"oOZemnX[Šm_U"Z
[ejkX4X@Ú"XbÍ[jd\"ae—fX@aoO”m_bkjdXZemnXVW\^ÛsbkVŸ_V×]_bÍ[ZHU"YÚ"X4jkUsS@bÑZœž–sUOX[Y_U^Z S¡mn\"Y_—"XVŸnS¡mA²
 v"t_v»yQ†nv»t_vQƒsv"t_vOv´}Q{ ”" qsƒfx‚{s}qO¹´{  ¼‚p"qs½„r`}RƒQƒsvft_v"qOy ”" q ” v"|sy`{+yf†npfyÁ}•yuǧ}"zOz
y_p Þ v„p»ÇO†§}^zQv»y  vfáQ|ÊzQpn}qÁ}•yu|st  |nv"tnz"½c” <
‡ ,nzQvOp_{"v»ƒ`}q_r»†nv"t_vup¶pfyQy_v•¼n|sy¸y 
vfáQ|nzQpÊ}qÁ}•y¸wst`}^vQƒ_z"½™‡ ³ †nv~}qsysv" q‚{s}RƒÊ}  pfy‚}  qÉ|st_vn” {O{xst_ v†n p_{Ãq  yQ†§}qs¹…y  r  ǧ}yQ†
yQ†n v…C| B D ” r`}^pf¹Q t_p•¼.‡ \ ” ³ †nv»C| B D r vn{Éq yu†npfË_vɁ ¼nx †„ y r ǂ}•” yQ†„yQ†nv
{  z_}Rr`}Rƒ`} ” pfy‚}  qÃ|st vn{O{‡7¾•yÁ}Q{…” rsvn{s} ¹QqnvQrÃq y¶y †np"Ë_v+” ¼nx †uǧ}yQ†„yQ†nv 
{ z_}Rr`}Rƒ`} pfy‚} q‡ ³ †nv€}qsysv"q‚{s}RƒÊ} pfy‚} qÃ|Ot_vn{O{•xOt_v¶}Q{À¼nx †€zQp"tO¹_vft¸yQ†_p"q
‡ ¾
¹‚ }•Ësv»xQ|ßOß7¾•yuÇ  xnzfr¸y_p Þ vup¶z  qs¹„” r`}Q{ ” x‚{O{s}  q»\” y  y_vOp ” †u ½  ”^x¶ yQ†nv¸ƒfxOqs rsp•¼‚v"qOy_ps z_{
ƒuyQ†nv…C| B;D r`}^pf¹Otsp•¼~p"q_r¸yQ†nv¸r`}Rv p_{Ry‚}qs¹Ã|st v_{O{6‡
x q_ƒfx‚{^ v„{ ¼‚p"qs½
yQ†§}4qs¹`{ÉyQ†np"yÂ}y¿}¼_|  {O{s}4wÊzQvy  xOqOt_pfË_vsz¶}y´pOzOzuƒ  tu½  xÂ}q€
p~{•† tOy¸|npft_p"¹Ot_p"|O†c‡
,nzQvQpn{"v…t_vOpfr„·"†np"|sy_v"t„â t´vfË_v^q„w_vfyOy_vft¸tsvOpQr¸yQ†nv…ÇO† zQvÃw OfÞ ‡
jÍ[eUnoOgiU"jdjdUR”bkY_—T¤™Ù(® noOZem_X\"ŸsZem_UfaH[[em_U"Ÿnjd–hbkYʖsbdS4\RZHX”mn\RZZHm_X@œžVWX\^Y OœÉΊVWb͖_–sjdXaH\"Y_—"XÏ#U"g
ZemnX  FYOŸ_V ÊX4aH[4² Ì Zbd[ Y_U^Z.S@jkX\^acgiaeUfV bk— )m_UR”´SjdUf[eXU"Y_XY_X4X4–_[cZHUT—"XZZHU  F giU"aZemnX
ZemnaeX4XS@Ÿ_aHÚ"X4[cZHUTSU"YOÚfX@aH—"X?\"—f\"bkYA²
³ †_v¼`pfyQ†nv•¼`pfy‚} ” pOzÃv
fx_pfy‚}  q`{Épft_v¸¹‚}•Ësv"qÁ}q¶yQ†nv…|np"|nv"tc‡ ³ †nv"½´p"t_v»Ë_vftO½~{s}¼_|ÊzQv
yQ†n p"y„
½  x ” p"q„x‚{"v…†np"q_r ” pOz ” xÊzQp"y  t…y  ƒ`}4q_r»†  Dž¼nx ” † ” z  {"v»½  xuqnvOvfruy  ¹  y 
 ƒ  t„½  xst ” †  } ” v  ƒ¶vftOt  t™‡ Ü rÊ}Q{ ” x‚{Q{s}  q  q¿{x ” †Â}Q{O{•x_v´}Q{Ãw_vsz  DŽyQ†nv
zQvfËsvsz»ƒQt  ¼~p"q€p ” pfrsv•¼
} ” |np"|nvft™‡
b
ØcX4[ebd–_X4[ `X@bdY_—WbkjdjkŸÊ[ZHaH\^ZebdÚ"XU^g
Zem_XaHX4[eŸ_jÑZ¡[@os]Ê\^aeZU"g1ZHm_XÚR\^jdŸ_XU^g\"YhX@Û_\^VW]_jdXS4\^jÍSŸ_jÍ\RZHbkUfY;S@U"VWX4[
giaHU"V×bkZ VT\^lObkYn—)]`Uf[H[ebk _jdX–sŸ_]_jdbÍS@\RZHbkUfYU^gZem_XaHX4[eŸ_jkZH[X@jÍ[eX@”m_X4aeXf² Ì Y;U"a¡–sX4aZeUT[ŠŸn]_]ÊUfaŠZZHm_bd[4osZHm_X
\^Ÿ_Zem_UfaH[cY_X4X4–hZeUTbdYnSjdŸn–sXZHm_XaHX@jÍ\RZebdU"YÊ[Šm_bd]n[™ZemÊ\RZ Ÿn[eX4–hgiU"a?£c¢ÁbkY;ZemnX4[eXS4\^jÍSŸ_jÍ\RZHbkUfYn[4²
³ †_v¶z_}•y_vft_p"yQxst_vu}Q{»ƒ"xÊzOz  ƒ~{•x ” †Â}q_ƒ  t^¼‚pfy`}  q‡ ¾RƒuyQ†nv»t_vQƒOvft_vOv  |_v"q‚{Ãp"qs½
wnpn{O} ” ƒ_z^x§}Rrɼ`v ” †np"q‚} ” {+y_v"áOy¸w OfÞ yQ†nv^q„†_v ” p"q€ƒÊ}q_r~}q_ƒ  t^¼‚pfy‚}  qup"w  xsy~}•yc‡
¥m_X–sbÍ[HSŸn[H[ŠbdU"YhU"Y;]À®
WU^g 
bd— Y_X@X–_[ \)jkbkZŠZHjkXVWUfaeXSUfYn[ebd–sX4aH\^ZebdU"YA²6¥m_X4aeXbÍ[\VT\^ÛObdV#ŸnVCbdY
Zemnbd[ S@Ÿ_aHÚ"X"os nŸsZZem_X\"ŸsZemnU"aÒ [SaHbkZeX@aHbdU"Y;U^g
 `X@bdY_—TUfYMZHm_X(ΊaHbk—fmQZmÊ\^Yn–h _a¡\^YnS¡mnÏ)bÍ[\"bd–MZeUT `X
[em_U"aeZeX4a™ÐÊjkj§ZHbkVWXfo_”m_bÍS¡m;bÍ[Y_U"Z.\)S@aebkZeX4aebdU"YhgiU"a S¡mnUQUQ[ŠbdY_—W\)jkUsS@\^ZebdU"Y;U"YhZem_bÍ[ S@Ÿ_aeÚfX\RZ \^jdj ²ã¥mnX
Ðnjdj§ZebdVWXbd[ V)UfY_U^ZHU"Y_X–sXSaHX4\"[ebdY_—”bkZembdYnSaHX4\f[ŠbdY_
— W\^ZS@U"Yn[ŠZH\"YQZ son[ebdYnSXZemn X
nUR”„bÍ[ZemnX
]_aHUs–sŸnSÈZ U" g ?VW\^Û;\"Yn– _² ?S@SUfaH–_bkY_—ZeUWZHm_bÍ[ SaHbÑZHX@aHbkUfYAoOY_UžS@\"jdS@Ÿ_jÍ\RZebdU"Yhbd[ Y_X@X–sX4– $ZemnX
]_aHXgiX4aeaHX4–;SUfYsÐn—"ŸnaH\^ZebdU"YMbÍ[Y_UW—f\^ZeX”mn\^ZH[eUQX4Ú"X4a4²ã£™jkX\^aHjkœfo_S¡m_UOUf[ebkYn—)\"Y;Uf]ÊX4aH\^ZebdY_—)]ÊUfbkYQZ
aHX4ÙQŸ_bdaeX[™bdYQZeaHUs–sŸnSÈZHbkUfYU^g
U"Zem_X4a SaHbÑZHX@aHbd\nosbkYÊSjdŸn–sbdY_—)Zem_UQ[ŠXZHmn\RZZemnX\^ŸsZHm_U"a¡[VWX@YQZebdU"YbdYMZHm_X
bdYfZHaeUʲ Yn–hZemnXX@Yn–;U^gZemnX]n\^—fX®
W–_bd[HSŸn[H[ebkUfYMZHmn\RZZHm_X[ŠVT\"jkjdX@acÐnjdjkbdY_—WZHbkVWXgiaHU"Vןn[ebdY_—ž\
jÍ\^aH—"X—f\RZHXT¨iU"a \W[eVT\^jdjkX4aaeŸ_YnY_X@a ֕֕±#”bdjdjAjkX\"–MZeUT\T[eVW\"jkjdX@aVT\"S¡mnbkY_X ¦ Ÿn[ŠZ?–sUOX[Y_U^ZgiUfjkjdUR”„\RZ
\^jdj ²ã¥m_XVW\fS¡m_bdY_X[Šb F@XbÍ[–sXZHX@aHVWbkY_X–; QœžZem_X]n\"aŠZ [eGb F4X\^Yn–MZemnXaeXÙfŸnbkaHX4–hbkYQZHX@Yn[ebÑÐ`S@\RZHbkUfY
]_aHX4[H[ŠŸnaeXfoQYnU^Z  OœM\^YOœžU"g
ZHm_bÍ[@²
 q ” vupf¹_pÊ}quyf†nv»t_vQƒsvftsvOv´}Q{ ”" q_ƒfx`{s}qs¹É¼`p"qs½Á}Q{O{•x_vn{
zQv"y»¼‚v€}qOy_vftQ|stsvfyupf¹_pn}q
ÇO †np"yÂ}f{… yQ†_v»| B D r`}^p"¹Ot_p•¼ }Q{…pszQz„p"w  xsyc‡ \ ³ ” †nv»C| B;D2r`}Rpf¹Ot_p•¼Â}Q{»ƒ  t„†_pf˂}qs¹„p^q
|nv"t_pfy‚} qnpsz+| }qsy¶pfyuyQ†nv¸t‚}•¹f†sy¸¹_pfy_v»Ë_vOz }•yQ½up"q_ruyQ†nv»t‚}•¹f†sy„ƒ`}"zOzn}4qs¹»y‚}¼`vˆ‡
J  t¶p"qO½¶¹‚}Ë_v"q   ÝyQ†nvft_v¸p"t_vuyfÇ  |  {O{s}4wÊzQv„{  z^xsy‚}  q‚{  q¶yQ†nv»t‚}•¹f†sy¸†np"q_r€{s}RrOv



–— ˜A™&— ˜Aš ›fœ:Tž6Ÿ j›G #¡› ŸP¢Y—£¥¤¦Fž ›Y¢
¦T§ ›j¨B6Ÿdœqž#™.!¦6˜:œG©g¤6ª ˜<«!£ ˜ŸK£ ¢.›A©

!

’ ib

4 QXU<MF587 ZX29x• ” v T vtW<M `5 _’*=5Es-“367E5

Chapter A. What The Establishment’s Scientists Say

p"qsr  q_v  q´yQ†_v¶zfvQƒQy¸†np"q_r€{s}•rsv…ǧ}•yQ†„yQ†nv´{"p¼‚v»¹_pfy_v»Ë_vsz \” }•yO½™‡   Ç_vfË_vftˆÝžyQ†nv
t‚}¹Q†sy¸†np"q_r€{s}•rsv…†npn{u{@¼‚pszQ”"zQvftuƒ`}"zQzn}qs¹» y`}¼‚vˆ‡
Ü qsr´pf¹spÊ}q™ÝhyQ†_v¸tsvQƒsvft_vQv q_ƒfx`{s}qs¹up^q yQ†nv"t€}Q{O{•x_vˆ‡`} Þ v~}4q¸¼‚p^qs½¶v"qs¹‚}q_vOvft‚}qO¹
{s}yQxnpfy‚}  q‚{
ÝWÇnv¸†_pfË_v…†nvft_vup€{s}•yQx_pfy‚}  q€}q¶ÇQ†§} ” †Ã¼  t_v»yQ†np"q  qnv ” t‚}y_vft‚}  q€}Q{
qnvQvQ” rsvQr™‡ ³ †n v ” zQp•¼_|§”}qs¹¸ƒ  t ” v€}Q{  qnv  ƒuyQ†nv ” t‚}y_vft‚}^pyQ†npfy„rsvfysvft^¼
}q_vn{ÀÇO†np"y
¼‚p †§}qnv¶{† xÊzfr…w_v † {"v"q‡ ³ †nv yQ†nv"t»|npft_p•¼`vfy_vft€}f{…yQ†_v»| B D r`}^p"¹Ot_p•¼.‡
Ì Z.[ŠX4X@VT[cZemÊ\RZZemnX@œh\"ŸsZemnU"a¡[mn\•Ú"XU" n[HSŸnaeX–h[eU"VWXX@jdX@VWX@YQZ¡\^aHœTaeX[ŠŸ_jkZH[ Oœ;–sU"bdY_—)Zem_X4bka
S@\"jdS@Ÿ_jd\^ZebdU"Yn[4² 
 nU"aXÛ_\"V)]njkXfo‚Zem_X)jd\f[Z[eX@YQZeX4YnSX)U^gãZHm_X)V)b͖_–sjdXW]n\^a¡\^—faH\"]_m(U"Y«]î TbdjkjdŸn[ŠZea¡\RZeX[ ZHmn\RZ\f [
 bÍ£c[¢¶Y_U"aHZ.X4\"[ŠS¡UfmnVWX4X[6ZebkmnZH[™bkY_jk—WbdVW”cbÑZHXbkY_[Šm_—#UfڕŸ_\"jÍjk–MŸnX  `U^Xg$]_®"Ÿ_of _ZejdmnbÍ[ŠX.m_–sbdY_bÍ[e—TS¡mnbdYÀ\"ae®4—f¯"X¯fÚ"°_X4² jkUsSbkZœ#aHX4\fS¡m_X4[6bkZH[™VT\RÛsbdV#Ÿ_V²6¥m_bd[
³ †nvft_v´}Q{q  ¼‚v"qsy`}  q  ƒ¸yQ†nv„pszOzfvf¹_vQr»ƒOp ” y  ƒÄOÄe·  t_vOp ” †nvn{¸}•yÊ{uzn}ȼ
}•y‚}qO¹»Ë_psz^x_v
*
ƒ "1‡fÆQÆ ³ †nvft_v´}f{Ãq  r`}Q{ ” x‚{O{s}  q€}q¶yQ†nv…ÇO†  zQvupftOy‚} ” zQv»Þ p"w  xsy”^ ÄOÄe·  t_vQp ” †§ }qO¹
}•yÊ{+¼‚p"á‚}¼nx"¼ H·  1 "A'1ÆOÆ_‡ ,_vftQ†np^|‚{ɁO"yQÞ´†nv» t_vQƒOvft_ vOvÃÇnp_{À¼1}Q{R” y_p v"qÊz"½ Qf¼OÞ ¼‚v"qOy‚}qs” ¹ q
r`}•ƒOƒsvf”"t_ v^qsyupftOy`} ” zQvn#
{ à Ü µs· Ü Æ{+w
t´p^q yf†nvft„r`}^v pn{•y‚}qs¹»w 'ÀÇO†§} †u†nv
†np_{ q_ƒfx‚{"vfrÃǧ}•yQ†„yQ†‚}Q{…pftOy‚} ” zQvˆ‡
X@—Q\^a¡–sbdY_—#ZHm_XSUfYnSjdŸn–sbdY_—W]n\"aH\"—"a¡\^]_mhU"Y;] ®  
b ¥mnXŸn[ŠXU"g
ZHm_X”™UfaH–ÎeS@U"Yn[ŠZH\"YfZ¡Ï#bÍ[Y_U"Z.SU"YÊ[ŠbÍ[ZHX@YQZZem_aHU"Ÿn—"m_UfŸsZZem_bÍ[]n\"]ÊX4a4²$¢?UWZem_X4œ
VWX\^YSU"YÊ[Z¡\^YQZ \"SaHUf[H[c—"X4U"VWXZHaeœTUfa SU"YÊ[Z¡\^YQZ \"SaHUf[H[ X@œOY_Ufjd–_[YOŸ_V ÊX4a4onU"a ÊU"ZemA²
³  yQ†nv¸t_vOpQrOvft`{ " ³ †nv¸t_vQƒsv"t_vOvÀ¼‚vQp"q‚{…p ” t  {O{ɹ_v  ¼`vfyOtO½up_{»r`}•ƒOƒsvft_v^qsy
¹_v  ¼‚v"yOtO½up"qsr´p ” t  {O{ _v"½Qq  zfrn{ÀqOx"” ¼nw_vft„pn{…r`}RƒOƒsv"t_v"qs~
y sv»qQx"¼nwnvft ʇ ¾ÃtsvOpszOz"½


r ” q y¸xOq_rsvftÊ{Ry_p"q_” ryQ†nvur`}RƒOƒOvft_v"q vÉwnvf” yfÇnvOv"quyQ†_v¸yfǁ  ” pn{"vn{6‡ Ü t_v"qˆ Ɗy ”
p yQxnpOzOz"½»
yQ†_vn{"v pn{"v_{ÉyQ†nv€{"p•¼‚vs› ܁ †_p"qs¹_v´}q¶¹_v ¼‚vfyOtO½uzQvOpQrʔ^{Éy p †np"qO¹_v

}q svf½Qq z"rÊ{ÀqOx"¼_wnvft»qOx"¼_wnvftc‡ Ü qs½Q† ǙÝhyQ†nv»t_vQƒOvft_vOv»r`}•r¸q y q‚{s}RrOvftup
”" ¼n|Êzfvfy_vsz"½…r`}RƒOƒOvft_v"qsyÃ|  {O{s}4w§}"zn}•yQ½c‡ ·  q‚{Rysp"qsyu·  ¼‚vOp"q`{ÉyQ†npfy„·  }Q{
pn{O{s”}•¹fqnvQr…y  p€{•|nv ” }•ƒ`} ” tQxQqOqnvft€{R½Ê{Ry_v•¼Ý  t~zn} Þ v»yQ†nvCÄOÄ ”" ¼O¼  q™ÆQÆ)¼  rsvOz¶}q
ÇO†§} †¶pOzOz¸yf†nv»tQxOqOqnv"t`{u}q¶yQ†nv…Ç tnz"r…†npfË_v»yQ†nv€{"p•¼`v¸Ëspsz^xnvˆ‡
! b ÚR ?\"[ejk[eŸ_Ÿ_XVWgiUfbdY_a —)\^ZejdjAmnae\^ŸnZY_ZeY_m_X@X4aœM¬•—QVW\RX4ZH\"X?Y;[eœOS@[ŠU"ZeYnX4[ŠVTZH\"[Yf”Z bk\fjdjASaH[eU"UfVW[H[™X—fZHX@bkVWUfV)X4[ X@ZejkXaHœ"\"oQ–MZemnZeUWX@Yjd\"U"ae O—fX?ÚObkX4UfaeŸnaH[eU"jka¡œf[4os²Ÿn¥[Šbdm_Y_X4—Tœh\–sÐ_b͖;ÛsX4Y_– U^Z
YnX@X4–hZHUW–_UW\WjdU^Z S4\^jÍSŸ_jÍ\RZHbkUfYMZHUW–_XZeX4aeVWbdY_XZemnbd[4²
Ü q_ru½_vfyuyQ†‚}Q{ ¼‚vfyQ†  r€}Q{…yf†nvɼ  {Ry¸x‚{"vfrü`vfyQ†  r€}4q´yQ†_v~}4q_rfx‚{RyQtO½ @{  ¼‚v…vfËsv"q
ǧ}"zOz¶{"pf½uyQ†_v¶vfá ” z^x‚{s}Ë_v ¼‚v"yQ†  r '
‡
ç b £™UfYOÚ"X@a¡[eX@jdœ"oQbÑg6ZemnX@œžVWX4\"Y(SU"YÊ[Z¡\^YQZ \"SaHUf[H[ X@œOY_Ufjd–_[YOŸ_V ÊX4a4onb ² X"²™£c¢ÁS4\^Y;ÚR\^aHœ
ZHm_aHU"Ÿ_—fmTZem_XaHŸ_Yh\f[ãZHm_XÚ"X@jdUsSbkZœWڕ\"aebdX4[4oQZem_X4YžZHm_X@œžmÊ\•Ú"X.YnU^ZVW\f–sX ZHm_X@bdaS@\f[ŠXÚ"X4aeœ)”™X4jkj ²
“ bkYnS@XZem_X4œžmn\•ÚfX\f[e[eŸ_VWX4–;[ŠZeX4\f–sœM[ŠZH\^ZeX\^Yn–hZHm_X  )–sUOX4[YnU^ZX@YQZeX4abkYQZHUWZem_X

]É ¯9É ¾K³Yઽ µ#°˜½ »9Ƃ¸aÆC¼¼Ÿc°ª°ªº Ò °ª
ŠÃ¼-ÈY°ªµºªµCµE³ª¯>¸š½ Ùeƨ¶9¯ª¼Y³9͸a³ªÁ-´¹¸Ü³A³AºŸ¶A¯˜½ µ¡¾Þ»>¼>°ž¸Q¶A¼-ÈA»9¸×ÆC¶A´ª¼>ÈAÆC¸a°+°+ƨÑ]Ð ¼9¾K½ Ò Ò ÈªÆCµE¸a³Yµ:½ ¼-º Ð
½ ¾HµE¯ª°˜½ ºªµÂ°ª¸×¶ª¸a°iµC³Yµ:½ ¼-º5½ ƨºª¼9µ‚´+¼A¸Þ¸a°+´+µØÉ-ÍK¼-ÈAÒ Ñ%Ò ½ i°µÂ¼_Ò °¹³ª¸×ºwͯ9³Yµ¡½ µ¡¸a°¹³AÒ ÙŸÃ°¹³Aº Ð

!

W ib

4<QXU MT587 ZX29x• ” v T vtW<M `5

’*=5Es-“367E5

–— ˜A™0— ˜<š ›0œqž6Ÿ" j›G #¡› ŸP¢Y—£¥¤¦Fž ›Y¢
¦T§ ›`¨B!Ÿ\œqž#™.!¦6˜:œG©N¤6ª ˜<«!£ ˜ŸK£ ¢: `©



¬ ­

Section A.4. Referee 3

S@\^jÍSŸnjd\^ZebdU"YAoQZemnX@Y;Zem_XUfY_jdœMaHX4\"[eU"YMZemn\^ZV)X4YQZebdU"Y;giU"aZHm_XÚ"X4jkUsSbkZœTZHU)ÚR\"aeœM–_Ÿ_aebdY_—)ZemnX
Ðnjkj§”cU"Ÿnjd–; `X ÊXS@\^ŸÊ[ŠXg
ÚR\"aebdX4[\f[\#giŸnYnSÈZHbkUfY;U"g
ZHm_XÐnjdj§gia¡\"SÈZHbkUfYA²$¥m_X@œMmn\•Ú"XY_U"Z
–sX@ÚfX@jdU"]`X4–MZem_bÍ[ \^aH—"ŸnV)X4YQZ[eŸ žSbdX@YQZejdœ"²
svfyü‚v€{RyOt_v_{O{Ãpf¹_pÊ}4q¶yf†n vɼ‚pÊ}qu” |  }4qsy  ƒ¸yQ” †nv„pftOy‚} ” zQvˆ‡E·   Ë_p"t‚}^vn{ƒ  t
rÊ}RƒOƒsvftsv"qsy…tfxOqOqnvftÊ{Ãp"q_r  tur`}^v pn{Ry‚}4qs¹É¼‚p †§}qnvn{‡7¾•yÁ}Q{| {RyfxÊzQpfy_vfr…yQ†npfy
yf†nv»Ë_vsz \ ” }•yO½¸r  vn{Éq  yuË_pftO½„rfxOt‚}qs¹¸tQ xQq‡ Ü Orʁ }Q{ ” x‚{Q{s}  q„p^w  xsy    }f{¸p"q ”
v^qsy‚}•t_vOz"½¸r`}RƒQƒsvft_v"qOy€}Q{O{•x_v…t_vszQpfysvQr»y yQ†nv»¹ r¸Ë_v^qsy‚}qs¹urOvn{s}•¹Qq„ƒ t¸ÇO†§} †
  t_v•¼‚pÊ}4q‚{ ”" q`{Ry_p"qsy™‡
bÌ g
ZHm_XXÛ_\^VW]_jdX4[c—fbkÚfX@Y;bkY;ZemnX]n\^]`X@a –sUTYnU^ZaeX4]_aHX4[eX@YQZZem_XS¡mn\"aH\fSÈZHX@aHbd[ŠZebÍS@[™U^g6\)ZœQ]nbdS4\^j
–sbkXS4\"[ŠZebdY_—WVW\fS¡m_bdY_X"os”mOœžZHUW]_aeX[ŠX4YQZcZHm_X@V\RZ.\"jkj Ö;Ó¸mOœh\^aHXZem_X(ÎeVWU"aHX–sX@ZH\"bkjdX4–
S@\^jÍSŸnjd\^ZebdU"Yn[HÏ#YnU^Z]_aHX4[eX@YQZeX–§osbkYÊ[ZHX4\"–;U"g1ZemnXZeaHbkÚObÍ\^j§aHX4[eŸ_jÑZ¡[cZemn\^Z.\^aHX[Šm_UR”Y`Ö
³ †nvn{^v„v"á_p•¼n|Êzfvn{Érsv•¼  q‚{RyOtspfy_vyf†npfyuyQ†nvCÄOÄ ”^ ¼O¼  qˆÆOÆ)¼‚vfyf†  r€}Q{»vftOt  qnv  x‚{
p^q_r¸yQ†npfyuyQ†n” vCÄOÄep"xsyQ† ”  t`{
ÄOÆO” Æ#¼‚vfyQ†  r´{•†  xnzfr…wnv„pQr  |sysvQr  t  yQ†nv"t…¼`vfyQ† O rn{
w_pn{"vQr qÂ{ }Rv"qsy‚}RƒÊ} |st`}q }|nzQvn{6‡2¾w_vszn}^vfËsv…yQ†npfyuyQ†§}f{¶}f{»puË_vftO½¸¹ r
tsvOpn{ qc‡

-ç(ç

–— ˜A™&— ˜Aš ›fœ:Tž6Ÿ j›G #¡› ŸP¢Y—£¥¤¦Fž ›Y¢
¦T§ ›j¨B6Ÿdœqž#™.!¦6˜:œG©g¤6ª ˜<«!£ ˜ŸK£ ¢.›A©

!

’ ib

4 QXU<MF587 ZX29x• ” v T vtW<M `5 _’*=5Es-“367E5

Chapter A. What The Establishment’s Scientists Say

!

W ib

4<QXU MT587 ZX29x• ” v T vtW<M `5

’*=5Es-“367E5

–— ˜A™0— ˜<š ›0œqž6Ÿ" j›G #¡› ŸP¢Y—£¥¤¦Fž ›Y¢
¦T§ ›`¨B!Ÿ\œqž#™.!¦6˜:œG©N¤6ª ˜<«!£ ˜ŸK£ ¢: `©



¬ ®










   ¡   

 r      r 

p

    

T A£
T zS `U £ m JU
S
%S `U Hbžd
T (U
T Š£ T
T !
£ Tv
T Hb Ïv
aU /£
Kb¡} 5SMv
£ ~v T fU
T ¥v £
U T–T
ÏS T
Š£ T £
ˆU
T (U
/U
ŠU
/m
T (U
T `U
T ’¬ "v
QbwS T A£
wv
£
gv
nU T
T–T

W¬ "v
~v :¬ `U T
Mbd
Mh
T ˆ¬ "v
v
ØU ]mwU -b
S ;R9?=5B9R3GHˆU#Mf5K3 ;Y3G=5K4!2vÏS*D=9AVF5K= T–T M4G= T–T 3GH¥v2=9˜vL=;j9A23!Dky‚wqØ{‚b-“Me4G= T–T ;˜vh35B3@D3A£3!5
… 23DWX
5K3<9AVF5,D3GHQb†
} ; 2Q5B9L9:7aU 3 T =9R35¨y‚wqwC{ HT3A£ 3 T Q\U!3GHC7ED9RQv 2=9[7 ;1DQ"‹v 4 = T–T 3HS{¨}_wq‚}_bJS 2=6H2QXU!3H
9A26=9L9A27 ;"D3Š‹
v 4!5B3=9:7 QXD~hv Q\V T HgU!5KQ/£ 3@W!3<9>9R3!5ibž_} UFU!5KQˆ7aU =9R3 T M9:hv QeM 3=!5K; =ZQSH[v 5KQ!9R3= T 3<9>9R3!5m9RQ
y 9R3Š£ 3n H/6£ =!5lHMGvXHa7E5B34A9RQ5*Q/`m 5K3 ;?3=!5l462=FD6H03HXV64 =9:7 Q\D%Om Q5L{¨}_wq#} ho = T 3<9>9R35w-S D3A£ 3!5m; VTW`"U 7 9>9R3H`tŠb
F
{nQ"v©J
S 26= £ 3"HT3G47 HT3GHe9A26=9_7 9_7 ;j9:7a[U 39RQe;Y3!D6H9A23 T 3<9>9R3!5*=FD6He9RQWU =`A¬ 3(7 9LQXU!3D"9RQ9A23UFVFW T 7 4(bwJS 26= £3
= T QXDZ@4 Q5,5K3 ; U!QXD6H3D4 35#
v 7 9A2žF\=FV T ’k5K= T Q"hv 35.vHOm Q5:[U 35mH7E5K3G4<9RQ5*Q/bm 4<QfUg(U VFD!7 4G=9:7 QXD1Om Q5L{¨}_wq‚#} v
v[27 462HT3 ;:46587EW!3 ;%#U MfW6=9>9 T 319RQNUTVFW T 7 ; 2@7a(U U!Q5B9?=FDG9#7ED-Om Q5EU =9:7 QXDHb¨_} DQXU!3D T 3<9>9R35*9RQS“f5i_b ’*=!5l=FDav
 7E5K3G4A9RQ5*Q]_m “@=5:A¬ 3<9:7EDZgOm Q5`{¡}_wq##} vt7 ;#= T ;YQ@=9>9?=64!23HKb F T 3G=;Y3e5K3G=6H@9A23 ;Y3 T 3<9>9R35B; b¨#d 23 Mf5K3A£ 3G= T =
L
T Q!9`Q/Lm 7ED-Om Q5EU =9:7 Q\D=FW!Q\VG9nU =FDMe=;<U!34A9R;_Q/m {¨}_wq‚}_h ; QXU!35K=9:7 Q\D; b˜JS 26= £ 3;<VFW("U 7 9>9R3H@^H£ 3ko ä t
=5P9:7 4 T 3 ;`9RQ@9A2!7 ; 4<Q\D-Om 35B3D4 3ko ! 9A2@7EDkq T 3A£ 3 T =FD6H``
t =FD6H0QXD T M(QXD3%Lv =;_=64G4<3UG9R3H’,o QXD T M !
=64 4 3!U9?=FD4 34<QJ
U U=5B3He9RQ s  9RQ0=FDGMCW!QHM(3 T ;Y3 tŠbet€ 3=6H0=FW!QXV9 7 91235B3`be` VT587EDZ’[U MfW=9>9 T 319RQ
?V 7ED;?35P9¹e
X ;Y47 3!D64<37EDeHa7 34 =;R9:7EDZtvQ1U =FDGM4!VT587 QXV;`9A2!7EDZ;126= £ 319?=`A¬ 3!D0U T =64<3=FD6H|SMhv QXD6H35ckj =5B3"9A23<M
4<Qa7ED47 H3DG9?= T ipd
€ 3G=6H0=FW!Q\VG9`9A23 ;?3=FD6HNU T 3=;?3 T 3<9n[U 3k!¬ DQ"v v 2=9jM QXV9A27ED`¬(b
\4G=FDTDQ!9#W!3 7 3 3"9A23";A7 9AV=9:7 Q\D9A2=9 \= 7ED
23@2QT;R9:7 7 9‡M \=
5B34<37 7EDZ >5KQ p9A23
3 ;?9?=FW 7 ; 2 3!D9_7 ;"VTDFW!3 7 3 =FW 3Tva=;[7ED6H7 7 H\V= [2Qg26=;_;<U!3DG9j9A23 =;?9
M 3=!5K;[7ED05B3G;?3=!5l462(9RQ
7 (U!5KQ 39A23"H7 34G=;R9:7EDZ m9j^-5B;?9 L=;j3<ˆFU!34A9:7EDZ9RQg5K3G4<367 3"= h3 4<Q [3#9RQe9A234 VTW !=9R3!5 [23!D
#M&7 V;q7 Q\D;_Ha7 ;Y=FUFU!3G=5B3Htv -5K3G= 7 Ž 3GH@9A26=9 7 915B3 Q 3G;_=5KQXVFDH [Q\D3 M= QXDZ
7 9A2= Q7 Ha7EDZ
3 W=5,5l=;?; [3!D9L9RQ@9A233 ;?9?=FW 7 ; 2 [3DG9`HXV319RQ@3<ˆFU!QT;q7EDZ&Q n9A2319A5‡VG9A2;#=FDH@9A233!5‡5KQ5B;`9A23
3 ;?9?=FW 7 ; 2 3!D9#2=; ; U!QXD;?Q5K3GH *W!3 7 3 319A2=9`9A2313G;R9?=FW 7 ;<2 [3!D9`HTQ3 ;1DQ!9 L=FD9[U!3GQXU 319RQ DQ
9A26=9L9A23<Mf26=6Hg7ED 3G;R9R3GHC7ED05K3 ;Y3G=5K4!2 [27 462&U!5KQaHXV64<3G;_3!5‡5BQ\D3GQXV; QHT3 ; =FD6H04<Q\DG9:7EDFV3G;`9RQ&HTQ&;?Qdv
3 3!D9A2Q\VZ\219A23<M !DQ
9A23 ;?3@5K3 ;Y3G=5K4!2 hQ5 ;A [QaHT3 ;`=!5K3;Y47 3!D9:7 ^\4 = M&5,VFWFW!7 ; 2
23<M@HQ\D 9
L=FD9[U!3 Q\U 319RQ !DQ }=FW!Q\VG9j9A2367E5 "7 ; V;Y31Q [Q\D3 M

ç"ä


 …Ž
“ ZeX4Ú"X ?–sÚR\^a¡–sœ  ?¢£ #o
¯
®Ó X[Z
.bk—f—"bdYn[ Uf\f–§o “ Ÿ_bkZeX°f°
Uf[eX@VWUfYfZo Ì  ®4°

_®

Chapter B. My Relationship with Die Casting Establishment

$@"/



1_+d+-"‹+J

t



# 



­f\"YOŸn\^aHœ  _o§®¯"¯f°
“ Ÿ_  ¦ XSÈZ ?Ÿ_X4[ŠZebdU"YÊ\^ _jdX?X@Zem_bÍS@[
¢.X\^a ©(a² .–_ڕ\"aH–_œ
Ì \"VהaHbÑZHbkY_—WZHUWXÛs]_aHX4[H[™VœhS@U"YnS@X@aHYn[\^ `U"ŸsZ ]`Uf[H[Šbd _jdXbkVW]_aHU"]_aHbdXZebdX4[bdY;Zem_X”\•œWZemÊ\RZ
 ?¢£ Á\•”\^a¡–_[caHX4[eX4\^a¡S¡mž—faH\"YfZ¡[@² .[.\ .¢£ ~VWX@V ÊX4a4o Ì  ÊX4jkbdX@ÚfXZemn\^ZZem_X[ŠX]`Uf[H[Šbd _jdX
bkVW]_aHU"]naebdXZHbkX[SU"Ÿnjd–haeX[ŠŸnjÑZ bdYVW\"lObkY_—ZemnX–sbkXS4\"[ŠZebdY_—WbkYʖsŸn[ŠZeaHœžjkX[e[.SU"VW]`XZHbÑZHbkÚfX?ZHmn\^Y;ZHm_X
]_jÍ\"[ŠZebÍS@[\^YʖhU"Zem_X4aaeX4jd\^ZeX–MbdYn–sŸn[ŠZeaHbdX4[4² Ì gœfU"ŸM”\^YQZZeUTX4Y_mn\"YnSXZemnXSU"VW]`XZHbÑZHbkÚfX@Y_X[e[U"g
ZHm_X
–sbdXS@\"[ŠZebdY_—WbdYn–sŸn[ŠZeaHœ"o_œfU"ŸhU"Ÿ_—fmfZZHUž[ŠŸ_]n]ÊUfaŠZ –sbdXS@\f[ZHbkY_—WbdYn–sŸn[ŠZeaHœžX@Zem_bÍS@[ \"Yn–;\^Yn[e”™X4acZem_X
ÙQŸ_X4[ŠZebdU"Yn[cZHmn\RZ.\"aeXa¡\^bÍ[ŠX–žm_X4aeX4bkY1²
© \^YOœžU"g
ZHm_XaHX4[eX4\^a¡S¡mM\•”\^a¡–_[caH\"bd[eX[ŠX4aebdU"Ÿn[ÙQŸ_X[ZHbkUfYn[\^Yn–S@U"YnS@X@aHYn[\^ `U"ŸsZZHm_XXZHm_bdS4[U^gZem_X
]_aHUOS@X4[H[\^Yn–;S@\f[ZÚfX@aHœM[ŠX4aebdU"ŸÊ[c[emn\f–sUR” [cU"YhZem_XbdYQZeX@—faebkZœTZHm_Uf[eXbkYOÚ"UfjkÚfX4–MbkY;ZemnX]_aeUsS@X4[H[@² Ì Y
Zem_XgiUfjkjdUR”bdY_—]Ê\^a¡\^—"a¡\^]nmn[ Ì ”bkjdjA[e]ÊX4jkj§UfŸsZ [ŠUfV)XU"g1ZemnXZem_bdY_—f[ Ì mn\•Ú"X?giU"ŸnYn–§² Ì [eŸ_—f—"X4[ŠZcZeUWœ"UfŸ
\^Yn–\"jkj‚ZHm_Uf[eXSU"YÊSX@aHY_X–h\" ÊUfŸsZZem_X–sbdXS@\f[ZHbkYn—)bdYn–sŸÊ[ZHaeœMZemn\^ZœfU"Ÿ`¬•Zem_X4œM[em_U"Ÿ_j͖hm_X@jd];ZeU
SjÍ\^aHbÑgiœžZem_X[ŠXÙQŸ_X[ZHbkUfYn[@o_\"Yn–hX@jdbkVWbdYn\RZHXU^ZemnX@a]_aHU" _jdX@VT[bkg
ZHm_X@œhXÛsbÍ[ZbdY;UfaH–_X@acZeUTbdYnSaHX4\f[ŠX?ZemnX
–sbdXS@\"[ŠZebdY_—WbdYn–sŸn[ŠZeaHœ‚Ò []_aHU^ÐnZH[\^Yʖ;S@U"VW]`XZebkZebdÚ"X4Y_X4[H[”bkZemU^ZHm_X@abdYn–sŸn[ŠZeaHbdX4[4² Ì \^jÍ[eU)”cU"YʖsX@a
”mOœ  ?¢£ ~–_X@VWU"Yn[ŠZea¡\RZHX4[Y_UT–sX[ŠbdaHX?ZHUT]n\^aeZebÍSbd]n\^ZeXbkYhZemnXbkVW]`U"aeZH\^YQZ.\fS¡m_bkX4Ú"X4V)X4YQZH[ Ì mÊ\•Ú"X
VT\"–sXf²
?Y “ X@]sZHX@V ÊX4
a  _o§®¯"¯ _o Ì bdYsgiUfaeVWX4@–  ?¢£ ~Zemn\^Z \^aH ÊX4a4Ò [cV)Us–sX4jAU"YhZemnXSaHbÑZHbdS4\^jA[ejkUR”
]_jdŸ_Y_—"X4aÚ"X4jkUsSbkZœžbÍ[Ÿ_YsgiUfŸ_Yn–sX–§on\"Yn–§oOZemnX@aHXgiU"aHX[ŠUÊosbd[\"jkjAZem_XU"Zem_X4aaeX[ŠX\^a¡S¡mž n\"[eX4–hU"Y
\^aH ÊX4a4Ò [VWUs–sX@jˆ¨ –sU"YnX Oœ;¢.a²$ؙaHX@ÚObÍS¡lTgiaHU"V ?m_bdU “ ZH\^ZeX .Y_bkÚfX@a¡[ŠbkZœ_±È²$¥
U)Vœž—"aHX4\^Z [ŠŸ_aH]_aHbd[eX
Ì jdX4\"aeYnX4–MgiaeUfV Zem_X©«\^a¡S¡m`)¬ .]_aebdj6®4¯f ¯
bd[H[ŠŸnXU"g6¢?bdX£c\"[ŠZebdY_—T¤ãY_—fbkY_X4X@acZemÊ\RZ  ?¢£ Ámn\"[
U"YnS@X\"—f\"bkYM\•”\^a¡–sX–T¢.a²$ؙaHX@ÚObÍS¡lW”bÑZHm;\#—"a¡\^YQZˆZHU)S@U"YQZebdYOŸ_X?mnbd[caHX4[eX4\^a¡S¡mTbdYžZemnbd[\"aeX\_² jÍ[ŠUÊoO\
œ"X\^a\Rg ZHX@a œfU"Ÿ[Z¡\RZeX–žZHmn\RZ.\)aHX@]`U"aeZU"YhZem_XaHX4[eŸ_jkZH[cgiaHU"VÅØcaHX@ÚObÍS¡l`Ò [SUfŸ_jd–h `XU" sZ¡\^bdY_X4–MgiaeUfV
 ?¢£ #onY_UTUfY_XZemn\^Z Ì lOY_UR”„U"gmÊ\"[ `X@X@Y(\" _jkXZHUÐÊYn–;U"aU" _ZH\^bdYhZem_bÍ[aHX@]`U"aeZ4² Ì \"Yn–;VT\^YOœ
U^ZHm_X@a¡[mn\•Ú"X?ZeaHbdX4–hZeUW—"X@ZZem_bÍ[aHX@]`U"aeZ4oO _ŸsZ?bkY;ÚR\^bdYA² Ì Z jkX\•Ú"X[™VWX”cU"Yn–_X@aHbkY_—)”m_X@Zem_X4a [ŠUfV)X4U"Y_X
–sUOX4[YnU^Z”c\"YQZU"Zem_X4aH[cZHUWlQYnUR”¶\^ `U"Ÿ_ZZem_bÍ[aHX4[eX4\^a¡S¡mA² Ì ”bdjkj1]n\•œ A ZHU)Zem_XÐna¡[ŠZ ]ÊX4aH[eU"Y;”m_U
”bkjdj§giŸ_aHY_bÍ[ŠmVWX”bkZem;Zem_bÍ[aHX@]`U"aeZ4² Ì \"jd[eUWjkX\^aHY_X4– ¨ibdHY  ?¢£ #Ò [?¢.X SX@V ÊX4a _o§®4¯"¯

]_Ÿ_ _jdbÍS@\RZHbkUfYʱ™ZemÊ\RZ U"YÊSXVWU"aHX .¢£ Á\•”\^a¡–sX4–h¢.a²$ؙaHX@ÚObÍS¡lž”bkZem(\^Y_U"Zem_X4a—"a¡\^YQZZeUT–sU
aeX[ŠX\^a¡S¡mMUfYMZHm_bd[.[e\"V)XZHU"]_bÍSgiU"a \"Y_U^ZHm_X@a _Ÿn–_—"XZ œfX4\"a¨Š®4¯f¯"°f±² aHX¢?a²ãؙaHX@ÚObÍS¡l‚Ò [caHX4[eŸ_jÑZ¡[
aeX\^jdjkœžZemn\^Z bkVW]_aHX4[H[ŠbdÚ"X•Ö .\f[m_XS¡mn\^Yn—"X4–Mm_bÍ[VWUO–_X@j ÖÓ¸mn\RZ bÍ[cZemnXSŸ_aHaeX4YQZVWUs–sX4jÍÖÓ¸mOœ
mn\•Ú"X”cXY_U^Z m_X\^a¡–M\" ÊUfŸsZ bÑZÈÖ
Ì \"jd[eU)jkX\^aHY_X4–hbkY;ZHm_X[e\"VWXbÍ[H[ŠŸ_XU"g6¢?bkX£c\f[ZHbkYn—W¤ˆY_—"bdY_X4X@acZemn\^Z.¢.a²ãØcaeX4ÚObdS¡lž\"Yn–;m_bd[
SUfjkjdX4\"—"Ÿ_X[™mÊ\•Ú"X ÊX4X@Y(\•”\^a¡–sX4–ž\"Y_U^ZHm_X@a—faH\"YQZcUfYhZHU"];U^gZem_XU"Zem_X4aH[cZHUT–sUWaeX[ŠX\^a¡S¡mMU"YhZemnX
ZeUf]_bdSX4YQZebkZejdX4–…Îe¢?X@ÚfX@jdU"]_VWX@YQZ \^Yʖh¤ˆÚ•\"jkŸÊ\RZebdU"Y;U^g
Zem_X “ X@Yn[eU"a “ œs[ŠZeX4V;² Ï Ì YhZHm_X
“ X@]_ZeX@V ÊX4aȬ SÈZHU" `X@a®4¯f ¯
bd[H[ŠŸnX"o_”cXjkX\^aHY_X4–MZemn\^Z.©(a² \"aeœ ãaHbk OœOj osS¡mn\"bkaHVT\^Y;U^g
Zem_X
 ?¢£ ˆaeUsSX[e[c¥
X4S¡m_Y_UfjkUf—"œT¥\"[el aeUfŸ_]AoObd[c]n\"aŠZU"gAZem_XaHX4[eX4\"aHS¡mTZHX4\"V;²$¥m_bÍ[©(a² ãaHbk OœOjÊbÍ[
Zem_XS¡mÊ\^bdaeVT\^YhU^g
Zem_XÚfX@aHœžSU"VWVWbkZŠZeX4X”m_bdS¡mhgiŸ_Yn–_X4–hZem_XaHX4[eX4\"aHS¡m1² .g6SU"ŸnaH[eX"o Ì \"VC[eŸ_aeXfoOZem_bÍ[
SUfŸ_jd–hY_U"Z  ÊXf² Ì ¦ Ÿn[ŠZ ”™UfŸ_j͖MjdbklfX.ZHUWm_X4\"aœ"U"ŸnacX@Ûs]_jd\"Yn\RZHbkUfYA² Ì [bÑZjdX@—fbÑZHbkVT\RZHX•¬RXZemnbdS4\^j‚ZeUWmn\•ÚfX\
VT\^YU"YhZem_XS@U"VWVWbÑZeZeX4X\•”c\"aH–sbdY_—#Zem_XS¡mn\"bkaHVT\^Y\)—"a¡\^YQZ¡Ö
Ó UfaelObdY_—WU"YhZem_X[H\^VWXaHX4[eX4\^a¡S¡mM]naeU ¦ X4SÈZ”bkZem;Zemnbd[ © a4² ˆaebd OœQj‚”\"[¢?a4²ÊؙaHX@ÚObÍS¡lT”m_UT\^jÍ[ŠU




4<QXU MT587 ZX29x• ” v

W ib

T vtW<M `5

’*=5Es-“367E5

–— ˜A™0— ˜<š ›0œqž6Ÿ" j›G #¡› ŸP¢Y—£¥¤¦Fž ›Y¢
¦T§ ›`¨B!Ÿ\œqž#™.!¦6˜:œG©N¤6ª ˜<«!£ ˜ŸK£ ¢: `©
¬



N

aHX4SX4bkÚfX4–h\W—"a¡\^YQZcVWX4YfZHbkUfY_X4–\" ÊURÚfX"² Ì [cZem_X4aeX\WSUfY_Y_XSÈZebdU"Y; `XZ”cX@X@Y;ZHm_Xgª\"SZcZHmn\RZ \"aeœ
ãaHbd QœOj§SUOUf]ÊX4aH\^ZeX4–h”bkZem(¢.a²nز_ØcaeX4ÚObdS¡lžUfYMZHm_X[eX@Yn[eU"a]_aHU ¦ XSÈZ \^Yn–hœ"UfŸ;–_X4Sb͖sbdY_—WZeUWaHX@Y_X4”
¢?a4²nØcaHX@ÚObÍS¡l`Ò [c—"a¡\^YQZU"YhZem_XS@aebkZebÍS@\"jA[ŠjdUR”„]_jdŸ_Y_—fX@aÚfX@jdUOS@bÑZœM]_aeU ¦ X4SZ¡Ö Ì ”™UfŸ_jd–hjdbklfX?ZHUWjkX\^aHY
”mn\^ZZem_XaHX4\f[ŠUfY_bkYn—giU"a S@U"YQZebdYOŸ_bdY_—)ZeUWgiŸ_Yn–¢?a4²ÊؙaHX@ÚObÍS¡lž\Rg ZHX@aœ"UfŸhmÊ\"–hjkX\^aHY_X4–MZemn\^Z m_bÍ[
aHX4[eX4\^a¡S¡mž”\"[]_aHU" njkX4VW\^ZebÍS^²
.–n–sbÑZHbkUfYn\^jdjdœ"o Ì jkX\^aHY_X4–MZemn\^Z.©(a² “ ZeX4Ú"X .–sÚR\"aH–sœM”c\f[—"bdÚ"X@Y\)jd\"ae—fX\"VWU"Ÿ_YQZU^g6VWU"Y_X4œTZeU
[ŠZeŸn–sœ;–sbÍ[Z¡\^YnS@XS@U"VWV#ŸnY_bdS4\RZHbkUfYn[@² Ì \^VC[eŸ_aHXZemn\^Z.©(a4² ?–sÚR\^a¡–sœhS4\^Y;X@Y_mn\"YnSX .¢£ Ò [
\^ nbkjdbÑZœTbdYh–_bd[ŠZH\"YnSXjkX\^aHY_bdY_—\"Yn–žZHmn\RZcZemnbd[bÍ[c”mQœTmnX?”\"[c\•”c\"aH–_X4–WZHm_bd[c—faH\"YfZ² Ì \^V×\^jÍ[eU)[eŸ_aHX
ZemÊ\RZ.©(a² .–sÚR\"aH–sœMmn\"[ \"jkj‚ZHm_XSaHX4–_X@YQZebÍ\^jÍ[cY_X@X–sX4–hgiU"a [eŸnS¡m;aeX[ŠX\^a¡S¡mA² ?Y_XS@\^YUfY_jkœM”™UfYn–sX@a
”mOœžm_bÍ[]_aHX4[eX@YQZH\^ZebdU"Yh”c\f[Y_U^Z.\f–_–sX4–MZeU)ZHm_
X  ?¢£ ~]naeUsSX4X4–sbdY_—Q[@² ?Y_XVT\•œM\^jÍ[eU)”cU"YʖsX@a
”mOœTZemnX@aHXbd[\)Y_X4X4–hZeUž–sUT[eŸnS¡m;aeX[ŠX\^a¡S¡mM”m_X4Y;[eUWV#ŸnS¡maHX4[eX4\^a¡S¡mžmn\f[\^jdaeX\"–sœT `X@X4Y(–sU"Y_XbdY
Zemnbd[ \"aeX\# OœTZHm_X”cU"aHjd–§Ò [cgiU"aHX@VWUQ[ZX4–sŸÊS@\RZHbkUfYn\^j§X@Ûs]ÊX4aŠZ¡[@²ã© \•œO `XbÑZ bÍ[ ÊXS@\"Ÿn[ŠX–_bd[ŠZH\"YnSX
SUfVWV#Ÿ_Y_bÍS@\^ZebdU"Y;”™Ufaels[–s!b `X4aeX4YQZejdœTgiU"Ia .¢£ ² Ì [Zem_X4aeX\WSUfY_Y_X4SZebdU"Y; ÊX@Z”™X4X@Y(©(a² “ ZeX4Ú"X
.–sbd–_aeXڕSÈ\"ZHaHU"–_aȜžÖ  ÊÌ X4”cbkYnU"—žŸ_jÍ\•–h”cjk\"bdaHl"–sXXZe–TUWZHjdm_X4bd\"[ aeYh—"a¡Ze\^m_YQXZaH\"X4Yn\f–h[ŠUfm_Ynbd[c[ œ"m_UfU"Ÿhj͖sÚfbdY_U"—TŸnS¡\mn[H]`\RUfgi[eX?bkZeZebdmnU"bdY([\"VW[ Uf Y_X@ .œT¢ZH£ UT ©(Ò [a4² aeX .[Š–sX\^ÚRa¡\^S¡a¡m–sœ Ì
\^jÍ[eU)”cU"Ÿnjd–hjkbdl"XZHU)lOY_UR”¶bÑg$©(a² .–sÚR\"aH–sœ‚Ò [–sŸsZHbkX[ \"[–sbdaHX4SÈZHU"aU^g6X4–_ŸnS@\^ZebdU"Y;bkYnS@jkŸÊ–sX
lOY_UR”jdX4–s—fX\"Yn–;aeX[ŠX\^a¡S¡mžbkY;ZHm_bd[.\^aHX4\_² Ì g$[ŠUÊos”mQœhbd[cZHm_X@aHX\)Y_X@X–žZHUT]n\•œM©(a² .–sÚR\"aH–sœ
\"–n–sbÑZHbkUfYn\^j§VWUfY_bkX[cZeUž–sU)ZHm_X”™UfaelWZHmn\RZ mnX”c\f[™mnbkaHX4–hgiU"abdY;Zem_XÐÊaH[ŠZ]_jd\fSX•Ö
Ó X.”cX@aHX bkY_giU"aHV)X–T OœT©(a4²fÓ \"jklObdY_—^ZHU"YžUfYWZem_X `X@mn\"jÑgAU"g  .¢£ ¶bkYTZHm_X .URÚf˜O¢?X4S®¯"A¯ bÍ[H[ŠŸ_X
ZemÊ\RZ \^aHU"Ÿ_YʖM© \"aHS¡mhU"a ]_aHbdj$®4¯"¯
OoO”cX?”cU"Ÿ_j͖hmn\•Ú"X?Zem_X[eU^g Z”\^aHX.UfYMZHm_XSaHbÑZHbdS4\^jA[ejkUR”u]njkŸ_Yn—"X@a
Ú"X4jkUsS@bÑZœf² Ì [cZHm_X@aHX\WSUfY_Y_X4SZebdU"Y; ÊX@Z”™X4X@Y;Zemnbd[ [eU^g Z”\^aHX"Ò [c\^]_]n\"aeX4YQZ–_X@jÍ\•œ"X4–h\^]_]`X4\"aH\"YnSX\^Yʖ
ZemnXgª\"SÈZZHmn\RZZHm_XaHX4[eX4\^a¡S¡mžbdY ?m_bkUWmn\f[]_aHUO–_ŸnSX–žZHU^ZH\"jkjdœžbdYnSUfaeaHX4SZ \^Yn–hU ʘQ n\f[ŠXaHX4[eŸ_jkZH[¡Ö Ì
\^VÅ[ŠŸ_aHXZemn\^ZZem_X4aeX\"aeXaHX4\"[eU"YÊ[™]naeX4Ú"X@YQZHbkY_—  ?¢£ ~giaeUfVCSUfV)]njkX@ZebdY_—ž\^Yn–h]_Ÿ_ njkbÍ[ŠmnbkY_—WZHm_bÍ[
[eU^g Z”\^aHX  Ì ”™UfŸ_j͖ ¦ Ÿn[ŠZjkbdl"X?ZeU)lOY_UR”¸”mn\RZcZemnX@œM\"aeXf² Ì \"V×\^jÍ[ŠU)[ŠŸnaeX?Zemn\^Z™ZHm_X–_\RZHX.ZHm_bÍ[\^aeZebÍSjdX
S@\"VWXUfŸsZ#¨ .URÚn¬R¢?X4S)®4¯fA¯ f±ˆ”\"[cU"Y_jdœhS@U"bdYnSb͖sX4YfZ¡\^jdjkœTbdVWVWX4–sbÍ\RZHX@jdœh\Rg ZHX@a Ì [ŠX4YQZœfU"Ÿ;V#œh]n\^]`X@a
\^YʖM]_aHU"]`Uf[H\^j§UfYMZHm_X[em_U^Z [ejkX4X@Ú"XT¨ “ X@]sZHX@V ÊX4a®4¯fA¯ f±²
Ó¸mÊ\RZ.–sUWœ"UfŸMZHm_bdY_l_Ö
 bdl"X4”bd[eX"o Ì jkX\^aHY_X4–MZemn\^Z ©(a4²6ÓÀ\^jdlObkY_—"ZeUfYAosU"Y_XU"g1ZemnX—fURÚ"X4aeY_UfaH[ˆU^g  .¢£ oÊ\^jÍ[ŠU)aeXSX4bkÚfX4–M\
—"a¡\^YQZ² Ì [cZHm_X@aHX\WSU"YnY_X4SZebdU"Y; ÊX@Z”™X4X@YhZem_bÍ[—"a¡\^YQZ ÊX4bkYn—ž\•”c\"aH–sX–WZeUž© a4²sÓÀ\^jdlObkY_—"ZeUfY;\"Yn–Mmnbd[
]`Uf[ebÑZHbkUfYÊÖÓ¸mn\^Z.\^ `U"ŸsZZemnXSU"YnY_X4SZebdU"Y; ÊX@Z”™X4X@Ym_bÍ[aeXSX4bkÚObdY_—#ZHm_X—"a¡\^YQZ\^Yn–;m_bÍ[cgiU"aHVWX@a
]`Uf[ebÑZHbkUfY;\f[cZem_X–sbdaHX4SÈZHU"aU"g  ?¢£ ÁaeX[ŠX\^a¡S¡mÊÖ Ì \"VC[ŠŸnaeXZemÊ\RZ —"a¡\^YQZ”c\f[\•”c\"aH–_X4–ž Ê\"[eX4–hU"Y
VWX@aHbÑZ UfY_jdœ"² UR”cX@ÚfX@ao Ì mn\•ÚfX[eX@aHbkUfŸn[SUfYnSX4aeYn[\" ÊUfŸsZm_bÍ[aeX[ŠX\^a¡S¡mA² Ì \^V[ŠŸnaeX?Zemn\^ZZem_X[ŠX
SUfYnSX4aeYÊ[c\"aeXŸ_Y_giU"Ÿ_Yn–_X4–§o_ nŸsZ Ì ”cU"Ÿnjd–hjkbdl"XZHUTlQYnUR”„”mn\^Z© a4²$ÓÀ\^jdlObkY_—"ZeUfYAÒ [S@aeX–sX@YQZHbd\"jd[\^aHX
bdYhZHm_bÍ[ \^aHX4\U^gaeX[ŠX\^a¡S¡mA²
¥m_XZHm_aeX4XV)UQ[ZbdVW]ÊUfaŠZ¡\^YQZ.\^aHX4\f[™bdY–sbkXS4\"[ŠZebdY_—T\^aHXZem_XS@aebkZebÍS@\"jA[ŠjdUR”u]_jdŸ_Y_—fX@aÚ"X4jkUsS@bÑZœfoOZem_X
] g^u–sbÍ\^—"a¡\^Vos\^YʖžZHm_XaeŸnY_Y_X@a [eœs[ZHX@VC–_X4[ebk—fYA²ã¥m_XaHX4[eX4\^a¡S¡mM[e]ÊUfYn[eU"aHX4–ž O@œ  .¢£ €U"Y;ZHm_X
SaHbkZebÍS@\^jA[ejdUR”„]_jdŸ_Y_—fX@aÚ"X4jkUsS@bÑZœTbÍ[ \^ Ê[ŠUfjkŸsZHX@jdœžŸ_YsgiUfŸ_Yn–sX–; ÊXS@\^ŸÊ[ŠXbkZ ÚQbdU"jÍ\RZHX4[cZHm_X n\"[ebÍS?]nmQœs[ebdS4[
jÍ\•” [@²$¥m_XbdVW]_jkX4VWX@YQZH\^ZebdU"Y;U^gZem_X]  ^ –sbÍ\^—"a¡\^V bÍ[ \"jd[eU)\" n[eU"jdŸsZeX4jkœžŸnYn[ŠUfŸ_Yn–; `X4S@\"Ÿn[eX\"—f\"bkYAo
bkZ ÚQbdU"jÍ\RZHX4[™ZemnX n\"[ebdS]_mOœs[ebdS4[jd\•” [4² ?Y_XU^g1ZHm_X\^ Ê[ŠŸ_a¡–sbkZebdX4[U"g1ZemnX]_aeX4ÚObkUfŸn[cV)Us–sX4jAbÍ[cZem_Xb͖sX4\
ZemÊ\RZ ]_jdŸ_Y_—fX@a –sbÍ\^VWXZHX@amn\f[cZeUž–sXSaHX4\f[ŠXbkYUfaH–sX4acZeUWbkYÊSaHX4\"[eXZem_X—Q\RZHXÚfX@jdUsSbkZœ"²$¥m_bÍ[
SUfYnSjdŸn[ebkUfY ¨ªU^gZem_X]naeX4ÚQbdU"ŸÊ[™VWUs–sX4jͱcÚObdU"jÍ\RZeX[[ŠX4Ú"X4aH\"jÊ]_mOœs[ebdS4[jd\•” [4² .[ \W–sbdaeXSÈZ.S@U"Yn[eX4ÙQŸ_X4YnSXfo
ZemnX–sX4[ebk—fYhU"g
ZHm_XaHŸ_Y_Y_X4a [Šœs[ŠZeX@V ¨ª\"[]nŸ_ _jdbd[em_X4–;bdHY  .¢£ ~jdbÑZHX@a¡\RZHŸ_aeX•±™bd[4on\RZ `X4[ŠZ4o
XÛOZHaeX4V)X4jkœM”c\f[ZHXgiŸ_j ²
.[ œ"U"Ÿ\^jÍ[eUlOY_UR”o .¢£ Co “ cosZemnX¢.X4]n\^aeZeVWX@YQZ U"g¤ãYnX@aH—"œ"os\"Yn–;U^ZemnX@a¡[[Š]`U"Yn[eU"aHbdY_—
aHX4[eX4\^a¡S¡mžbdY;Zem_X[ŠX\"aeX\"[cXÛ_SX4X4–MZem_XZHX@Yn[ U^g
VWbdjkjdbdU"Yn[4on\^YʖMœfXZ ]_aHUs–sŸnSXX4aeaHU"Y_X4U"Ÿn[™aHX4[eŸ_jÑZ¡[@² Ì
\^V×Zem_XUfY_X”m_UT–sbÍ[eS@URÚ"X@aHX4–TZem_XS@U"aHaeXSÈZ]_aHUOS@X4–sŸnaeXbkY `U^ZHm\"aeX\"[4² Ì Z mÊ\"[ `X@X@YVœ

-ç s


–— ˜A™&— ˜Aš ›fœ:Tž6Ÿ j›G #¡› ŸP¢Y—£¥¤¦Fž ›Y¢
¦T§ ›j¨B6Ÿdœqž#™.!¦6˜:œG©g¤6ª ˜<«!£ ˜ŸK£ ¢.›A©



4 QXU<MF587 ZX29x• ” v

’ ib

T vtW<M `5 _’*=5Es-“367E5

Chapter B. My Relationship with Die Casting Establishment

SUfYfZHbkYOŸ_UfŸn[\RZeZeX4V)]_ZZeUTVT\^lfX .¢£ ~]n\^aeZU^gZem_X[ŠX\fS¡m_bdX@Ú"X4VWX@YQZH[4²ãX@Z4o_œfU"Ÿ[ZHbkjdjAmn\•ÚfX?YnU^Z
aeX[Š]`U"YʖsX4–MZeUWV#œMaeX4]ÊX\RZeX–MaHX4ÙQŸ_X[Z¡[cgiU"a \)—"a¡\^YQZ² Ì [cZHm_X@aHX\aHX4\f[ŠUfYžZHmn\RZ bkZ mn\"[™Z¡\^l"X4YhœfU"Ÿ ®
œ"X\^a¡[ˆZHUT—"bdÚ"XVWX\YnX@—f\^ZebdÚ"X\^YÊ[Š”cX@aÈÖ Ì [Zem_X4aeX\WSUfY_Y_XSÈZebdU"Y; `XZ”cX@X@Y(\"YQœMU^g1ZHm_X\^ `URÚ"X
bkY_giU"aHVW\^ZebdU"Y\^Yn–;m_UR”¶jkUfY_—WbÑZ mÊ\"[cZH\"l"X4YhœfU"ŸÊÖ
ãjdX4\f[ŠX[ŠX4X?ZHm_XbkVW]_aHX4[H[ŠbdÚ"X]n\"aŠZHbd\"j ˜OjkbÍ[ZcU^gAZHm_XZem_bdY_—Q[ˆZHmn\RZ Ì mn\•Ú"X\"S¡m_bdX@ÚfX4–§² Ì \"V Zem_XU"YnX?”m_U
giU"Ÿ_YÊ – \"ae `X@aÒ [V)Us–sX4j§ZeUW `XZeU"ZH\^jdjdœM\^Yn–\" n[ŠUfjkŸ_ZeX@jdœT”aHU"Y_—ʲ Ì \^VÅ\^jÍ[ŠU)ZemnXU"Y_XaHX4[e]ÊUfYn[Šbd _jdX
giU"aÐnYʖsbkYn—WZem_X]  ^ –sbÍ\^—faH\"V bkVW]_jdX@VWX@YQZ¡\RZebdU"YhZeUT `X”aHU"Y_—ʲ Ì \^VCZem_XUfY_X”m_UWbd[
aeX[Š]`U"YÊ[Šbd _jdX?giUfaÐnYn–sbdY_—WZHm_XSUfaeaHX4SZc]  ^ –sbÍ\^—faH\"V bkVW]_jdX@VWX@YQZ¡\RZebdU"Y1² Ì \^VCZem_XUfY_X”m_U
–sX@ÚfX@jdU"]`X4–MZem_XS@aebkZebÍS@\"jA\^aHX4\WSUfYnSX4]sZ4² Ì \^V ZHm_XU"YnX”mnUž–sX@ÚfX@jdU"]`X4–MZem_XXSU"YnU"VWbdS4\^j‚aHŸ_Y_Y_X4a
–sX4[ebd—"YSU"YÊSX@]_Z4² Ì YV#œžœfX4\"aH[cU^g6aHX4[eX4\^a¡S¡mžbdY;Zem_X\"aeX\#U"g6–sbdXS@\f[ZHbkY_— Ì mn\•Ú"XY_U"Z.SU"VWX\"S@aeUQ[e[
\^YOœžaHX4[eX4\"aHS¡mMZemn\^Z ”c\f[c[e]`U"Yn[eU"aHX4–M Q@œ  ?¢£ ~”mnbdS¡m;”c\f[SUfaeaHX4SZ\"Yn–ʬ•Ufa”m_bdS¡m;]_aHUs–sŸnSX–
Ÿn[eXgiŸ_j§aHX4[eŸ_jkZH[ Ì [cZemnX@aHX\"YQœžS@U"aHaeX4jd\^ZebdU"YT `XZ”cX@X4YMZHm_Xgª\"SÈZcZemÊ\RZ \^jdj`Zem_XbdV)]`U"aeZH\"YQZ–_bd[HSURÚfX@aHbkX[
¨ ZHmn\RZ Ì \^V\•”c\"aeX?U^gH±cmn\•ÚfX ÊX4X@Y(–sbÍ[eS@URÚ"X@aHX4–žY_U^Z bdYO˜Q nŸsZ U"ŸsZ¡[Šb͖sXU^g  ?¢£ Ö Ì ”cU"Ÿ_j͖Mjdbdl"XZeU
m_X4\"a \^ `U"ŸsZ.\"YOœfZHm_bdY_—WbkY;V#œ;\^aHX4\U^g
X@Ûs]ÊX4aŠZHbd[eX[ŠŸn]_]ÊUfaŠZHX4–h Oœ  ?¢£ ~”mnbdS¡mbÍ[Ÿn[ŠX@giŸ_j1\"Yn–
SUfaeaHX4SZ¡Ö Ì [cZemnX@aHX\)S@U"Y_YnX4SÈZHbkUfYh `XZ”cX@X4Y;Zem_XgiUfaeX4—"U"bdY_—bd[H[ŠŸnX4[\^YʖMZHm_Xgª\"SZZemn\^Z.[ŠUWVT\^YOœžU"g
Zem_X–_bkXS4\"[ŠZebdY_—WX@Y_—fbkY_X4X@a¡[ Ì mn\•ÚfX?VWX@Z.–sUTY_U^Z `X@jdbkX4Ú"XbdY([eS@bkX4YnSX•Ö
©(U"aHXaeXSX4YfZHjkœfo Ì mÊ\•Ú"XjkX\^aHY_X4–MZemn\^Z œ"UfŸ_a[ŠXSaHXZH\"aeœn¬^\"[H[ŠbÍ[Z¡\^YQZ4oQ¥1aHbÍSbÍ\)©«\^aH—"X@j oOmn\"[YnUR”„ `X@X@Y
\•”c\"aH–_X4–žUfY_XU^g6œ"UfŸ_a—"a¡\^YQZH[\^YʖhbÍ[–sUfbkY_—WaHX4[eX4\"aHS¡mhU"Y;]ÊUfjkjdŸsZebdU"Y1² Ì \"VC[ŠŸnaeXZemnX—"a¡\^YQZc”\"[
—"bdÚ"X4Yh n\f[ŠX–MUfY;ÙQŸn\"jkbkÐÊS4\RZebdU"Y\^YʖhVWX4aebkZU"Y_jdœ"² Ì ”™UfŸ_j͖MjdbklfXZeUWlOY_UR”„”mn\^Z.© [4²ã© \^aH—"X4j Ò [
SaHX4–sX4YQZebÍ\^jÍ[bkY;ZemnX]ÊUfjkjdŸsZebdU"YaHX4[eX4\"aHS¡mM\"aeX\\"aeX•Ö .\f[[Šm_X–_U"Y_X\^YOœžaHX4[eX4\"aHS¡mMU"Y]ÊUfjkjdŸsZHbkUfY
 ÊX@giU"aHXÖ Ì g$[em_Xmn\"[–_U"Y_XaHX4[eX4\^a¡S¡mžbdY;Zemn\^Z.\^aHX4\_oO”m_X4aeX”\"[bkZ ]_Ÿ_ _jdbÍ[Šm_X–nÖÓ¸mOœM”\"[eYAÒ Zm_X@a
aeX[ŠX\^a¡S¡mM”cU"aHlT]_Ÿ_ _jdbÍ[Šm_X–nÖ Ì g6bÑZ?”c\f[™]nŸ_ _jdbd[em_X4–Ao_”m_X@aHXS@\"Y Ì U" sZ¡\^bdY;\TS@U"]OœTU^gZemnXaeX[ŠX\^a¡S¡mÊÖ
Ì [Zemnbd[ZHU"]_bÍS]n\^aeZU^g$© [4²ã© \^aH—"X4j Ò [–sŸsZebdX4[.\RZm_X@a ¦ Uf ÊÖ Ì g$[ŠUÊosbd[eYAÒ ZZem_bÍ[ \W–sUfŸ_ _jdX]n\•œOV)X4YQZ¡Ö
?a]ÊX4aemÊ\^]n[4os”c\f[cZem_bÍ[ \"YhX@ÛQZHaH\W[eX@]n\"aH\^ZeX–ž]n\•œOVWX@YQZ¡Ö;Ó¸mnX@aHXS@\^Y Ì U" sZ¡\^bdYMZHm_XÐnYn\"YnSbÍ\^j
aeX4]ÊUfaŠZUfYhm_UR”„Zem_XVWUfY_X@œh”c\f[c[e]`X@YQZ¡Ö
¥1Uf—"X@Zem_X4a”™XV#ŸÊ[Z ]_aHU"VWU"ZeX–sbkXS4\"[ŠZebdY_—WlOY_UR”jkX–s—"Xf² Ì \^V–sU"bdY_—WV#œMŸsZeVWUf[ŠZZeUWbdYnSaHX4\f[ŠXZHm_X
SUfV)]`XZHbÑZHbkÚfX@Y_X[e[ U^g1ZHm_X–sbdXS@\f[ZHbkY_—WbdYn–sŸn[ŠZeaHœž”bkZemU"Ÿna \^a¡S¡mMaHbkÚR\^jÍ[ 6Zem_X]_jÍ\"[ŠZebÍS@[bdYn–sŸÊ[ZHaeœfoOZem_X
SUfV)]`Uf[ebkZeXVT\RZHX@aHbd\"j`bdYn–sŸÊ[ZHaeœfon\^Yn–hU^ZHm_X@abdYn–sŸÊ[ZHaebdX4[4² Ì \"VCS@\"jkjdbdY_—WU"Y;X@Ú"X4aeœfU"Y_X?ZeU ¦ UfbkYVWXZeU
\"–sÚR\"YnSXZemnXlQYnUR”jkX–s—"XU^g
Zem_X–_bkXS4\"[ŠZebdY_—W]_aeUsS@X4[H[@²
¥mn\^YnlMœ"UfŸžgiUfaœ"U"Ÿna SU"YÊ[Šb͖sX@a¡\RZHbkUfYA²
“ bdYnSX4aeX4jkœfo
X@Y_bÍS¡lhØ\"a˜s©(X@bda4o ãm1² ¢²
ØcUf\"aH–MU^g URÚ"X@aHY_UfaH[
‘/‘a‚ . .¢¢£ Á
£ ~VWX@V ÊX4aH[
.YOœ"U"YnX”mnUWS4\^aHX\" ÊUfŸsZ.–sbdXS@\f[ZHbkY_—WbdYn–sŸn[ŠZeaHœ



4<QXU MT587 ZX29x• ” v

W ib

T vtW<M `5

’*=5Es-“367E5

–— ˜A™0— ˜<š ›0œqž6Ÿ" j›G #¡› ŸP¢Y—£¥¤¦Fž ›Y¢
¦T§ ›`¨B!Ÿ\œqž#™.!¦6˜:œG©N¤6ª ˜<«!£ ˜ŸK£ ¢: `©



¬ 





>),+
(} , o"

a#' $&&/ e"/ `

F T

T "v

T

1m :U
/m fUgU
¡}_wq#}_b#S £
T "v
T Š£
]\5^ `U
¨}_wq#}U
T
T
T
`U T ]mwU
]\ ^ b
Ÿ¤ %v
T
%¬ /m -m EU HbŸ{`£ m
T `b
%v T T nS
[U

\=FV ’k5l= Q h3!5n7 ;`9A23 OQ5 [35 Ha7E5B34A9RQ5*Q k4<Q (VFD!7 4G=9:7 QXD;`=9"{
J26= 3"9A5O7 3H&9RQNUTVFW 7 ; 2
=5P9:7 4 3 ; =FW!QXV9`4!5O7 9:7 4G= ;<2Q ‹;<2Q!9L; 3 3 3(=FD6H@9A23&U ‹H7 =Z\5K= p9A2F5BQ\VZ\20{
1=ZT=Ž7ED3
n3!5K3e7 ; =FD(3Aˆ!= (U 3Q #MCW=9>9 319RQUFVTW 7 ;<2"9A23(=!5B9:7 4 3@5K3 ZT=5lH7EDZCU
JQXV :VHTZ3 23 9A235
{
26=;W!3G3!D3DG9A2FV;q7 =;R9:7 41=FW!QXV91UTVFW 7 ; 2!7EDZe9A2!7 ; 7ED6H&Q h7ED OQ5 =9:7 QXD
3D= l9R3!5j“C5
’k5l= Q h3!5*;Y=7 H@9A26=9123 hQXV HgUTVFW 7 ;<2@7 9 *2=6H&9RQ04 QXD9:7EDTV3 [M;R9A5‡VZTZ 3

T
¨}_wq‚}
T "v

}




 "!$#&%&')(*+(
,%.-/#0
1! 32)2)2

%S

9j^-5K;R9 X;?3DG9_=

T 3 9>9R3!5-9RQS“f5ib_’k5l= T Q"vh3!5ØoC}_VZ

$\^ŸnjA©+²_ØcaH\"jkUR”cX@a

 ?¢£ #oʤ™–sbÑZHU"a
¯
®Ó X[Z
.bk—f—"bdYn[ UQ\"–§o “ ŸnbÑZHX°"°
UQ[ŠX4V)UfYQZ4o Ì  ®4°

_®





v




(b
ib

s(tŠj

¢?X4\^a © a4²ãØca¡\^jdUR”™X4a
ãjdX4\f[ŠX?ÐnYn–;X4YnSjdUf[eX4–MZ”™U(¨ "±SUf]_bdX4[U^g
Zem_X]Ê\^]`X@aTÎe¥mnXVW\^Zem_X4VT\RZebÍS@\"j‚Zem_X4U"aHœžU^g
Zem_X]( ^
–sbÍ\^—faH\"VWÏ)[eŸ_ _VWbÑZeZeX–h OœžVœs[ŠX4jÑggiU"aœfU"Ÿ_aaHX@ÚObkX4”²$¥m_bd[ ]n\^]`X@abÍ[bdYfZHX@Yn–_X4–hZeUW `XSU"YÊ[Šb͖sX@aHX4–
giU"a]nŸ_ _jdbdS4\RZebdU"YbdY 46587:9<;>=@?A58BDCFE<B@C<58BG7D7@H,²
_Ufaœ"UfŸ_aSU"YOÚfX@Y_bdX@YnS@X Ì bdYnSjdŸn–sX\W–sbÍ[Šl; ¢  “ giUfaeVT\RZ”bkZem(©(bÍSaHUf[eU^g ZÓ  .¢€giU"a”bdYn–sUR”
giU"aHVT\RZ¨i]‚Ù s² ”bd–ʱcU^gZem_X]n\"]ÊX4a4os]`Uf[ŠZH[HSaHbd]sZȬR]_bdSZÐnjkX[U^g
Zem_XÐʗ"Ÿ_aHX4[¨iÐn—"Ÿ_aHX4[®\"Yn– f±È² Ì g
ZemnX@aHXbÍ[ \"YQœžZem_bdY_—)Zemn\^Z Ì S4\^Y–sUWZeUWm_X4jk]]_jdX4\f[ŠX–sUWY_U"Z m_X4[ebkZH\RZHXjkX@Z V)XlOY_UR”²
¥mn\"Y_lžœ"UfŸMgiUfaœ"UfŸ_abkYQZeX4aeX[Z bdY;U"Ÿ_a”cU"aHl‚²
X[Š]`X4SZŠgiŸ_jdjkœ;[ŠŸn _VWbÑZeZeX4–Ao
¢?a4² X4Y_bdS¡lhØc\"a˜s©(X@bda
‘/‘a‚  \^\)aHaH[eœTm_UfÓ¸aŠZ bkY_–slObdXjdX@S@a \"[ŠZebdY_—Wjdbd[ŠZ
X@YÊSj ¢?¢?Usbd[eSl Ÿ_VWX@YQZ¡[@o
n3H7 HDQ!95B3G;<U!Q\DHT3GH@9RQ@9A27 ;

$\^ŸnjA©+²_ØcaH\"jkUR”cX@a

T 3 9>9R3!5>va;?QSX;Y3!D9[27aUp=FD@=6HTHa7 9:7 QXD6= T QXD3"QXDWk34<3/UW!3!5Itv   sfb


 ?¢£ #oʤ™–sbÑZHU"a
¯
®Ó X[Z
.bk—f—"bdYn[ UQ\"–§o “ ŸnbÑZHX°"°
UQ[ŠX4V)UfYQZ4o Ì  ®4°

_®

¢?X4\^a © a4²ãØca¡\^jdUR”™X4a
Ì mÊ\•Ú"XY_U^ZaHX4SX4bkÚfX4–Mœ"U"Ÿna™aHX@]_jdœTZHU)VœžSX4aŠZHbÑÐnX–MVT\"bkj‚ZHU)œfU"Ÿ;–_\RZHX4–@ Ÿ_—fŸn[Z o§®4¯f¯
bkY;”m_bÍS¡m
Ì X@YnS@jkUQ[ŠX–žZHm_X]n\^]`X@a Ïf¥m_XVT\RZemnX@VT\RZHbdS4\^j‚ZemnX@U"aHœžU"g1ZemnX] ^ –_bd\"—"a¡\^VTÏ\"ŸsZemnU"aHX4–ž OœhV#œs[ŠX4jÑg
giU"aœfU"Ÿ_aS@U"Yn[ebd–_X@a¡\RZebdU"Y ¨ª\TS4S?”\"[\"jd[eUW[ŠX4YfZZHU  \^aHaHœTÓ¸bkY_lOjdX@agiaHU"V .\^ae>Z F4X@jdjͱ² ãjdX4\f[ŠX
SUfYn[ebd–sX4a]_Ÿ_ _jdbÍ[Šm_bdY_—WV#œh]n\^]`X@abdY;Zem_XX\^aHjkbdX4[ŠZ]ÊUQ[e[ebk njkXbÍ[e[eŸ_Xf² Ì  `X@jdbkX4Ú"XZemn\^ZZem_bÍ[]n\"]ÊX4abd[ U^g
XÛOZHaeX4V)XbdVW]ÊUfaŠZ¡\^YnS@X?ZHUWZem_X–_bkXS@\f[ZHbkYn—ÐÊX@j͖§²
Ì Ÿ_Yn–sX4aH[ŠZH\"Yn–žZHmn\RZ œfU"Ÿ;mn\•Ú"X `X@X@YÚfX@aHœT _Ÿn[eœM”bkZem;Zem_XjÍ\"[ŠZXÛsm_bd _bkZebdU"Y(\^Yn–;SUfY_—"aHX4[H[4²
UR”cX@ÚfX@ao Ì ZemnbkY_lMZemn\^ZZem_bÍ[]n\"]ÊX4a –sX4[eX@aHÚ"X[\W]_aeUfVW]sZm_X4\"aebdY_—n²
Ì –sUWY_U^Z.\"—"aHX@X”bÑZHm;œfU"Ÿ_a[ŠZH\^ZeX@VWX4YfZ bdY;œ"U"Ÿna ¢.XSX@V ÊX4Ia _oA®¯"¯ jdXZŠZHX@aZHUWV)X[ŠZH\^ZebdY_—)Zemn\^Z
Ï"¥mnbd[]n\"]ÊX4abd[ m_bk—fm_jdœTZeXS¡m_Y_bÍS@\^!j  ZeUOU)ZeX4S¡mnY_bdS4\^j§”bkZem_UfŸsZ.\)jkX[e[  ZeX4S¡mnY_bdS4\^j‚ n\fS¡lQ—faeUfŸ_Yn–

-ç


–— ˜A™&— ˜Aš ›fœ:Tž6Ÿ j›G #¡› ŸP¢Y—£¥¤¦Fž ›Y¢
¦T§ ›j¨B6Ÿdœqž#™.!¦6˜:œG©g¤6ª ˜<«!£ ˜ŸK£ ¢.›A©



4 QXU<MF587 ZX29x• ” v

’ ib

T vtW<M `5 _’*=5Es-“367E5

Chapter B. My Relationship with Die Casting Establishment

X Ûs]_jÍ\^Yn\^ZebdU"YhgiU"aUfŸ_a—"X4Y_X@a¡\^j‚aHX4\"–_X@a¡[d² Ì –sUTYnU^Z ÊX4jkbdX@ÚfXZemn\^Z.–sbÍ[eS@U"Ÿ_YQZebdY_—Wœ"UfŸ_aaeX\"–sX4aH[cbÍ[
m_X@jd]sgiŸ_j ² Ì mn\•Ú"XVWXZ.[eU"VWXU^g6œ"UfŸ_aaeX\"–sX4aH[\^YʖMmn\•ÚfXgiU"Ÿ_Yn–hZHm_X@VCZeUW ÊXÚfX@aHœžbdYfZHX@jdjkbd—"X4YQZ4o_\^Yʖ
giŸ_aeZem_X4aeVWU"aHXZem_X4œMaHX4\"jkjdœžS@\"aeX\^ `U"Ÿ_ZcZHm_X–sbdXS@\f[ZHbkY_—WbdYn–sŸn[ŠZeaHœ"² Ì  ÊX4jkbdX@ÚfXZemn\^ZZem_X4œMS@\"Y ¦ Ÿn–s—"X
giU"aZHm_X@VT[eX@jdÚ"X4[4² X4Ú"X@aeZemnX@jdX4[H[@o Ì mÊ\•Ú"XœQbdX@j͖sX–žZHU)œfU"Ÿ_a–sX4VT\^Yn–;\^Yn–hmn\•ÚfX?X4jkbdVWbkYn\^ZeX–MVT\^YOœTU"g
Zem_XVT\^Zem_X4VW\^ZebÍS@\"j1–sX@aHbdڕ\^ZebdU"Yn[™giaHU"V ZHm_bÍ[]n\^]`X@a ZeUT[e\^ZebÍ[giœMœ"U"Ÿna –sX4[ebkaHX?ZeUTmn\•ÚfX\TÏf[ŠbdVW]_jkXÏ
]_aHX4[eX@YQZH\^ZebdU"YA²$¥m_bÍ[]n\"]ÊX4a4osm_UR”cX@ÚfX@aoQ[ŠZebdjdj1SUfYfZ¡\^bdYn[cZemnXX4[H[ŠX4YfZHbd\"jd[™ZHUT ÊXŸ_YʖsX@a¡[ZHUOUO–;SjdX4\"aejdœ"²
ãjdX4\f[ŠXY_U"ZeXZemn\^Z Ì ”bdjdj§”bÑZHmn–sa¡\•”uZemnX]n\^]`X@a bkg Ì –sUTY_U"ZaeXSX@bdÚ"X\)aHX@]_jdœM[ŠZH\RZHbkYn—)œfU"Ÿ_a
bkYQZHX@YQZebdU"Yn[ Oœž­Q\^YOŸn\"aeœ®"o§®¯"¯f°_oQbkY;”aebkZebdY_—ʲ Ì –sUW ÊX4jkbdX@ÚfX.ZHm_bÍ[]n\^]`X@a”bdjkjAS¡mÊ\^Y_—fX ZemnX”\•œT]  ^
–sbÍ\^—"a¡\^V S4\^jÍSŸ_jÍ\RZHbkUfYn[\^aHX?VT\"–_X"²$¥m_X]  ^ –sbÍ\^—faH\"V;os\f[™œfU"ŸhlQYnUR”oQbÍ[™Zem_XS@X@YQZea¡\^j‚]n\"aŠZU^g
Zem_X
S@\"jdS@Ÿ_jd\^ZebdU"Yn[\"Yn–;–sX4[ebk—fYMZHmOŸn[ZemnX]n\^]`X@abkZH[eX@jkgbÍ[U"g[H\^VWXbkVW]`U"aeZH\^YÊSX"²
Ì mnU"]`XZemn\^Z œ"U"ŸhaeX\^jdjkœh–sUT[ŠX4X?ZHm_XbdV)]`U"aeZH\"YnSXU"g6\f–sÚR\^YnS@bkY_—WlOY_UR”jdX4–s—fX?bdY;Zem_X–_bkXS4\"[ŠZebdY_—
bkYʖsŸn[ŠZeaHœ"o_\^Yʖ§oOm_U"]`X.ZHmn\RZœ"UfŸM”bdjkj§S@UQUf]ÊX4aH\^ZeX?”bÑZHmžZemnUf[eX?”m_U)mn\•ÚfX.VT\"–sX.Zem_XVT\ ¦ Ufa™]naeUf—"aHX4[H[
bkY;ZHm_bd[.\^aHX4\_²
¥mn\^YnlMœ"UfŸžgiUfaœ"U"Ÿna SU"YÊ[Šb͖sX@a¡\RZHbkUfYA²
“ bdYnSX4aeX4jkœfo
¢.a² X@YnbdS¡l;Øc\"a  ©(X4bka
‘/‘a‚ ØcU•VWÛOX4ZeV#X4a4 `o_X@©«a¡[ S£™jdbkV#ZebÍS^o “ S@U^ZeZ4osÓ¸bdjd[eU"YAo U"jdjÍ\^Yn–§o_ØcX4m_jkX4a4o_¢?Ÿ_]_aHX"oÊ\^Yn–[eU"VWXU^ZemnX@Ia  ?¢£
‹MR6‚ ãU"bdYnŸ;S@jk]_Ÿnae–_Ufbk nY_\^—ž n\"jkœžjkj‚lOZHY_m_URX”¶U^ZH Om_œžX@aY_bdURYO”uÚ"XZH[mnZH\Rbk—QZ \RZebdU"\"YÊae `[ˆX@ZHamnÒ [™\RZ VW”Usmn–sX@X4aHjAXbd[ ÊZe\"U^[eZ¡X4\^–hjdjkU"œhY;\^bÑYnZ–;o_X@\^Úf nX@[eY;U"jdbџsgZHZeX@m_jdœžX4œM””caeUfX@Y_aHX —
[e]`U"Yn[eU"aHX4–M Qœ  .¢£ ²¨ .jkj1Zem_XaHX4[eX4\"aHS¡m_X4aH[™\^—faeX4X4–h”bÑZHm;VWXbdYhZHm_XjÍ\"[ŠZS@U"Y_—faeX[e[¡±

T–T
%U

T

aU
b –T T

kU

5U
T

T

gv

T aU
fb

= 7 €9A2=923
… 3 A9 26=9 3<9>9R35mZQ9#27 pZTQ7EDZ@=FD6HN23 =FD=ZT3GHe9RQ&Z3 9 [3(= 3<9>9R3!5b7ED [27 462&23(4 
;?3DG9 [@
3 2!7 ;15K3 7 ;q7 Q\D; … 3 vd5K3G=6Hf=FW!Q\VG9#7 9 7ED [MfD3<ˆ9 3<9>9R
3 5 HT=9R3H =FDTV6=!5BM tv   r



$\^Ÿ_jA©É²nØcaH\"jkUR”cX@ao

 ?¢£ #oʤˆ–_bÑZHU"a
¯
®Ó X[Z
.bk—f—"bdYn[ Uf\f–§o “ Ÿ_bkZeX°f°
Uf[eX@VWUfYfZo Ì  ®4°

_®

OU

zx

s



.¢ X\^a ©(a²ãØcaH\"jkUR”cX@a
¥mn\^YnlMœ"UfŸžgiUfaœ"U"Ÿnagª\RÛh–_\^ZeX–;¢?X4S@X@V ÊX4a^¯_o§®¯"¯
bdY”m_bdS¡m;œ"UfŸ;\"jkjdX@—fX4–MZemn\^Z œ"UfŸh[eX@YQZ VWX
œ"UfŸ_aaeX4ÚObd[ebkUfYn[™ZeUWV#œh]n\^]`X@aTÎH¥m_XVT\RZemnX@VT\RZHbdS4\^j‚ZemnX@U"aHœžU"g
ZHm_X] ^ –_bd\"—"a¡\^V² Ï ƒ GH†](†`…
…c†(‘/†`• (†ˆFJGMLWR-PH‘(‰|‡A‰f•aGM›  jdj§ZemnX]n\^aeZebdX4[cZHmn\RZ —fU^ZZem_bÍ[bdYsgiU"aHVT\RZHbkUfY;\"Yn–MVœs[ŠX4jÑg
ÐnYn–hZem_bÍ[
]n\^]`X@aZHUTU^g6XÛOZeaHX@VWXbdV)]`U"aeZH\"YnSXf²
Ì –_bd–;Y_U"Z aeX4ÚQbÍ[eX?VœM]n\"]ÊX4a \"S@S@U"a¡–sbdY_—#ZHUWœ"U"ŸnaS@U"VWVWX@YQZH[ U"YhZem_bÍ[]n\"]ÊX4a4o_\"—f\^bdYAos[ebkYnS@X Ì –sb͖
Y_U^ZaHX4S@X@bdÚ"X?\"YOœ"² Ì –sXSb͖sX4–žZeUWaeX4ÚObd[eX4–WZHm_X]n\^]`X@abkYÊSX Ì –sb͖MY_U"ZcaHX4S@X@bdÚ"X–M\^YOœWaHX@]_jdœWgiaeUfV œ"UfŸ
giU"aVWU"aHXZemn\"Y
)VWUfYfZHmn[4² Ì aHX@ÚObd[eX4–;\"S4SUfaH–sbdY_—ZeUWœ"UfŸ_a SUfVWV)X4YQZH[U"Y;V#œh]_aHX@ÚObkUfŸn[c]n\^]`X@aUfY
Zem_XS@aebkZebÍS@\"jA[ŠjdUR”„]njkŸ_Yn—"X@aÚfX@jdUsSbkZœ"² .[ Ì [Z¡\RZHX4–;bkYVœžjkX@ZŠZHX@a.–_\^ZeX–h¢?X4S@X@V# `X@a _o§®4¯f ¯
so Ì [eX@YQZ
œ"UfŸMZHm_XaeX4ÚObd[eX4–hÚ"X4aH[ebkUfYh\f[ Ì [eX@Yn–MZeUž\"jkj‚ZHm_XS@Sjdbd[ŠZ4² Ì aHXȘO[eX@YQZœ"UfŸMZHm_X[e\"VWXÚfX@a¡[ŠbdU"YhU"Y
¢.XSX4V# `X@a "¯_o§®4¯f ¯
s² ˆjkX\"[eX?Y_U"ZeXZemÊ\RZZemnbd[bÍ[ZHm_Xjd\f[ZZHbkVWX Ì ”bkjdjA[ŠX4Yn–;œ"UfŸMZHm_X[e\"VWX]Ê\^]`X@a
[ŠbdYnS@X Ì  `X@jdbkX4Ú"XZemÊ\RZ œ"UfŸh”bdjdjASjÍ\^bdVÅ\^—Q\^bdYžZHmn\RZ œfU"Ÿ–sUWY_U^Z aHX4S@X@bdÚ"X\^YOœžU^gV#œ;[ŠŸ_ nV)bkZŠZ¡\^j ² Ì Y
S@\f[ŠXZemÊ\RZ œ"UfŸ;S@jd\"bkVÅ\^—f\"bkYhZemÊ\RZœ"UfŸ;–sb͖;Y_U^Z aHX4S@X@bdÚ"X?Zem_X]Ê\^]`X@aœ"UfŸ;S4\^Y;—"X@Z.\)S@U"]OœTgiaHU"V
\^YOœ"UfY_X”m_UTbd[UfYMZHm_XS@SjdbÍ[Z² ãjdX4\"[eX ÊX\•”\^aHX.ZHmn\RZ Ì S¡mn\^Yn—"X4–MZemnXZebkZejdXU^gZem_X]n\"]ÊX4a
¨ª¢?X4S@X@V# `X@ao no§®4¯"¯
ÚfX@a¡[ŠbdU"Y`±$ZHUT ÊXÏ UR”uZHUTS@\^jÍSŸnjd\^ZeXZem_X(] ~^u–sbÍ\^—faH\"V×SUfaeaHX4SZejdœOÏn²



4<QXU MT587 ZX29x• ” v

W ib

T vtW<M `5

’*=5Es-“367E5

–— ˜A™0— ˜<š ›0œqž6Ÿ" j›G #¡› ŸP¢Y—£¥¤¦Fž ›Y¢
¦T§ ›`¨B!Ÿ\œqž#™.!¦6˜:œG©N¤6ª ˜<«!£ ˜ŸK£ ¢: `©

¬:®



Ì ”™UfŸ_jd–;\^]n]_aeXSbÍ\RZHX?bkgœfU"Ÿ;aeX[Š]`U"YʖžZHUTV#œžX ,© \"bkj§ OœM­Q\^YOŸn\"aeœ(®
no§®¯"¯"°n² ˆjkX\"[eXS@U"Yn[eb͖sX@aZHm_bd[
]n\"]ÊX4a”bÑZHmn–sa¡\•”Yhbkg Ì ”bdjkjAYnU^Zm_X4\"agiaeUfVל"UfŸh OœTZHm_XVWX@YQZebdU"YnX4––_\RZHXbkY;”aHbÑZHbkY_— ¨ªX@VT\^bdj§bÍ[
ÐnY_X•±c”m_XZHm_X@a Zem_X]n\"]ÊX4abd[\fS@S@X@]sZHX4–§²
Ì m_U"]`XZemn\^Z œ"U"Ÿ;aHX4\^jdjdœM–sUT[ŠX4XZem_XbdVW]ÊUfaŠZ¡\^YnS@XU"g6\f–sÚR\^YnS@bkYn—lOY_UR”jdX4–s—fXbkY;ZemnX–sbkXS4\"[ŠZebdY_—
bdYn–sŸn[ŠZeaHœ"os\^Yʖ§osm_U"]`X?Zemn\^ZcœfU"Ÿž”bdjkjAS@UOU"]`X@a¡\RZeX.”bÑZHmMZHm_Uf[eX?”mnU#mn\•ÚfX.VT\"–sX?ZemnX?VT\ ¦ Ufa™]naeUf—"aHX4[H[
bdYhZHm_bÍ[ \^aHX4\n²
“ bdYnSX4aeX4jkœfo
¢?a4² X4Y_bdS¡lhØc\"a  ©(X4bka

‹MR6‚¨IKP|R-PJ…c†M™ L`GJI]—À“]LGHI(— ‡Š‰HF`‡ŸF]…¹“K†M…–RNWIQf†`™‚• R[‡9IJ‡9FH™š™–LWFJGHŒFJ“MRAIK™aPM‡9†`™–LO—%…iIQGM›
•aGH‘]™ÜPHK•ÜGM›|FH™š™‚‡Š‰M†ˆIH‡Š‰M†M…e•aGM(†]R>‡A• ›fF`‡A•–IKGHR%‡Š‰JF(‡n—1‰H†`…c†Œ“HF`R>†(IKG|• ‡
n3@5B3G;<U!QXD6HT3GH@9RQ&9A27 ; T 3 9>9R3!5m=FD6Hf4626=FDZ3GHg27 ;#=9>9:7 9AVHT3  a
S 9A2Q\VZ\2G9Šb
x=FDFV=5PM  v  rKb

?¢ X4\^a © a4²ãØ\^a  ©(X@bda
¥mn\"Y_lžœ"UfŸMgiUfaœ"UfŸ_aaeXSX@YQZ \^aeZebÍSjdX[ŠŸn _VWbd[H[ŠbdU"Y\^YʖMZHm_bÍ[giU"jdjkUR” ,Ÿ_];X ,VT\^bdj ² Ì \^V×Y_UR”¶bkY
]`Uf[H[ŠX[e[ebkUfYMU"gœfU"Ÿ_a\^aeZebÍSjdXÏ .UR”uZeUTS4\^jÍSŸ_jÍ\RZHX?ZHm_X] )–sbÍ\^—faH\"V×SU"aHaHX4SÈZHjkœf² Ï Ì Z bÍ[cZem_XÚfX@a¡[ŠbdU"Y
–_\^ZeX4–­Q\^YA² _o§®4¯"¯f°_² Ì mÊ\•Ú"XaeX\"–hbÑZ.\"Yn–h\"VC]_aHX@]Ê\^aHX4–TZHUTaeXSUfV)VWX4Yn–MbkZgiU"a]nŸ_ _jdbdS4\RZebdU"Y;bdY
¢?bkX£c\f[ZHbkY_—T¤ˆY_—"bdY_X@X4a4² Ì –sbd–;Y_U"Z aeXSX4bkÚfX\"YQœMX4\^aHjdbkX4a[eŸ_ _VWbÍ[e[ebdU"Yn[U"g1Zemnbd[ \"aŠZHbdS@jkXfo Ì ”\"[
SUfYsgiŸn[ebkYn—)bkZ ”bkZem;Zem_XX\^aHjkbdX@a\"aŠZHbdS@jkXZemÊ\RZ Ì aeX@ZeŸ_aHY_X4–MZeUWœfU"ŸA²ã©(œh\^]`U"jdU"—"bdX4[4² UR”cX@Ú"X4a Ì \"V
Ú"X4aeœT]njkX\"[eX4–;\RZZemnX”c\•œTœfU"Ÿ;mn\•Ú"X\^]_]naeUQ\"S¡m_X–TZemnbd[ \"aŠZHbdS@jkXf² Ì Z.\^]_]`X4\"aH[cZHU)]naeURÚOb͖sXÚ•\"jkŸÊ\^ _jdX
bdYsgiU"aHVT\RZebdU"Y;bdY\"YhUf  ¦ X4SZebdÚ"XVT\^Y_YnX@aos”m_bdS¡mbÍ[\^jdj§”™XmÊ\•Ú"XX@Ú"X4a \"[el"X–TgiU"a² .[bÍ[V#œh]ÊUfjkbÍSœ
giU"amnbk—fm_jkœžZeX4S¡mnY_bdS4\^jAVT\^ZeX@aHbÍ\^j o Ì \^VCaeXÙfŸnX4[ŠZebdY_—)ZeX4S¡mnY_bdS4\^j§]`X@a¡[ŠUfY_Y_X4j§U"Y;Zem_
X .¢£ ~[Z¡\  ZHU
aHX@ÚObkX4”uZHm_X]n\^]`X@a \f[”™X4jkj ² Ì S@X@aeZH\"bkY_jdœTZHm_bkYnlžZemnbd[]Ê\^]`X@amn\f[\VŸnS¡m ÊX@ZŠ[email protected]¡mn\"YnSXU"g
\^]n]_aeURÚR\"j os\^Yʖh\f[ Ì [H\^b͖§o Ì ”bkjdjAaHX4SUfVWV)X4Yn–hbÑZ² Ì ”bdjkj§jdXZ œfU"Ÿ;lOY_UR”„U"gUfŸ_a–sX4S@bd[ebkUfYhbdY
”cX@X@ls[4² ãjdX4\"[eX–sUTY_U^Z”bkZemn–_aH\•”¶bÑZŠ˜Q—"bdÚ"XŸn[\)jdbÑZeZejdXVWU"aHX.ZHbkVWXZHUWaeX4ÚQbdX@”¶bÑZ Ì ”cU"Ÿnjd–hjkbdl"XZHU
]_Ÿ_ njkbÍ[ŠmbkZ.\^Yn– Ì Zem_bdY_lžZHX4S¡m_YnbdS4\^j§aHX@ÚObkX4”™X4a”bkjdj1\^—faeX4X.ZHm_bÍ[ZebdVWX"²
“ bdYnSX4aeX4jkœfo
$\^ŸnjAؙa¡\^jdUR”cX@a


T–T SHvL=7 9R3H¥mOQ5m=gv2!7 T 3=FD6H@9A23DOSX;?3DG9"“f5ib-’k5l= T Q"vh3!5m= T 3<9>9R3!5mHF=9R3GHŒ§63!W

… 3



\v

fb

  r


?¢ X4\^a © a4²ãØca¡\^jdUR”™X4a4o
]n]n\^aHX@YQZejdœ"osœfU"Ÿ–sUWY_U^Z mÊ\•Ú"X?Zem_XZHbkVWXZeUTjdUOU"lžURÚfX@aV#œM]n\^]`X@a \f[œ"U"Ÿ;]_aHU"VWbÍ[ŠXf²6¤ˆÚ"X4Y;\
Y_X4—f\RZHbkÚfX.aHX@]_jdœT”bdjkjA–sX4VWU"Yn[ŠZea¡\RZHX ZemÊ\RZœ"UfŸžmn\•Ú"X[eU"VWX?S@U"Ÿ_aeZeX[Šœf²6ØcŸsZ\^]n]n\^aHX@YQZejdœ)Zem_X]n\"]ÊX4abd[
Y_U"Z bkVW]`U"aeZH\^YQZ \"[œfU"Ÿ_aX@ÛO]`X@aeZH[cZHU"j͖;œ"U"Ÿ\^Yʖ Ì \^V×UfY_jdœh\W[ŠVT\"jkj§ `U^ZHm_X@aHbkYn—WS@UsS¡lQaHUf\fS¡mA²
ãjdX4\f[ŠX[eX@XZemnbd[]n\"]ÊX4a ”bkZemn–sa¡\•”Y
Ì \^VC[eU"aHaeœWZHmn\RZ ”cX–sUWY_U^Z.\"—"aHX@X?Zemn\^Z.\^Y;U"]`X@Y(–sbÍ[eS@Ÿn[H[ŠbdU"YhU"Y;ZeXS¡m_Y_bÍS@\^j§bÍ[H[ŠŸ_X[[ŠmnU"Ÿ_j͖M `X
–sUfY_XbkYœ"UfŸ_aVT\^—Q\ F@bdY_Xf² ãUfŸ;Ufaœ"UfŸ_acZeX4S¡mnY_bdS4\^j§X@ÛO]`X@aeZH[–_UTY_U^Zmn\•ÚfX?ZHUT\^—"aHX@X”bkZemV#œ
aHX4[eX4\^a¡S¡mA² Ì  `X@jdbkX4Ú"XZHmn\RZ œfU"Ÿ;mn\•Ú"X?ZeUWjdXZ œ"UfŸ_aaHX4\"–_X@a¡[ˆZHU ¦ Ÿn–s—"Xf² Ì \"VC[eŸ_aeXZHmn\RZZHm_X@aHXbd[YnU
U^ZHm_X@aaHX4\f[ŠUfYn[™ZeUWœ"UfŸ_a –sXSbÍ[ŠbdU"YA² Ì \^VC\" n[eU"jdŸsZeX4jkœM[eŸ_aHXZemn\^Z œ"U"Ÿ;–sUTY_U"ZcZ¡\^lfXbdYQZeUTœfU"Ÿ_a
SUfYn[ebd–sX4aH\^ZebdU"YMZem_Xgª\fSÈZZemÊ\RZ  ?¢£ Á”bkjdj§mn\•Ú"XZHUW[ŠZeUf];ZeX4\fS¡m_bdY_— “ ¤ ?¤ I  £   “ ¤ “
”m_bÍS¡m(\^aHX?”aHU"Y_—W\"S4SUfaH–sbdY_—ZeUWZHm_bd[ aeX[ŠX\^a¡S¡mA²
¥mn\"Y_lžœ"UfŸMgiUfaœ"UfŸ_a]_aeXSbdU"Ÿn[cZHbkVWX
¢?a4²ãØ\^a  ©(X@bda




–— ˜A™&— ˜Aš ›fœ:Tž6Ÿ j›G #¡› ŸP¢Y—£¥¤¦Fž ›Y¢
¦T§ ›j¨B6Ÿdœqž#™.!¦6˜:œG©g¤6ª ˜<«!£ ˜ŸK£ ¢.›A©



4 QXU<MF587 ZX29x• ” v

’ ib

T vtW<M `5 _’*=5Es-“367E5

Chapter B. My Relationship with Die Casting Establishment

ãjdX4\f[ŠXY_U"ZeXZemn\^ZZem_bÍ[jdXZeZeX@a?\^Yn–MZem_XaHX4[ŠZU^gZem_XS@U"aHaeX[Š]`U"YʖsX@YnS@X.”bkZemœ"UfŸhbdY;Zem_bÍ[VT\RZeZeX4a
”bkjdjA `XSbdaHS@Ÿ_jÍ\RZeX–MbdY;Zem_X–_bkXS4\"[ŠZebdY_—WbkYn–_Ÿn[ZHaeœf² Ì \"VC[ŠŸnaeXZemÊ\RZ œ"UfŸ;[ŠZH\"Yn–; Oœžœ"UfŸ_a–sX4S@bd[ebkUfY
\^Yn–;œfU"Ÿ;”™UfŸ_jd–hjdbklfXU"Zem_X4aZeUT[eX@XZemnbd[ S@U"aHaeX[Š]`U"YʖsX@[email protected]Ú"X@Y;bkgZHm_X@œh\^aHX .¢£ ~VWX@V ÊX4aH[4²
n3!5K3e7 ;j9A23 T 3<9>9R35ØS-5K3G4<367 £3Hg7ED05K3<9AVF5,De= T 3<9>9R35‚m>5BQfU \
F =FV T ’k5K= T Q"vh35ا63!W ä v  rfb
¢.X\^a ©(a²ãØ\^a ,© X@bda 
Ì Ò jdjAmn\•ÚfXœ"U"ŸhlOY_UR”uZHmn\RZ œfU"Ÿ;mn\•Ú"XbkYÊSU"YOÚfX@Y_bdX@YnS@X4–hVWX\^Yn–hU^ZHm_X@a¡[U"Y;U"Ÿ_a [ŠZH\  ZeUs–_\•œM”bÑZHm
œ"UfŸ_aŸ_YQZeUR”\^a¡–§oOŸ_Y_Y_XSX[e[H\^aHœžSUfaeaHX4[e]ÊUfYn–sX4YnSXf² Ì g6œ"UfŸhmn\f–h\)”cU"aHlObkY_—ZeX4jkX4]_m_UfY_XU"acgª\RÛhZem_bÍ[
X ,VT\^bdj§”™UfŸ_jd–;Y_U"Z ÊXY_XSX[e[H\^aHœ"² .[bkZ bÍ[ Ì VŸn[Z aHX@]njkœTZHUWœ"U"ŸnajkX@ZŠZeX4a \^Yn–hZ¡\^l"XbkZZeUT[eU"VWX@UfY_X
X@jÍ[ŠXfÒ [U žSX\^YʖMmn\•ÚfX.ZHm_X@V X ,VT\^bdj§bÑZZHUWœ"U"Ÿ;aHbk—fmfZ \•”\•œ"²
Ì ZHaebdX4–hZHUZHX@jdX@]_mnU"Y_XœfU"ŸMjÍ\"[ŠZ ”cX@X@lMU"Y¥mQŸnaH[4²®•¬ "¯#”bkZem;ZHm_XY_X@” [cZHmn\RZ ”cXmn\•Ú"X\"—"aHX@X4–žZeU
]_Ÿ_ _jdbÍ[Šmœ"UfŸ_a \^aeZebÍSjdX"o$Î UR”¸ZHUh£c\^jÍSŸ_jÍ\RZHXZem_X] 
¶–_bd\"—"a¡\^V×SUfaeaHX4SZejdœ"² Ï Ì ”c\"YfZHX4–MZeUž\f[ŠlTœfU"Ÿ
ZeUž[eX@Yn–MZemnXX@YQZebdaeX]Ê\^]`X@aos”bÑZHm;—faH\"]_m_bÍS@[\^YʖMXÙfŸÊ\RZebdU"YÊ[@osUfY\W–sbÍ[el`²$ØcX4S4\^Ÿn[eXU^gZem_XS@Ÿ_aHaeX4YfZ
[Z¡\RZHŸn[U^gU"Ÿ_aX  VT\"bkjA[eœs[ZHX@Vo Ì ”cU"Ÿnjd–;\"–sÚObÍ[ŠXœfU"Ÿ;Y_U^ZZHU)X  VT\"bkj§bkZ4² “ X4Yn–;bÑZ UfY(\^YOœžU^g
Zem_X
giU"jdjkUR”bdY_—  “ œOÙQŸ_X[Zo ?VWX@—Q\ Ì …Ufa ?V)X4—f\)­ ² .[eX©(bÍSaHUf[eU^g Z žSX ¯
sosÓ UfaH@– _² U"a
Ó UfaH– 6X4aŠgiXSÈZ _² ²
¥m_X]_aHU" _jdX@VCbd[ Ì SUfŸ_jd–_YAÒ Z aHX4\fS¡mMœfU"Ÿ; Qœh]_m_UfY_X"² Ì ZeaHbkX–h[eX@Yn–_bkY_—TœfU"Ÿ\gª\RÛh[eX@ÚfX@a¡\^j`ZebdVWX4[
¥mOŸ_aH[4²$\^Yn–;jÍ\"[ŠIZ _aHbd–_\•œf²$¥m_X@aHX”c\f[Y_UWaeX[Š]`U"Yn[eX"²6Ó XZeaHbkX–\)S@U"Ÿ_]njkXU^g$–s!b `X4aeX4YQZYOŸ_V ÊX4aH[
Zemn\^Z ”™Xmn\f–hgiU"aœ"UfŸA² .\•ÚObdY_—WY_UWaeX[Š]`U"Yn[eX"o Ì ZeUOU"lžZem_Xgª\^Û;\^YʖMVT\^bdjdX4–;bÑZZHUWœ"U"Ÿ\"[\)jdXZeZeX@a
U"Y(©(UfYn–_\•œ f¬ s² Ì [eX@YQZ ˆaebdU"aHbÑZœ  ,–_\•œž©«\^bdj§ZeUWœ"UfŸ_a \RZeZeX4YfZHbkUfY;\^Z Ì Y_Y_URÚR\RZHbkÚfX bdjÑZHX@a¡[@o1®"®

® ^Ze m Ú"Xf² “ ² ¤ ²don©(bdY_Y_X4\"]ÊUfjkbÍ[4o_©(bkYnYACo A

n² ãU"Ÿ[Šm_UfŸ_j͖hmÊ\•Ú"XaeXSX@bdÚ"X–MbkZZeUs–_\•œž\^Z jd\^ZeX[Zbkg
Zem_bÍ[ \f–_–saHX4[H[bd[S@U"aHaeXSÈZcgiU"aœ"UfŸAos”m_bÍS¡mbÑZ.[em_U"Ÿnjd–h ÊX[ebdYnSXbkZ ”c\f[cU"Y;œ"U"ŸnaVW\"YOŸn[eS@aebd]sZ²
UR”os”m_bdjdX Ì Ò VÅ ÊX4Yn–sbdY_—TURÚ"X4ac Ê\"S¡lO”c\"aH–n[ãZHUTbkYsgiUfaeVCœ"U"Ÿ;U^gœ"UfŸ_a \"S4SX@]_ZH\^YÊSX"osœfU"Ÿhmn\•Ú"XZemnX
Y_X@aHÚ"XZHU)”bkZemʖsaH\•”„Zem_X]Ê\^]`X@a \^YʖMZHm_aHX4\RZHX@YhZeUž[e]_aHX4\"–MY_X@—Q\RZHbkÚfX—fUf[H[Šbd]h\" ÊUfŸsZ VWXbkY;ZemnX
bkYʖsŸn[ŠZeaHœ Ì lOY_UR”„œfU"ŸhS@U"Ÿ_j͖sYAÒ Z mn\•ÚfX?lOY_UR”Y Ì ”\"[cZHaeœObdY_—#ZHUTSU"YQZ¡\"SÈZœfU"ŸAos _Ÿ_Z Ì V#ŸÊ[ZbdYsgiU"aHV
œ"UfŸMZHmn\RZ Ì S@\^Y1Ò Z X@ÛQZHX@Yn–;\^YOœTgiŸnaŠZHm_X@a S@U"Ÿ_aeZeX[ŠbdX4[™ZeUTœfU"ŸA² ?[œ"U"Ÿnac]Ê\^]`X@amn\f[ ÊX4X@Y(\"S4SX@]_ZeX4–Ao Ì
XÛs]`X4SÈZZHmn\RZ œfU"Ÿ;”bkjdj1S4\^YnS@X@j§œ"UfŸ_a”bÑZHmn–sa¡\•”jA\^Yn–[eX@Yn–hVWXZem_X]Ê\^]`X@aU"Y–sbÍ[ŠlhbkVWVWX4–_bd\^ZeX@jdœ
giU"a]_Ÿn _jkbÍS@\^ZebdU"YA² Ì g6Y_U"Z4o_]_jdX4\f[ŠX–sUWY_U"Z.[ŠŸn _VWbÑZ.\"YQœžgiŸ_aŠZHm_X@a \"aŠZHbdS@jkX[@²
“(MC5B3G;<U!QXD;?319RQ\
F =FV T “ˆb-’k5l= T Q"vh3!5ib
nX@ (¯_o§®¯"¯f°
¢.X\^a ©(a²ãØcaH\"jkUR”cX@a 
¥mn\^YnlMœ"UfŸžgiUfa \"S@S@X@]sZHbkYn—ZHm_X]n\"]ÊX4a.Ï .UR”¸ZeUžS4\^jÍSŸ_jÍ\RZHX?ZHm_X]  ^ –sbd\"—"a¡\^V×S@U"aHaeXSÈZejdœsÏ_² Ì
[ZHaeUfY_—"jdœž `X@jdbkX4Ú"XZemÊ\RZZemnbd[]Ê\^]`X@a”bdjkjAX4Y_mn\"YnSXZemnXŸ_Yn–sX4aH[ŠZH\"Yn–sbdY_—WU^g
œfU"Ÿ_aaHX4\f–sX@a¡[cU"YhZem_bÍ[
SX4YfZHaH\"j‚ZeUf]_bdS"²ã¥m_X@aHXgiUfaeXfoObÑZ ”bdjkj1m_X@jd];Zem_X4V×ZeUTVT\"l"X”bd[eX@a –sXSbÍ[ŠbdU"YÊ[bkY;Zemnbd[ \"aeX\_os\^YʖžZHmQŸÊ[
bkYÊSaHX4\"[eXZem_X4bka]naeUs–sŸnSZebdÚObÑZœf² Ì ”cU"Ÿ_j͖h ÊXmn\"]_]OœTZeUT[eX@XZemnX]n\^]`X@a ]nŸ_ _jdbd[em_X4–;bdY(¢.bdX£c\"[ŠZebdY_—
¤ãY_—fbkYnX@X@a²
.[œfU"ŸhlQYnUR” Ì \"V F@X\^jdU"Ÿn[™giUfaZem_X–sbdXS@\f[ZHbkY_—WbdYn–sŸn[ŠZeaHœ"² Ì \^VC–_U"bdY_—VœMŸsZHVWUf[ŠZcZHUW]_aeUfVWU^ZeX
Zem_XlOY_UR”jdX4–_—"X\^Yn–h]_aHU^Ð_Z¡\^ _bdjdbÑZœžU"g1ZHm_X–sbdXS@\"[ŠZebdY_—WbdYn–sŸn[ŠZeaHœ"² Ì –sUTY_U^Z \"]ÊUfjkUf—"b F@X?giU"a.–sUfbkYn—
[ŠUʲã¥m_Xm_bÍ[ZHU"aHœžU^gU"Ÿ_a S@U"aHaeX[Š]`U"Yn–_X@YnS@X?VT\^lfX4[bkZ jkUOUflM\"[cbkg6œfU"ŸhaeX@giŸn[ŠXZHUW]_Ÿ_ _jdbd[embkVW]`U"aeZH\"YfZ
bkY_giU"aHVW\^ZebdU"Y\^ `U"ŸsZZHm_XSaHbkZebÍS@\^jA[ejdUR”u]_jdŸ_Y_—"X4aÚ"X4jkUsSbkZœ"²ã¥mnXmnbd[ŠZeUfaeœM[em_UR” [™ZemÊ\RZ œ"UfŸhjdUf[ŠZZem_bÍ[
]n\^]`X@a”mnX@Y Ì Ðna¡[ŠZX@YQZbkZZeUWœ"UfŸhbd@Y .Ÿ_—"ŸÊ[Zon\^Yn–;\^jÍ[eUjdUf[ŠZbÑZ ”m_X4Y Ì aHX4[eŸ_ _VWbÑZeZeX–MbkZ bkY;X4\"aejdœ
¢.XSX4V# `X@a²ã¥m_bd[4on\"Yn–žZHm_Xgª\"SZZemn\^Z Ì mn\f–;Y_U^Zm_X\^a¡–žgiaHU"VŜ"U"Ÿh Oœ _X4 _aHŸn\^aHœ(®"o§®¯"¯"°nos\^Yn–
U^ZHm_X@abdYsgiU"aHVT\RZHbkUfYAos]_aHU"VW]sZeX–;V)XZHUT[ŠX4Yn–hZem_XX4VW\"bkj Ì [eX@YQZ4² Ì \^VC[eŸ_aHX?ZHmn\RZ bkg6œ"U"Ÿ;”cX@aHXbdY
V#œM[em_UOX4[™œ"UfŸM”cU"Ÿ_j͖žmÊ\•Ú"X?–_U"Y_X?Zem_X[H\^VWX"²$©(œM]_Ÿ_aH]ÊUQ[ŠX?”c\f[™YnU^ZcZeUWbkYÊ[ŠŸ_jkZH[\"YQœfU"Y_Xf²© œžU"Y_jdœ




4<QXU MT587 ZX29x• ” v

W ib

T vtW<M `5

’*=5Es-“367E5

–— ˜A™0— ˜<š ›0œqž6Ÿ" j›G #¡› ŸP¢Y—£¥¤¦Fž ›Y¢
¦T§ ›`¨B!Ÿ\œqž#™.!¦6˜:œG©N¤6ª ˜<«!£ ˜ŸK£ ¢: `©

¬:®­

\^bdV×bÍ[ZeUW]_aHU"VWU"ZeXZem_X–_bkXS4\"[ŠZebdY_—WbkYn–_Ÿn[ZHaeœžZeUWZemnX ÊX[Z U"g
V#œ;\^ _bdjdbÑZœf² Ì  `X@jdbkX4Ú"XZemn\^ZZem_UQ[ŠX
”m_UT–sUTY_U"Z \^—"aHX@X”bkZem]_aHU"VWU^ZHbkY_—WlOY_UR”jdX4–s—fX?bdY(–sbdXS@\"[ŠZebdY_—W[ŠmnU"Ÿ_j͖;Y_U^Z `XbkYOÚ"UfjkÚfX4–hbkY–sbdX
S@\f[ZHbkYn—n² Ì [ŠZeaHU"Yn—"jdœT ÊX4jkbdX@ÚfX?ZHmn\RZZHm_XX4–_bÑZHU"aU^g  ?¢£ ÁVW\"—fA\ F@bdY_X)¨ ¢.bdX£c\"[ŠZebdY_—T¤ãYn—"bdY_X@X4a¡±
[em_U"Ÿ_j͖h ÊXbdYQZeX@aHX4[ŠZeX–;bkY\^aeZebÍSjdX4[cZHUT]_aeUfVWU^ZeXlOY_UR”jdX4–s—fX"² “ Unosbkg6œ"U"ŸhÐnYn–hZHmn\RZ VœM\^aeZebÍSjdXbd[ \
SUfYQZeaHbk _Ÿ_ZebdU"YhZeU)Zem_bÍ[lOY_UR”jdX4–s—fX"oOZHm_X\^aeZebÍSjdX[Šm_UfŸ_j͖M `X]_Ÿ_ _jdbÍ[Šm_X–§²
Ì –sUWY_U^ZZ¡\^l"X]`X@a¡[ŠUfYn\^j§bdYn[eŸ_jÑZ.\"Yn– Ì ”bdjkj1 ÊX—fjd\f–žZHUW\"jkjdUR”„œfU"ŸhZeUW]_Ÿ_ njkbÍ[Šm;ZHm_bd[ ]n\^]`X@abdY(¢.bdX
£c\"[ŠZebdY_—T¤ãYn—"bdY_X@X4a4² Ì  `X@jdbdX@Ú"XZHmn\RZZHm_XVT\^—fA\ F@bdY_Xbd[\"Y(\^]_]_aHU"]naebÍ\RZHX.]_jÍ\"S@XgiU"aZemnbd[ \"aŠZHbdS@jkXf²$¥1U
\"S¡mnbkX4Ú"X?Zem_bÍ[]_Ÿ_ njkbÍS@\^ZebdU"YAo Ì ”bkjdjAm_X4jk]œfU"Ÿ;bkY(\^YOœž”\•œ Ì S@\^Y1²6¥mnX]n\^]`X@a”\"[”aHbÑZeZeX4YhŸn[ebdY_—
\^jd¥ j‚¤ ZemnXon\"ÐnYnjkX–ž[@² ZHm_Ì X”—"bdjka¡j1\^\"]njdm_[ebdUWS4[SU"\^YOaHÚfX?X@bdaeYZ™]ÊZHm_UQX[Z¡Ðn[eS@jdXaebd]sZeUWZÐnÓ jdX4Uf[4aH² – “ nm_² UfaŠ² ZHÌjkœf\^o VÌ ”\Rbdgijka¡j
\^[Šb͖TX4YnZe–MmÊ\RœfZ.U"ŸSUf\WYOÚ"–sX@bda¡[H[eSbkUfSYMUfYQ”ZH\^bdjkbdj Y_bdY_—
aHX4ÙQŸ_bdaeXaHXZœO]_bdY_—U"g6\"jkj‚ZHm_XX4ÙQŸn\^ZebdU"Yn[4² .[œfU"Ÿ;lOY_UR” oOÓ   ¢Á]_aeUs–sŸÊSX4[jdUR”¶ÙQŸn\"jkbkZœM[eXZHŸ_]
\^YʖžaHX4ÙQŸ_bdaeX[™[eU"VWX?ZebdV)Xf²$Ó UfŸ_j͖MœfU"Ÿž]_aHXgiX4acZeU)mn\•Ú"X?Zem_X—"a¡\^]nm_bdS.ÐnjdX4[™ZeU) `XbdY¥ Ì   giUfaeVT\^Z¡Ö
U"a \"Y_U^ZHm_X@acgiUfaeVT\RZÈÖ Ì mÊ\•Ú"XX@Y_mÊ\^YnS@X4–MZem_XS4\^jÍSŸ_jÍ\RZHbkUfYn[aeX[ŠUfjkŸ_ZebdU"Yh\"Yn–;]_jdX4\"[eX ÊX\f–sÚObd[eX4–
ZemÊ\RZ Ì mn\•Ú"XS¡mn\^Yn—"X4–;[ejkbd—"mQZejdœTZHm_X—"a¡\^]_mnbdS4[c\"Yn–MZeXÛOZ²
¥mn\"Y_lžœ"UfŸMgiUfaœ"UfŸ_a\"[H[ŠbÍ[Z¡\^YnS@X"²
“ bdYnSX4aeX4jkœfo
¢?a4² X4Y_bdS¡lhØc\"a  ©(X4bka









Y'
+ ""[+t+ ,


T–T ÏS
JU QbcF T



 #

#v T

T–T

T

… 3 v -2=6H09A2Q\VZ\2G9_7ED9A26=9_;R9?=Z39A26=9j9A23@U=FU!35 hQXV He^-D= M0W!3&UFVTW 7 ;<23GH0=;`9A233GHa7 9RQ5k2=6H
U!5KQ "7 ;Y3GH
3=;?34<Q\DG9:7EDFV39RQ5K3G=6H@9RQ&;?3G3&2Q
9A23;:=ZT=(4 QXD9:7EDTV3 ;

"v

b







 r

¢?X4\^a $\"Ÿ_jAØcaH\"jkUR”cX@a
¥
U)VœM—faeX\RZ[ŠŸ_aH]_aHbd[eXœ"U"Ÿ–sb͖;Y_U^Z ]_Ÿn _jkbÍ[em;VœM\^aeZebÍSjdX\"[œfU"Ÿ;]_aeUfVWbd[eX4–§² ãUfŸ\"jd[eUW–sbd–;Y_U"Z
\^YÊ[Š”cX@aV#œM]_aeX4ÚObkUfŸn[jkX@ZŠZHX@a² Ì \"VC[ŠŸnaeXZemÊ\RZ œ"UfŸhmÊ\•Ú"X\—fUOUO–haHX4\"[eU"YÊ[ˆgiUfaY_U^Z.–_U"bdY_—T[ŠUʲ Ì
¦ Ÿn[ŠZ ”™UfŸ_j͖MjdbklfXZeUWlOY_UR”„”mÊ\RZbÑZ bÍ[4² —f\"bkY1os”™UfŸ_jd–;œfU"ŸM `X]_Ÿ_ njkbÍ[ŠmnbkY_—WZHm_X\^aeZebÍSjdXbkY;ZHm_XY_XÛOZ
bÍ[e[eŸ_XÖ \^YOœžU^ZHm_X@abÍ[H[ŠŸ_X•Ö;]_Ÿ_ _jdbÍ[Šm_X–\RZ.\^jdj Ö Ì YS4\"[eXZemn\^Z œ"U"Ÿ;bdYfZHX@Yn–hZHU)]nŸ_ _jdbd[em;Zem_X\"aŠZHbdS@jkXfo
S@\"Y Ì aHX4SX4bkÚfX\)]_aHX@]naebdYQZU Ì S4\^Y;]_aHUQU"g  aHX4\f–TZHm_X\^aeZebÍSjdX]_aebdU"acZHUWZem_X]_Ÿn _jkbÍS@\^ZebdU"YÊÖ
¥mn\"Y_lžœ"UfŸMgiUfaœ"UfŸ_aSU"YÊ[Šb͖sX@a¡\RZHbkUfYh\"Yn–\"[H[ŠbÍ[Z¡\^YnS@X
X@YnbdS¡l

d 23!DOS\ZQ!9`=; VT5‡U!587 ;?3(j 9A23&U!3!5K;?Q\DH3= T 7EDZ¥v 7 9A2zU3nvL=; 4!2=FDZ3HKb … 2GM!i¦o¹U=<MFW!3"M Q\VvF9A23
5K3G=6HT3!5>vX4 =FD(Z\V3G;?;Bv[26=9L9A23&5B3=;?Q\D@7 ;ªtAbŸSX4G=FDTDQ!9#7aU=Z7ED37 m 9A23 T 3<9>9R35#vL=;`=FDeQ!IJ3!5*9RQNWFVGMOU3
QXV9ŠbBS"¤YV;R9BvhQXD6HT3!5Ïv[2Mf23nvL=; 4 QXD64<3!5‡D3GH0=FW!QXV95U3&DQ9j;<VFW`U"7 9>9:7EDZgU!5KQXU!QT;Y= T ;%o8Q5*9A27 ;%U=9>9R3!5
Q/k
m ;<VFW`"U 7 9>9:7EDZOm Q5bUFVTW T 7 4 =9:7 Q\DtŠ`b n3= T Lv = M;15K3<9AVF5,D3GHf=fU!5KQJ(U U9[5K3 ; U!QXD;?319RQ#U MfU!5KQXU!QT;Y= T ;vM=F2
;<VF5K3(bw*
q QXV T HN23@U!Q;Y;q7EW T M02= £ 3;<V6HFH3D T M~Om Q\VTD6Hˆ#U Mf5K3 ;Y3G=5K4!29RQW!31;YQC7a(U U!Q5P9?=FD9Šb F T 3G=;?3@5K3G=6HN27 ;
T 3<9>9R35.v\=FDH@M Q\V4 =FDHT3G47 H3%Om Q5*M Q\VT5K;?3 T m¹b
n3!5K3e7 ;“f5ibØF
y 9R3A£ 3 H]6£ =!5lH!MC5B3G;<U!QXD;?3"Q\DO§ 5O7Bv _} U!5  r
X@YnbdS¡l‚o



Ì nm \•Ú"XjkX@g Z Ú"UfbdS@XVT\"bkj‚giUfaœ"U"Ÿ1² Ì ”bÍ[Šm;ZeUT[e]ÊX\^lž”bkZemœfU"Ÿ\^ `U"ŸsZ ”mn\^Z \^]_]`X4\"aH[cZHU) `X
Y_UfY ,[eŸ_ _VWbkZŠZ¡\^j§U^g6œ"UfŸ_a]_aHU"]`Uf[H\^j Ì bdYn[ŠZeaHŸnSÈZHX4–;œ"UfŸMZHU)giU"aH”c\"aH–žZeUh£c© £»giU"aZemnXT®4¯"¯f¯S4\^jdj ²
Ì S@\^Y\^Yʖh[em_U"Ÿnjd–\^jÍ[eUaHX4[e]ÊUfYn–MZeUWZemnXÙfŸnX4[ŠZebdU"Yn[œfU"Ÿh\"aeX]`Uf[ebkY ¦ —ZHU $\^Ÿ_j ²
Ì S@\^Y; `XaeX\"S¡m_X–ž OœM]_mnU"Y_X\RZ _®4¯_² ^°f°_²
s²


ç

–— ˜A™&— ˜Aš ›fœ:Tž6Ÿ j›G #¡› ŸP¢Y—£¥¤¦Fž ›Y¢
¦T§ ›j¨B6Ÿdœqž#™.!¦6˜:œG©g¤6ª ˜<«!£ ˜ŸK£ ¢.›A©



4 QXU<MF587 ZX29x• ” v

’ ib

T vtW<M `5 _’*=5Es-“367E5

Chapter B. My Relationship with Die Casting Establishment

¥mn\^YnlMœ"UfŸAo
“ ZeX4Ú"X ?–sÚR\^a¡–sœ

y\7ED64<319A23HT3G=6H T 7ED3nmOQ5J9A2=9U!5KQXU!Q;:= T 26=6HCU6=;?;Y3GH T QXDZgW!3AmOQ5K3TvÏSMvhQXD6HT3!5K3GHf7 mm9A23!5K3%vL=;`=FDM0U!Q7ED9
7ED;<VFW`"
U 7 9>9:7EDZ&=FDMfU!5KQXU!Q;:= T b 15LU!3!5‡26=FU;`9A23!5K31vh3!5K313<ˆ64 3!U9:7 QXD;`9RQgW!3kU1=6H37EDzU#Me4G=;?3iŒ{nQtv\7 9
4<Q\V T H\DMh 9[W!3‚\
S =`p
U ;<VF5B3"9A26=9[231Lv =;˜Om Q T–T Q"v 7EDZe9A23"3Aˆ!=64A91U!5KQa4<3GH\VF5B3`bØyQtvÏSa9A23!D(;Y3!D91“C5cb
 H]£ =5lH!M(9A231Om Q T–T Q"#v 7EDZ T 3<9>9R35cb
} U5O7 T r\v   r
_
 †(F(
… …9œ Bf(F]…if\L ‚
¥mn\^YnlMœ"UfŸMÚfX@aHœžV#ŸnS¡mhgiU"aœfU"Ÿ_a]naeUfV)]_ZaHX4[e]`U"Yn[eXU"YhZem_X `X@mn\"jÑg6U^g $\^Ÿ_jAØca¡\^jdUR”™X4a4²
.[œfU"Ÿ;lOY_UR”o Ì \"V×ZeaHœObkYn—ZHUW]_Ÿ_ _jdbd[em;Zem_X\"aŠZHbdS@jkXUfYMZHm_X] ^ –sbd\"—"a¡\^V² Ì \"VC[ŠŸnaeXZemÊ\RZ œ"UfŸ
\^aHX\•”c\"aeX.Zemn\^ZZem_bÍ[bÍ[e[eŸ_Xbd[.SX@YQZHaH\"j‚ZeUT–sbdXS@\"[ŠZebdY_—WX@Yn—"bdY_X@X4aH[4² € `XZeZeX4a.–sX4[ebd—"Y\^Yn–\
[Šbd—"YnbÑÐÊS4\^YQZaeX–sŸnSZebdU"Y;U^g$SUf[ŠZ”™UfŸ_j͖MaHX4[eŸ_jkZcgiaHU"VÅbkVW]_jdX@VWX4YfZ¡\RZHbkUfYhU"g
ZHm_X]_aHU"]`X@a]g^


s– bÍ\^—"a¡\^V×S4\^jÍSŸ_jÍ\RZHbkUfYn[4²
.[ \)]`X@a¡[ŠUfYh”mnU)mÊ\"[–sX–sbdS4\RZHX4–hZem_XjÍ\"[ŠZ® œ"X\^a¡[cU^g
mnbd[jdbkgiXZeUTbdV)]naeURÚfX.ZHm_X–sbdXS4\"[ŠZebdY_—
bkYʖsŸn[ŠZeaHœ"on\"Yn–h\f[U"Y_X”mnU)mÊ\"[cZebdX4–;m_bÍ[jdbÑgiXZHU)Zem_X[eŸnS@S@X4[H[U^g
Zem_X–sbdXS@\f[ZHbkYn—)bdYn–sŸÊ[ZHaeœfo Ì
[ZHaeUfY_—"jdœT `X@jdbkX4Ú"X?Zemn\^ZcZHm_bÍ[\^aeZebÍSjdX[em_U"Ÿnjd–h ÊX]_Ÿn _jkbÍ[em_X4–§² .Yn–h”mn\RZ `XZŠZHX@a]_jÍ\"[email protected]]_Ÿ_ _jdbd[em;bÑZ
Zemn\"Y»Îe¢?bkX£c\f[ZHbkY_—W¤ãYn—"bdY_X@X4aHÏQÖ
Ì mÊ\•Ú"X]_jkX\"–sX–;”bÑZHm;X4Ú"X4aeœfU"Y_X.ZeUTm_X4jk]VWX]_Ÿ_ _jdbÍ[Šm;Zemnbd[ \"aŠZHbdS@jkXf² Ì m_Uf]ÊXZHmn\RZ œfU"Ÿ;”bkjdj1\^—faeX4X
”bÑZHmV)XZHmn\RZZHm_bÍ[ \^aeZebÍSjdX[Šm_UfŸ_j͖M `X]_Ÿ_ _jdbÍ[Šm_X–§² Ì g6œ"UfŸM”cU"Ÿ_j͖;jkbdl"Xfo Ì S4\^Y;XÛs]_jÍ\^bdYMgiŸ_aeZemnX@a
”mOœ Ì ZHm_bdY_lžZHmn\RZZHm_bd[.\^aeZebÍSjdXbÍ[bdVW]ÊUfaŠZ¡\^YQZ4²
Ì \"V×Ú"X4aeœM—"jÍ\"–MZemn\^ZZem_X4aeX\^aHXSUfV)]Ê\^Y_bdX4[c”m_Už\"aeX\"–sUf]sZebdY_—)Zemnbd[ZHX4S¡m_YnU"jdU"—"œf² Ì ¦ Ÿn[ŠZ ”bd[em
Zemn\^ZZem_X”mnU"jdXbdYn–sŸÊ[ZHaeœh”™UfŸ_jd–;–sU)ZemnX[e\"V)Xf²
—Q\^bdYAosZemÊ\^Y_lžœfU"ŸhgiU"aœfU"Ÿ_alObkYʖhjdXZeZeX4a4²
X@Y_bÍS¡l
‹MR6‚ Ì ”bdjkjA `XbdY;VœMU TS@X¥1Ÿ_X[e–n\•œT ÊX@Z”™X4X@Y(¯ ¡®"®\^VCS@X@YQZea¡\^j‚ZHbkVWXž¨ _® f±
R°R˜ "¯


S =`p
\
U ;<VF5B319A26=91“C5cb n H/6£ =!5lHMeH7 HNDQ!9[5B34<37 £ 3"9A23"4 QJUgU 3!D9R;jQ]‡m  >m 5KQJ€
U 9A23@5K3AmO3!5K3 3G;~o8;Y3 31}_UTU!3DHa7 ˆ
}wtAbž}_D6Hg7 m`23Ha7 HtvÏSt=`Up; VT5K319A2=9`9A23<MeHa7 HNDQ9`HTQN2= £3(=FDGM(3 Id34A9_QXD027aU v[26=9R;?Q3A£3!5ib … 2M
;<2QXV T H@7 9 26= £ 3=FDGM"3<IJ3G4<9hQXD27a1
U iˆ_} DMT2Q"1v vKSŠY¤ V;R9k9A2!7ED`¬ 9A26=9 23eLv =;Ø£ 35PM&WFV;?Mnv#7 9A2Q!9A23!5t9A2!7EDZ;
;?QN23(H7 HNDQ!92= £ 33!DQXVZX2"9:7a[
U 319RQ5K3 ;<U!Q\DH@9RQˆ#U M T 3<9>9R3!5ibØy Q-S 26=6H@9RQ&;?3!D6H27aUp=FDQ!9A23!5 T 3 9>9R3!5ib
ä  ä   r


 F(……9œBf(F]…ifL\‚
Ì \"(† C
V \"[ŠZeUfY_bÍ[Šm_X–žZHmn\RZ œfU"Ÿ–sUWY_U^ZÐÊYn–hZebdV)XZHUT\^Yn[e”™X4aV#œžjdXZeZeX4a.–_\RZHX4– “ Ÿ_Yn–n\•œ"o ]naebdj o  
®4¯f¯"°;¨i]_jdX4\f[ŠX[eX@X ÊX4jkUR”€SUf]OœTU^gZemn\^Z jkX@ZŠZeX4a¡±² Ì \"VהaHbÑZHbkY_—WœfU"ŸhZeUTjdXZœ"UfŸMZHmn\RZZHm_X@aHXbd[\
[ŠX4aebdU"ŸÊ[–_\^Y_—fX@abdYS@U"YQZebdYOŸ_XZeU)ZeX\"S¡mhZem_XS@U"VWVWU"Y_jdœžŸn[eX4–;]g^u–sbÍ\^—faH\"V;² .[ œ"U"Ÿh]_aHU" n\" _jkœ
lOY_UR”¿¨ªbÑg$œ"UfŸh–sUTYnU^ZlOY_UR”os]_jdX4\"[eXS¡m_X4S¡lMU"ŸsZ Ì  Ì Ò [ ”™X4 ;[ebÑZHX”””² –_bkX4]ÊX4aŠgiXSÈZ4² SUfVž±ÈosZHm_X
SUfV)VWUfY_jkœMŸn[ŠX–;]  ^ –sbÍ\^—faH\"VC\"[cbkZ.\^]_]`X4\"aH[bdHY  ?¢£ #Ò [ `UOU"ls[ÚObkUfjd\^ZeX[cZem_XÐna¡[ŠZ\"Yn–hZem_X
[ŠXSUfYn–MjÍ\•” [U^gZemnX@aHV)Us–sœOYn\"VWbdS4[@os `X4[ebd–_X4[YOŸ_VWX@aHU"Ÿn[U"Zem_X4a SUfV)VWUfY;[eX@Yn[eXZem_bdY_—Q[@² Ì g
 ?¢£ €ZHX4\fS¡m_X4[cZHm_bd[ VW\^ZeX4aebÍ\^j o  ?¢£ ~S@U"Ÿ_j͖; ÊXjdbd\" _jdX?giUfaÚ"X4aeœžjÍ\^aH—"X[eŸ_VT[U^g6V)UfY_X@œžZeU
Zem_X[ŠZeŸÊ–sX@YQZH[”mnU)mÊ\•Ú"X?ZH\^lfX@YhZem_X[ŠXS@U"Ÿ_a¡[ŠX[@² .[\ .¢£ ~VWX@V# `X@ao Ì [ŠZeaHU"Yn—"jdœTaeXSU"VWVWX@Yʖ
Zemn\^ZZem_X[ŠXS@jd\f[e[eX4[c `X[ŠŸÊ[Š]`X@Yn–_X4–;Ÿ_YQZebdj§ZemnXbkYn[ŠZeaHŸnSZeU"a¡[jdX4\^aHYžZHm_XSUfaeaHX4SZc]naeUsSX–sŸ_aHX4[4² Ì on\"[\



4<QXU MT587 ZX29x• ” v

W ib

T vtW<M `5

’*=5Es-“367E5

–— ˜A™0— ˜<š ›0œqž6Ÿ" j›G #¡› ŸP¢Y—£¥¤¦Fž ›Y¢
¦T§ ›`¨B!Ÿ\œqž#™.!¦6˜:œG©N¤6ª ˜<«!£ ˜ŸK£ ¢: `©

¬:®®

 ?¢£ ÁV)X4V# `X@aos”bkjdjAY_U"Z jkbdl"XZHUW[eX@X
.¢£ ~lOY_UR”bdY_—"jdœWZeX\"S¡m_bdY_—)Zem_X”aHU"Yn—VT\RZHX@aHbd\"j
\^YʖMVWU"aHX@URÚfX@ac ÊX4bkYn—ž[ŠŸ_X–hgiU"a –sUfbkY_—T[eUn²
Ì giX@X@jAZemn\^ZbkZ bÍ[ [ZHaH\"Y_—"X?ZemÊ\RZ ? ¢£ Â
–sbd–;Y_U"Z ]_Ÿ_ _jdbÍ[Šm;ZemnXbkYsgiUfaeVT\^ZebdU"Yh\" ÊUfŸsZZemnXSaHbÑZHbdS4\^j
[ejkUR”u]njkŸ_Yn—"X@aÚfX@jdUOS@bÑZœž\"Yn–MZem_X] ^ –_bd\"—"a¡\^V \^Yn–Mm_UR”uZHU)–_UZHm_X@VÅSU"aHaHX4SÈZHjkœf² Ì \^VC[eŸ_aHX.ZHmn\RZ
? ¢£ Á
V)X4V# `X@a¡[”bkjdjA `X@Y_X@Ð_ZgiaHU"VÅ[eŸnS¡m;lOY_UR”jkX–s—"Xf² Ì \^jÍ[eUÐÊYn–;bÑZ  `X@œfU"Yn–h _b 4F \^aHaHX.ZHmn\RZ
? ¢£ Â
–sUOX4[Y_U"Z ”c\"YfZZHUWS@UOU"]`X@a¡\RZeX”bkZem;ZemnUf[eX”mnU)VT\f–sXZem_XVWUQ[Z]_aHU"—faeX[e[™bkY;ZHm_X
Ÿ_Yn–_X@a¡[Z¡\^Yn–sbdY_—T–sbdXS@\"[ŠZebdY_—W]_aHUsSX4[H[4²ØcŸsZ bkg . ¢£ ´
ZeX\"S¡m_bdY_—)Zem_X”aHU"Yn—VWUs–sX@jÍ[VWbk—fmQZX4Yn–_[

Ÿ_] `X@bdY_—ž[ŠŸnbdS@bd–_\"jA\^Yn– Ì ”™UfŸ_jd–hjdbklfX?ZHUžS¡mn\^Yn—"X?Zemn\^Z bÑg Ì S4\^YA²
¥mn\"Y_lžœ"UfŸMgiUfaœ"UfŸ_a\RZŠZHX@YQZebdU"Y1osZebdVWX"on\"Yn–;Ÿ_Yn–sX4aH[ŠZH\"Yn–sbdY_—
“ bdYnSX4aeX4jkœfo_¢.a² X@YnbdS¡lMØ\"a ©(X@bda
‹MR6‚ X@aHXbÍ[V#œM]naeX4ÚQbdU"ŸÊ[™jdXZeZeX4a4²

"v S
¬"tAb

(b

{nQ
\ZQ!9_=05K3 ; U!QXD;?3
‘ !
3 D7 4

`b

1m EU T OoY`5L’*=5ÜlA“e37E5m=;

26=9_=eH7 IJ3!5K3!D9j9RQ\D3 _{ Q9R319A23 OQ5 = 7 9‡M
…

“e= M

†`F]…  … wF]… Œ†M•š…



QXUFU!Q;Y3[9RQ

 v   r




ãX4[4o Ì \^VCmnX@aHX"² Ì ”\"[cUfY;ÚR\fS@\RZHbkUfYh\"Yn–hZeaHbkX–žZHUžSU"YQZ¡\"SÈZœfU"Ÿ; QœM]_m_U"YnX `XgiUfaeX Ì jkX@g Z giU"a
ÚR\"S4\RZebdU"Y1²6¢?Ÿ_aHbkYn—) nŸn[ŠbdY_X[e[™Zea¡\•Ú"X4j o Ì ”c\f[c[eU"aHaHœZHUWY_U^Z `X\^ _jdX.ZHUTS@\^jdjA–sŸ_aHbdY_—#ZHm_XZebdVWX]ÊX4aebdUs–
œ"UfŸhbdYn–sbÍS@\^ZeX–§²
.[ $\^Ÿ_j‚VT\•œžmn\•ÚfXVWX4YfZHbkUfY_X4–Aos”™Xmn\•ÚfX\"]_]_aHURÚ"X–M\^YʖM”bdjkj1 ÊX]_Ÿn _jkbÍ[em_bkYn—Tœ"U"Ÿna\"aŠZHbdS@jkXUfY
S@\"jdS@Ÿ_jÍ\RZebdY_—   _²¥mnX ÊX[ZÐ_ZgiUfaZem_bÍ[bÍ[\^YŸ_]‚SUfV)bdY_—WbÍ[e[eŸ_X–sX–sbdS4\RZHX4–MZeUT]_aHUsSX4[H[SUfYfZHaeUfj ²
ãjdX4\f[ŠXaHX4[ŠZ\f[e[eŸ_aHX4–MZemn\^Z bÑZ ”bdjdjA[Šm_UR”¶Ÿ_]bkY;ZHm_bd[.\^]_]_aHU"]naebÍ\RZHX?bÍ[e[eŸ_XU^g$¢£c¤ÃVT\"—f\ F4bkYnX"²
“ bdYnSXZHm_X@aHXmn\"[ `X@X4Y(SU"VWVŸ_Y_bÍS@\RZHbkUfYn[™giaeUfVל"UfŸMZHU $\^Ÿ_jA\"Yn–MVœs[ŠX4jÑg6\^Yn–;[ŠUfVWXU"g
ZHm_XbÍ[e[eŸ_X4[
\^aHX[ŠŸn n[ŠXÙQŸ_X@YQZejdœž]_aHX4[eX@YQZHX4–MZeUWU"Ÿ_a ¤ãÛsX4SŸ_ZebdÚ"X .bÍSX ãaHX4[eb͖sX@YQZ4o_¢\^Y(¥”\^aHU"—ÊoflObdYn–sjdœh–sbdaeXSÈZ
\^jdj‚giŸsZHŸ_aeXS@U"VWV#ŸnY_bdS4\RZHbkUfYn[cZeUWm_bdV²ˆ¥m_bÍ[”bkjdj1\"[H[ebd[ŠZbkYl"X4X@]_bdY_—Wm_bdV×ZHbkX–hbdYhZem_XjdUOU"](\^Yn–
\"[H[ebd[ŠZbkY—"X@ZŠZHbkY_—WaHX4[e]ÊUfYn[eX4[c n\"S¡lžZeUWœ"UfŸA² bÍ[ X ,VT\^bdjA\"–_–saHX4[H[bÍ[¥”c\"aeUf— –sbdX4S4\"[ŠZebdY_—n² U"aH—n²
¥mn\"Y_lžœ"UfŸAo
“ ZHX@Ú"X ?–sÚR\^a¡–sœ

ib  ]£

Øv

JUgU

_v kU v eU v ˆ{ £
T ]m
T JU 1v V
T "XKb˜S
T ¥v
T
]m kU
(b
S-26= £3"; VTW`U"7 9>9R3GH&Q9A235hU!5KQXU!QT;Y= T ;j9RQ{¨}_wq##} vJWFVG915B3= T–T M0D3Š£35h5K3G4<367 £3Hf=C5B3U T M-b “@= MTW!37 9[7 ;<DHh 9
3AˆU!3G4<9R3GH&9RQNW!3&5K3!U T 7 3GH@9RQi 5LU!35,26=FU;[7 9¡¤YV;R9`ZQ!9:"L
v =; T QT;R9Yi

2GMHTQ3 ;“C5
H =5KHM&DQ9 L=FD9b9RQ@4 Q (VFD7 4 =9R3 #7 9A2 [31=FD6H L=FDG9 3[9RQ [587 9R3[9RQ Tˆ346V9:7 3
7
<
4
3
K
5

3
q
;
7
T
H
!
3

D
Y
9
i
Š
… 2GM&H7 H@9A23<Me4!2=FDZ39A23"9:7 9 31Q 9A23=!5B9:7 4 3=FD6H&Q "7 9j9A23 hQ5lH >4 Q5,5K3G4<9 M
= ;?Q hQ\DHT3!5*=FW!QXV9`9A23 Qa4 =9:7 Q\D7ED9A23"3!D6H0Q m9A23 =ZT=Ž7ED3
…

TF

$@"/



,_+t+-"}+-

[

Œ/

SPD(9A2!7 ;_;Y3G4A9:7 Q\D(=FDQXU!3D T 3<9>9R3!5m9RQ 63GQ’*=!5l=FD&7 ;1U!5K3 ;?3DG9R3HKb_“C5cb_’*=5l=FDZT= £3=fU!5K3 ;Y3!D9?=9:7 QXDe7ED
“07EDTD3G=FU!Q T 7 ;jQ\DC“e= M tv   vFQXDpV>§VG9AVF5K31dn5K3!D6HT;_=FD6H’qbVT5‡5K3!D9F 5BQA¤‡34A9R;YX9RQ V.;Y3 T–T XN{¨}_wq‚}†9RQ
7 9R;%[
U 3/U W!3!5K;-b} 9j9A23(4<Q\D4 T V;A7 QXD"Q/m`2!7 ;1U!5K3 ;Y3!D9?=9:7 QXDavKSt=;A¬A3GHg27aU v2GM@7 mn9A23;q7 9AV6=9:7 QXDe7 ;_;?QN5BQT;RM
=;23eU!5K3 ;?3DG9R3Htv9A26=9L;?Q’
U =FDM4 QJ(U U6=FD7 3 ;j=5K3ZTQ7EDZ0W=FD`!¬ 5‡VTU9L=FD6He;YQ T HQbBtS U5BQa4<3G3GHT3GH9RQ@=;Š(¬ 27aU
v[2Mg{¨}_wq#‹} 7 ;`9R3G=64!2!7EDZ&;?QˆU =FDM(3!5‡5BQ\D3GQXV;%[U QaH3 T ;-_b n3ZT= £ 3U 3&“C5ibØFy 9R3A£ 3 H]£ =5lH!MHh ;




ä



–— ˜A™&— ˜Aš ›fœ:Tž6Ÿ j›G #¡› ŸP¢Y—£¥¤¦Fž ›Y¢
¦T§ ›j¨B6Ÿdœqž#™.!¦6˜:œG©g¤6ª ˜<«!£ ˜ŸK£ ¢.›A©



4 QXU<MF587 ZX29x• ” v

’ ib

T vtW<M `5 _’*=5Es-“367E5

Chapter B. My Relationship with Die Casting Establishment

T ˆU

ˆ¬ "v T
¥m ØU G

/m

‚¤

WTV;q7ED3 ;Y;`4G=!5lH0=FD6H@9RQ H [319A26=9[23e26=;DQ !DQ 3HZT3[Q 9A2!7 ;_=FD6H@9A2=9`;q7ED64<3@234G=FDTDQ!9 :VHTZ3(7 9 v
23(4G=FDTDQ!9_H7 ;:46V;?;#7 9 … =;12 3&U5B3U=5B3H OQ5 #M \V3 ;R9:7 Q\D;`Q5 L=;`9A2!7 ; [35B3 Me=e;<U!QXD9?=FD3 QXV;
5B3=64A9:7 Q\D6i

Šb

‚v

%U T

.¢ X\^a ©(a²ãØ\^a¡\^YAo
¢.UWœfU"ŸhS4\^aHaeœ “ ZeX@ÚfX ?–sÚR\^a¡–sœ‚Ò [ nŸn[ŠbdY_X[e[S@\"aH–h\^jdj‚Zem_XZHbkVWXÖ(Ó¸mQœ_ÖÓ¸mOœM–_U)œfU"ŸhY_U^ZZemnbkY_lMbÑZ
bkVW]`U"aeZH\"YfZZHUT–sbd[HSŸÊ[e[”mOœM[eUWVW\"YOœM–sbdXS@\"[ŠZebdY_—TSUfVW]n\^Y_bdX4[—fU Ê\^Y_lOaHŸ_]sZ.\^Yʖh\"aeX[eU"j͖nÖ Ì [bkZ
Y_U^Z bdVW]ÊUfaŠZ¡\^YQZgiU"aŸn[ZeUT–sbÍ[eS@Ÿn[e[”mOœMZem_X4aeX\^aHX[ŠUWVT\^YOœTÐÊYn\^YnS@bd\"j§]_aHU" _jdX@VT[bdYMZHm_X–sbdX
S@\f[ZHbkY_—WbdYn–sŸn[ŠZeaHœ_Ö(¢?U"YAÒ Z œ"UfŸh”\^YQZZeUWVT\^lfX–_bkXS4\"[ŠZebdY_—TSU"VW]n\"Y_bdX4[cVWU"aHX]naeU"Ð_ZH\" _jkX• Ö Yn–bkg
[ŠUfVWX@U"YnX?ZHX@jdjd[ œ"U"ŸMZemn\^ZZem_XaHX4[eX4\"aHS¡m;[Š]`U"YÊ[ŠUfaeX–ž Oœ  ?¢£ Ábd[aHŸ_ _ nbd[emAo_\^aHX@Y1Ò Zœ"UfŸh—fU"bdY_—)ZeU
S¡m_X4S¡lMbÑZÈÖ(¢.bÍ[HSŸn[H[bkZ ”bÑZHm;U"Zem_X4aH[bdHY  ?¢£ Ö#¢?U"YAÒ Z œ"UfŸ;S4\^aHX?”mnXZemnX@a .¢£ ´ZeX4\fS¡m_X4[
”aeUfY_—)Zem_bdY_—Q[HÖ ?abÍ[bkZZemn\^Z œ"U"Ÿ ¦ Ÿn[ŠZ.–sU"Y1Ò Z —fbkÚfX\W–_\"V)Y`Ö
Ì \"VC[eŸ_aeXZHmn\RZ bkZ bd[ bkVW]`U"aeZH\^YQZgiU"aœfU"ŸA² ãUfŸS@jd\"bkVWX–žZHmn\RZ bkZ bd[ bkVW]`U"aeZH\^YQZgiU"aœfU"Ÿ;bkY;ZHm_X
]_aHX4[eX@YQZH\^ZebdU"YA² “ UÊos]ÊX4aemn\"]n[œ"UfŸ;S4\^aHXZeUW”aebkZeX\"YhX@Ûs]_jd\"Yn\RZHbkUfYhbdY;Zem_XYnXÛOIZ  .¢£
VT\^—fA\ F@bdY_X"² Ì ”™UfŸ_j͖MjdURÚ"X?ZeUTaHX4\f–žbkZ4²
“ bdYnSX4aeX4jkœfo
X@Y_bÍS¡lhØ\"a˜s©(X@bda
Y'

),+



  je)Y/_),Ž"/+J 




S-26=6H04<QXD £7ED4 3GH !=5,5BM … 7ED(¬ T 35k7EDzU"7 H   sOoÂv23Df23nvL=;_;?9:7 T–T vhQ5E¬7EDZ[mOQ5jk=!5B9RŽ<3 T–T t<v9RQ0=;A¬
“f5ib  H]6
£ =!5lH!M[[v 2Mg{¨}_wq‚}}4<Q\DG9:7EDFV3H&;<VFUTU!Q5B9wmOQ5-9A231v[5KQXDZ’U[QaH3 T ;%o89R3G=64!2!7EDZ@9A23"3!5‡5KQXD3 QXV;
‘ =!5‡W!3!5ih ;~[
U QaH3 T =FD6H¥m>V3 T 7EDZˆU=;Y;q7 £3"ZX5l=FDG9R;`9RQ 27 QOyF9?=9R3 hD7 £35B;A7 9,M/tAb n31vh3!D9L9RQS{¨}_wq#}
=FDH09?= T q¬ 3He9RQ“C5ib  H]£ =5KHMe=FW!Q\VG9`9A2!7 ; b¨}lm 9R3!5L234 =`[
U 3@W6=64T¬ vd233AˆU T =7ED3H@9A2=9j9A23 M(9RQ T HN27aU
9A2=91X
S Ha7 HXDHh 9 =FUFU!5BQF=6462f{¨}_wq‚} 7ED9A23@5O7 Z\2G9BLv =<M b˜oC[v 26=9 7 ;_9A26=9Yi"gt h7 ;_3!D9A2FV;A7 =;A€
U 9A23D
3A6
£ =FU!Q5K=9R3Htv\=FDHN234<QXD9:7EDFV3G;j9RQ&;:=<M9A26=9 vJW!3G4G=FV;Y30{¡}_wq#} T 7aq¬ 3G;j3Š£ Q T VG9:7 Q\D=FDHNDQ!95B3Š£ Q T VG9:7 Q\Dv
9A23 Me4 =FDFDQ!9j; VTUFU!Q5B9`=FDMQ/m˜#
U Mf5K3A£ Q T V9:7 QXD6=!5BM@7 H3=;-_b n3;<VZZT3 ;R9R3He9A2=9%-S D3G3GHT3GH@9RQ T 3G=5‡D9RQ
W!3!26= £ 3&W!3ŠOm Q5B3f{¨}_wq#} h
v Q\V T H@3Š£ 35 4<QQXU!35K=9R3%#v 7 9A2z[U 3(bŸSHLv =;_; VT5‡U!587 ;?3GH0=FD6H&;<26=`A¬ 3!DHbgV … 2=9
2=FUFU!3!D3GHdv !
 =5,5BM!i-X XS =;Šq¬ 3HN2!7aU¥_b ’kVG9%-S 5B3= T–T MeHa7 HXDHh 9`Z3 9`=FDM(9,MFU!3Q/jm 5B3= T 5K3 ; U!QXD;?3`b ! =9R35w8o 3DH
Q/m  s(t5S T 3=!5‡D3HN23@26=6H5K3G4<367 £ 3HS{¨}_wq‚}_h ;#H3G;q7 Z\D=AL
v =5KHQb
dQ\VvF9A23&5K3G=6HT3!5>vX4 =FD4 QXD64 T V6H3
v[26=926=FUFU!3!D3GH ÏXS =`U :¤ V;?9j; VTUFU T M7EDZeMGQXV~v 7 9A29A2318m =64A9R; b
y 3A£ 3!5l= T U =FDTV 8m =64A9AVF5K3!5K; Q/bm H7 34 =;?9:7EDZ’U =64!2!7ED3 ;vJ’kV T 35.v*cFk“gvAFm587ED4 3Tva=FD6H L ’Øw{ U!5K3 ;?3DG9R3H@9A2367E5

U!5KQH\V64A9R;[7EDg“07EDTD3G=FU!Q T 7 ; 7EDg_
} U!587 T   b … 23!DOtS =;AA¬ 3GH@9A23/U [v 2M(9A23<MHTQgDQ!9_=6HT=FU9`9A23@D3Av
9R3G4!2TDQ T QTZ7 3 ;v(v 7 9A29A2313<ˆ64 3!U9:7 QXD(Q]m
m 9A230’kV T 35.v9A23@5B3G;<U!Q\D;Y31Lv =;`4 QJ(U U T 3<9R3";q7 T 3D4 3(b¨_} D6H%Y¤ V;R9
’kV T 35m;Y=7 H@9A26=9`9A23 Mgh
v 3!5K37EDG9R35B3G;R9R3GH d2Q"hv 3A£ 3!5>vF9A23 MfD3Š£ 35 T =9R3!5m4G= T–T 3GHQcb FX3!5‡2=FU;Gva9A23 M T Q;R9n#U M
UT2QXD3@DTV`(
U W!35cb} 5B3U!5K3 ;?3DG9?=9:7 £ 31>m 5KQJp
U QXD31Q]m 9A23"Q!9A23!5 4 QJ(U U6=FD7 3 ;`3A£ 3!D(9RQ T Hˆ[U 3";?QJU 3<9A27EDZ@QXD
9A231Q5lH35JQ]m~V
d3=F2v(h
v 3!¬ DQ"cv 9A2=9h9A23 ‘ =!5‡W!3!5 =FD6HN’k5B3Š!£ 7 4/¬[[U QaHT3 T ;_=!5K39RQ!9?= T–T M%[v 5KQXDZtvtWTV9Øhv 3"HQ
DQ9`4G=!5K3  :¤ V;?9jZTQ&=ŠL
v = M sFM QXV(=5B3@W!Q!9A23!587EDZgV;]šXfb
S 26= £ 3&D3A`v ;˜Om Q5-MGQXV(ZXVM;-j ‡Š‰M†|GM†]— MGHI(—%™ †`J›J†• R¥‰M†M…c†ˆ‡9IŒR>‡9F/LWFJGHr• ŽeLIKP|—ŸFJGH‡n‡>INWF  †
‡ŠU ‰M=`†’A¬ 31Q• 9A†23‘/F`HaR>7 3(‡>•ÜGM4 =›r;R9:•aGJ7EDQZfPM7ER>D‡AH\…cL’V;?9A‹`5P…iMCIJR-U!‹K5BQT†`;<… U!‚3L5*IK;?P|Q@R-9A‰H2IK=9`Pf™–M ŒQ\V~FMfv IK7 ‹HT–T ‡5U‡Š5BQT‰M;<†|U!3!GM5m†(=— ;Ÿ‡9hv †(3 ‘(T–T‰KtGHU IfT 3™šIH=;?›K3• †(HRQNœ
dDQ!Q\9 VT ;<QF2QfQX"¬ V =T H 9
9A23; 2Q5B9L9R35:
U ;_=;7aU U!Q5P9?=FD9Šb
d 23@D3<ˆ9[7 ;?; V3"Q/nm 9A23kL 7 3[mq =;R9:7EDZ|d{ DZa7ED3G3!5ØYo “@= M!/x VFD   7 ;?;<V3 twLv =; HT3GHa7 4 =9R3GH@9RQˆU =64!2!7ED3
U!5KQH\V64A9R;-b … 23<9A23!5*9A27 ;BL
v =;_4 Q7ED647 HT3!D9?= T vTM QXV0W!319A23BY¤ V6HZT3(b
S ;<VFW`"U 7 9>9R3GH0=fU!5BQ\U!Q;:= T 9RQS{¨}_wq‚} Yo {nQ/£ 3/U W!3!5 ä v   I(jt =FW!QXV9 ‘ =5‡W!3!58’k5K3A£ 7 4¬1hv Q5:¬¥Oo 9RQ¥[v 27 462
X












4<QXU MT587 ZX29x• ” v

W ib

T vtW<M `5

’*=5Es-“367E5

–— ˜A™0— ˜<š ›0œqž6Ÿ" j›G #¡› ŸP¢Y—£¥¤¦Fž ›Y¢
¦T§ ›`¨B!Ÿ\œqž#™.!¦6˜:œG©N¤6ª ˜<«!£ ˜ŸK£ ¢: `©

N

¬:®

T /tAbždØv
To
S A£
£
£
(jBS‚U
T S /U
T
A£ ¬`h Bv E¬_m fU
wv Mt t T /m
T–T T ¬
¡}_wq#} U
rVEv Þm T
X
zy  £
/m Ev
JU `b (t ZV
ŠX T ˆ{ BbÏ
aU k{ T
T Š£ T T b £

"v
/m Ev %v wm
’{
T A£ T T T T
]£ /U
]m
T ¨}_wq‚}
(}m
I KS

T
T
T T "v T
/mŸwqØ{ "v

]m ]m :v nm
T Qb
T
£ T - b

/m Ev
Š£
S
/m
T
–
T
T
T
`U %v
¬ Hb
T
} m T–T JUgU zSHv
ko /x
t /mewqw{
T "v mŸS
U
/m
A£ ¬
£
zo
T
¨}_wq‚} EU /tAbŸS `U
Š£ /¬(h
%U ˆU
T ~v
Bv
Šv v £ HbBS"¤ ˜v
JU T `U
`b
T
§ T aU ¨}_wq#}
]\_^ `U ZVi} T ¥U /U T
T ]U
Hb XŒ}m BS
"v ]\ ^ `U
T
Mb T–T
£
%U
T `b
v Bv
"v
JU
S £ `U H£ ko ä t
m ¥o ¥q T Š£ T Mt ¥m Øo t £
T
T m¹j

Bv T–T
T #m JU ibe€ Mb
-D3 3!5h5K3G4 37 3GH0=C5B3U M
hQ@9A2!7EDZ;2= 3&26=FUTU!3D3H&;q7ED64<3
1=6H319A23&U!5BQ\U!Q;:= .7ED"9A23
U!5KQXU!QT;Y= XHT3 [Q\D;?9A5K=9R3[9A2=9[’k5K3 7 4 ; hQ5 >5BQ
27 Qf7 ; 5BQ\DZ
UFVTW 7 ;<27EDZQ m9A23"=!5B9:7 4 3eW<M
’ 7 … = 7EDZ9RQXD7EDf{
1=ZT=Ž7ED31=FW!Q\VG9L9A23 hQ\DHT3!5 >V 5B3G;?3G=5l462 07ED 27 Q F9?=9R3 hD7 35B;A7 9,M
=FD6H@9A23;YQ l9 L=!5K3[9RQ04 Q [3
R= .;:47 3!D9:7 ^\4 e=!5B9:7 4 3@W<M  `VT587EDZ&9A26=9L9:7 3 Œ= ;?Q
=6H 35P9:7 ;Y3GHN2Q }ZTQQH@9A237E5*;YQ l9 L=!5K3 L=; OQ5 ;<2Q!9j; 3 3 34 = 4!V =9:7 Q\D; jk= 3"M QXV(;Y3 3D=FDGM 
=6H 35P9:7 ;Y3 [3DG9R;_QXD9A23ZX5K3G=9`;<V64 4 3 ;?;_Q ;<2Q!9`; 3G3 3"4G= 46V =9:7 QXD; =9R3 M6i
n3!5K3e7 ; =FDQ9A235n7EDG9R35B3G;R9:7EDZ&4 Q7ED647 HT3!D64<3Fv l9R35  tv \;?3!D9`=CU!5KQXU!QT;Y= 9RQS{
#vX9A234 Q 3!5
U6=Z3"Q
g;<2Q 7EDZ(9A23&W!3<9?= 35B;A7 QXDQ ;?Q l9 L=5K3 OQ5m4G= 46V =9:7EDZe9A23(46587 9:7 4 = ; Q
U VFDZT3!5
3 Qa47 9‡M J3<9 vJDQ&;?Q l9 L=5B3e2=;_3 35hW!3 3DfUTVFW 7 ;<23GH … 2M6i ;[7 9 =64 47 HT3!D9?= 9A26=9j9A23=FVG9A2Q5*Q
9A23"=5B9:7 4 3e7ED9A231;:= [3e7 ;?; V3 L=;1’ 7 … = 7EDZ9RQXD
_D6Hf= l9R3!5 = 9A2!7 ; 4 Q [Q9:7 QXD L=;_;<VF5‡U!5O7 ;Y3GH@9RQ 3G=5‡D@7ED(9A23 :“e= M! TVTD3   _7 ;?; V3"Q
=ZF=Ž7ED319A26=9jQ\D3"Q n9A23@’k5K3 7 4 Z\5BQ\VTU026=6HN5B34<367 3Hf=0U!587 Ž<3 ,;?3 3@U7 4A9AVF5B3&W!3 Q o7 XZT3<9
{
U!3!5 "7 ;Y;q7 QXD
X= ~; VT5K319A2=9"’k5B3 !7 4 ; ZX5KQXVFU02=; =6HT3";?Q (V64620U!5KQZ\5B3G;?;[7ED9A23 =;?9
M 3=!5*9A26=9L9A27 ;[7 ; [2M(9A23(= L=5KH L=;_Z7 3!D
YV;R9 L=FDG9j9RQ 3G=5,D 2=9j9A23G;?3=64 4 Q (U 7 ;<2 [3!D9R;
=5B3
6Q5m= QXDZ9:7 [3f{
HT3 ;:46587EW!3GH@9A23(4 =;Y;`Q\D9A23@U
H7 =Z\5K= ~=; = †4 QT;?3 =9A23 =9:7 4G=
HT3 ;Y4!5O7EU9:7 QXD
l9R3!5 X;?3DG9j9A23@U6=FU!3!5 =FD6H&9RQ H@9A23 p=FW!Q\VG92Q }9A23eU
H7 =Z\5K=
7 ;_3!5‡5BQ\D3GQXV;Gv
9A23<Me4!2=FDZ39A23(HT3 ;:46587EUG9:7 Q\D … 3 7 9#7 ; ZQQaHtvFM 3 9L9A23<Mf26= 39RQ0;:=<M9A26=9 7ED9A23@U6=;R9 =9R3!587 =
L=; [5KQXDZ0=FDHNDQ †9A23<M@=!5K3"9R3G=64!2!7EDZe;YQ [3 9A2!7EDZ@3 ;?3 kQ5m=!5K319A23 M6i
J26= 3; VTW "7 9>9R3GHe^ 3
U6=FU!3!5K;`9RQ@9A23(4 QXD O3!5K3!D64<3  %$f7ED
3 3 =FDH _=FD6H OQXVF5
26= 3eW!3G3!D
5K3 ‡34A9R3H0QXD9A23"ZX5KQXVFDHT; h3 vTM QXV@4 =FD05K3G=6H&9A23 3<9>9R3!5mM QXVF5B;Y3
n3!5K3e7 ;`9A23 3<9>9R35 >5KQ
“f5 dQXWFW






®
_X4 À®4¯"¯f¯
¥m_X Ì YQZeX4aeYÊ\RZebdU"YÊ\^j§¥1XS¡m_Y_bÍS@\"j
£™U"Ÿ_YnS@bkjã¨ Ì ¥.£±VWXZ UfY;­Q\^YOŸn\"aeœ  ZemhZeUWaHX@ÚObdX@”¶\"jkjA[eŸ_ _VWbkZŠZHX4–
\^ Ê[ZHaH\fSÈZH[4² Ì Z ”c\f[\RZZemÊ\RZZebdVWXZemn\^ZZem_X4œh–sUR”Yn[eX@jdX4SZeX–žZHm_X\^ n[ŠZea¡\"SZH[™ZeUWgiUfaeV×Zem_XS@U"aHXU"g
X4\fS¡mhU"g1ZHm_XT® )[eX4[H[ŠbdU"Yn[4²$¥m_X#£c\^jdj§giU"a $\"]ÊX4aH[™giUfaZem_XT®¯"¯"¯W£™U"Y_—faeX[e[\"Yn–h¤ãÛs]ÊUQ[ŠbkZebdU"Y
]_aHUs–sŸnSX–«®
]`Uf[H[Šbd _jdX\" n[ŠZea¡\"SÈZ¡[™giaeUfVהm_bÍS¡mhZHUTS¡m_UOUf[eX?giaHU"VosU"g
ZHm_bd[YOŸ_V ÊX4a.\^]naeU•ÛsbdVW\^ZeX4jkœ
¯ \" n[ZHaH\fSÈZ¡[™”cX@aHX[ŠX4jkXSÈZHX4–MZeUT `XaeX4ÚQbdX@”cX4–h\"[cÐnYÊ\^jA]n\"]ÊX4aH[4² Ì –sb͖;aeXSbdX@ÚfX\"jkj )\" n[ZHaH\fSÈZ¡[\^Yn–
–sbÍ[ZHaebd _ŸsZHXZem_X4V×ZHUWZem_X\"]_]_aHU"]_aHbd\^ZeX£™U"Y_—faeX[e[ £™mn\"bkaHVWX@YA²$¥m_XUfY_X\^ n[ŠZea¡\"SZjdbÍ[ZHX4–;bkYœfU"Ÿ_a
\"S4SX4]sZH\"YnSXjdXZŠZHX@abÍ[bdYMgª\fSÈZZemnXU"Y_XgiU"a”mnbdS¡m”cX”cU"Ÿnjd–hjkbdl"XZHU)aHX@ÚObdX@”„Zem_XÐnYÊ\^j§]n\"]ÊX4a4²ã¥m_X
£™U"Yn—"aHX4[H[£™mÊ\^bdaeVWX@Y;”bdjkjA `XaHX@ÚObkX4”bkYn—#ZHm_XÐnYn\"jA]n\^]`X@a¡[\^Yn–;”cX”bkjdjA `XSU"aHaHX4[e]ÊUfYn–sbdY_—”bkZem
\^jdjA\^Ÿ_Zem_UfaH[\f[cZeUT\^YOœMS¡mn\"Y_—"X[caeX4ÚQbÍ[ebkUfYn[c”m_bdS¡m(\"aeXgiX@jkZZeUW `X\^]_]naeUf]_aebÍ\RZHX"²
¥m_X£™UfY_—"aHX4[H[£™mÊ\^bdaeVWX@Y\^aHXbkYʖsŸn[ŠZeaHœžXÛs]`X@aeZH[ \"Yn–MbkZ bÍ[Zem_X4aeX[eU"jdX–sbd[HSaHXZHbkUfY;\f[cZeUW”m_bÍS¡m
]n\"]ÊX4aH[\"aeX[eU"jdbdS@bÑZHX4–h n\"[eX4–hU"Y\^ n[ŠZea¡\"SZZeU"]nbdS\^YʖMÐnZZeUT\)]n\^aeZebÍSŸ_jÍ\^a [eX4[H[ebkUfYA²
Ì Z bÍ[Ÿ_YsgiU"aeZeŸnYn\RZHXZemn\^Z ”™XS@\"Y_Y_U"Z\fS@S@X@]sZ \^jdj1\" n[ZHaH\fSÈZ¡[™Ufa]n\^]`X@a¡[”m_bÍS¡m;\"aeX[eŸ_ _VWbkZŠZeX–§²
¤ãYQZHX@aHbkY_—W\^Y(\" n[ZHaH\fSÈZ–sUOX4[YnU^Z SUfYn[ZHbÑZHŸ_X\^Y\^Ÿ_ZeU"VT\^ZebÍS\fS@S@X@]sZ¡\^YnS@XU"g1ZHm_X\^ n[ŠZea¡\"SZȬRU"a™ÐnYn\^j
]n\"]ÊX4a4²
¥mn\"Y_lžœ"UfŸMgiUfaœ"UfŸ_abkYnÙQŸ_bdaHœ"on\"Yn–M”cXjkUOUflTgiU"aH”c\"aH–žZeUTaHX@ÚObdX@”bdY_—œfU"Ÿ_aÐÊYn\^j§]n\"]ÊX4a4²
X4—f\^a¡–_[4o
¢?X@Y_Y_bÍ[ ­Ê² U" n 
 ?¢£

S‚U

£

`U

]m
]—Ÿm ä IMt …cR>‡ `•aGH Kb
I ä `v zU

Þv (b "v

T

T

(V;R92= 3;<VFW "7 9>9R3GH@9A23
 Q jU6=FU!3!5K; Q!9A23!5 7 ;Y3 _nQ }4G=FDM QXV(3<ˆFU =7ED(9A26=9jQXD M
QXV9jQ
j=64G4<3UG9R3H {nQ!9R39A26=9L9A23Q!9A23!5b5K3 ;?3=!5l4623!5K; d5l=9:7 Q&Q b=64 4 3!U9?=FD4 3
  Q #MfU6=FU!3!5K;

QXD9A237E5LU=FU!35B;[7 ;  v [27 462 [3 =FD;`9A26=9jQ!9A23!5LU=FU!35B; =5B3"9A2F5B3G3"9:7 [3 ;1W!3 9>9R3!5*9A26=FD "7ED3



s

/m˜U

1o

aU



–— ˜A™&— ˜Aš ›fœ:Tž6Ÿ j›G #¡› ŸP¢Y—£¥¤¦Fž ›Y¢
¦T§ ›j¨B6Ÿdœqž#™.!¦6˜:œG©g¤6ª ˜<«!£ ˜ŸK£ ¢.›A©



4 QXU<MF587 ZX29x• ” v

-h

’ ib

/m

zU (b

T vtW<M `5 _’*=5Es-“367E5

  
  
  
 "!#  

  


Chapter B. My Relationship with Die Casting Establishment

FT

m Hh T a¬
~v

Šb

3=;?31^-D6HN235B3"9A23=FW;?9A5K=64<9R;_=FD6H0HT3G47 HT37 MGQXV H 7 A39RQg23G=5m; V4!29RQXU7 4<;`Q5bDQ9
9A23"9RQ\U!7 4&{
4!2QT;?3Tv\7ED 2=9`;?3G;?;q7 Q\D(=FDH0Q\D [26=9`HF=<M 89A2!7E5lHfHF=<M

¨}_wq#}

~v

Oo

d

6!
#"
,%& #   
$

' %0 
T

T /U

JUgU T

/tAb

Bv

‘ V3G;?; [27 462

b¨} /£ T
Üm EU (bžd
T
:v
¥U T

2319?=FDZT3!D9:7 = ZT=9R3"3 3 [3DG9#7 ;_4 Q QXD M@V;?3Hg7ED05‡VTDFD35 HT3 ;q7 Z\D;
DQ 3 =FUTU!5KQT=64!2"9RQ&9A2!7 ;
5,VFDFD35mH3G;q7 ZXD@26=;[W!3G3!D(H3 3 QXU!3H9RQ&=64627 3 3(W!3 9>9R3!5m4 QXD9A5BQ Q 3!5-9A23D3 3H3HfU!35 OQ5 =FD64<3 #23
D3 o=FUTU!5KQT=64!2e7 ;[W6=;?3H&QXD;Y47 3!D9:7 ^\4U!587ED47EU 3G; 7ED 2!7 4!2"9A237ED9R3!5‡5B3 =9:7 QXD;<27EUeW!3 9 h3G3!D"9A23 [3 9?=
U!5KQXU!3!5B9:7 3 ; =FD6H&9A231ZT3 Q [3<9A587 4 = U=5K= 3<9R3!5K;[7 ; H3G;Y46587EW!3GH

Šv



fU

Š£ T

T `U



T ~v

T /£

Qb



' %0 
 % 
 
'

-"

T
T
]m
b¨d
T
T
(U `£ `U
/U ]£
(bBS JU
T
]m£ (U T
#G T
[v T
T
¹m -b /m g¬
]m 5£ `U ]U
–T T 1£ (U (¬`bžd
T Bv ~v
4G /U
1£ `U /U¥be
Š£
£ 1£ `U /Ub

‘ =;q!=7E5hU!Q5BQT;q7 9‡M(4<QXD;R9:7 9AV9R3 ;_= =!5KZ3@U6=!5B9jQ 9A2319RQ!9?= U!Q5KQ;A7 9,M JQN5K3GH\V4 3"9A23@U!Q5KQ;A7 9,MH\V319RQ
9A23"ZF=;q6=7E5J3!D9A5l=7ED [3DG9 v 6=646VFV €4 =FD&W!3=FUFU 7 3H9RQg5K3 [Q 39A23@5K3 ;A7 HXV6= =7E5n7ED"9A23"Ha7 3 ED(;YQ [3
4 =;Y3 ;`9A23(=FUFU 7 4 =9:7 QXDQ 6=646VFV
5K3 ;<V 9R;[7EDe=027 ZX2 \V6= 7 9,M4G=;R9:7EDZ 2!7 37EDQ9A235m4 =;?3G;`9A23
5B3G;<V 9R;j=5B3DQ9h;Y=9:7 ; 8=64A9RQ5BM D3Q -9A23 A3<M;h9RQ(9A231;<V64 4 3 ;?;_7 ;h9A23HT3 ;q7 Z\DQ -9A23 =64!VTV
;RM;R9R3 ev
3 ; U!3G47 = M9A23 6=646VFV €9?=FD
23eU5B3G;?3!D9j;?9AVHMHT3G= ;
7 9A2 2=9 =!5K319A23(HT3 ;A7 ZXD&5K3 \V!7E5K3 [3DG9R;
QXD9A23 =64!VTV p;RM;R9R3
k3 ;q7 Z\D46587 9R3!587 ==5B3&U5B3G;?3!D9R3GH@9RQ0=64!2!7 3 3=FD3 Id34A9:7 3 =64!VTV €;?M;?9R3

  



    6"!  6-<
'G'"

' %0 

}


  ,%  $"

-(  #0$ %&
' -< *%   
 "    -(

/m
"v

T

aU

T -b˜S
]m aU T

U5BQ\U!3!5mHT3 ;q7 Z\DQ m9A23"H7 34 =;?9:7EDZgU!5KQa4<3 ;Y;`4G=FD05B3HXV64<319A23 3G=6H@9:7 [31;q7 Z\D!7 ^\4G=FDG9 M PD9A2!7 ;1U6=FU!3!5
= Ha7 ;Y4!V;Y;q7 Q\D"Q\D02Q
e
9RQf=64627 3 3=0W!3 9>9R3!5 4G=;R9:7EDZ&=FD6H0=e;<2Q5P9R35 3G=6H@9:7 [3&V9:7 7 Ž7EDZ9A23 ;Y3"4!VG9>9:7EDZ
3GHTZ319R3G4!2TDQ QTZ7 3G;_7 ;"U!5K3 ;Y3!D9R3GH
U6=!5B9:7 46V =!5*3 (UF2=;A7 ;#7 ;_Za7 3D(QXD9A23&V;Y31Q m9A23;q7 (U 7 ^X3GH
4 = 4!V =9:7 Q\D;_=FUTU5BQF=6462

T

T T



Hb

#  +(

%$
- F& D  
$
* + (  !"
$*!$#,/'G%&'
€

/m

T ]U

Qb¡}

(U
b¨d
ŠbBS

£

T

T

aU

 ' *+(

6 - ,%&'& % 
+ %  
)(


' %0



Tv

WU Y¤
£
T

d3GH\V4<9:7 QXDQ b=7E5m3!D9A5l=FU [3DG95B3HXV64<3G;`9A23&U!5KQaHXV64A95B3 ‡34A9:7 QXD05l=9R3(=FD6H0= L=<M;[7 ;_= = .Q5m4<QXD64<35,D
<W MeHa7 34 =;R9:7EDZ&3!DZ7ED3 35B; #23"3 Id34A9R;_Q `5,VFDFD35 H3G;q7 Z\D"Q\D9A23(=7E5 3!D9A5K=FU [3!D9[26= 3&W!3 3!D
H7 ; 5B3GZT=5KHT3GHC7ED9A23&U6=;R9 EDCU!5B3G;?3DG9`;R9AV6H!MGvX3<IJ3G4A9R;_Q 9A23@5,VFDTD3!5nH3G;q7 ZXD4!2=5l=64A9R3!587 ;R9:7 4 ; =!5K3
;R9AV6H7 3H ‘ V7 H3 7ED3G;`=5K3eU5B3G;?3!D9R3GH@Q\D@2Q
9RQf7 U!5BQ 39A23e5‡VFDTD3!5mHT3 ;A7 ZXD;?Qe9A2=9 3 ;?; =7E58ZF=;j=5B3
3!D9A5K=FUFU!3GH

Kb

Qb

T

.-  
%$

/m
"v

 &0/  % 

$
 %
 # '+   6

- '

]m
aU ]£

`U

 1(32
'
/+4    
'G')"

 %&
-< %0

d 23  Q"v U6=9>9R3!5‡D&7ED9A23k[U Q T H0H\VT587EDZe9A237ED!7 9:7 = T U=5B9`Q]mm9A23e7ED¹¤.3G4A9:7 Q\De7 ;`Q\D3"Q]m 9A23@U=5K=`U3<9R3!5K;
v[27 462HT3<9R35:U"7ED3 ;`9A23;<V64 4 3 ;?;_Q]mm9A23(4 =;R9:7EDZKb¨d 27 ;[7 ;?; V3@26=;W!3G3!D;?9AVHa7 3GH&3<ˆFU!35O7aU3!D9?= T–T M-b
y 3A£ 3!5l= T ;<VF5,U!587 ;q7EDZ04<Q\D4 T V;A7 QXD;j4 =FDCW!3(HX5l=Av D~>m 5BQfUp9A23"3AˆU!3!587aU[3DG9R; bžd 23 ;?3@5K3 ; V T 9R; =FD6H

4<Q\D4 T V;A7 QXD;`=5B3@U!5K3 ;Y3!D9R3GH0=FD6Hf4 =FD0W!3&V;?3HNW<M(9A23H3G;q7 ZXD3DZa7ED3G3!5K;#7ED9A2367E5mHT=7 T MfU5K=64<9:7 4<319RQ
=64627 3A£ 3&W!3<9>9R35 4 =;?9:7EDZQb



4<QXU MT587 ZX29x• ” v

W ib

T vtW<M `5

’*=5Es-“367E5

–— ˜A™0— ˜<š ›0œqž6Ÿ" j›G #¡› ŸP¢Y—£¥¤¦Fž ›Y¢
¦T§ ›`¨B!Ÿ\œqž#™.!¦6˜:œG©N¤6ª ˜<«!£ ˜ŸK£ ¢: `©

¬:®

^ "Ž



+J" o

9j9A23   g
s {¨}_wq#} 4 QXD mO3!5K3!D64<3kS-26=6H0= T Q\DZ&4<Q\D-£3!5K;Y=9:7 Q\D~v 7 9A2C“C5cb =!5‡D3!5L’*=Gˆ9R3!5ib n3"9RQ T H
U[3"9A26=9nS-26=6HN5‡V&3GH0= T Q!9`Q/mmO3=9A235B;7EDN{¡}_wq#}_b*n3";<VZZT3 ;R9R3He9A2=9[… 7 mBSMvL=FD9R3GH@9RQ&ZT3<9[5K3G= T
5K3 ;<V T 9R;GvÏ\
S ;<2QXV T HNW!3eU!Q T 7 9:7 4 = T–T M=64<9:7 £3`b 319RQ T HˆU[3&2Q"v€W6=6H@9A23;A7 9AV=9:7 Q\D@26=6HW!3G3!D@7ED(9A23@U=;?9
=FD6HN2Q"v (
U V6462f{¨}_wq‚} 2=6HC7aUU!5BQ]£3HKb`’kV9[23!5K37 ;`;YQJU[3 9A2!7EDZWSX4G=FDTDQ!9[VTD6H35B;?9?=FDHQjh7 ;<DHh 9j9A235B3
=FDM QXD3%[
v 2Q&4G=!5K3 ; =FW!Q\VG9j9A23Ha7 3(4 =;R9:7EDZf7EDH\V;?9A5PM@=FDH¥v 2Q¥Lv =FD9R;#7 9j9RQ  QXVF5O7 ; 26ipS m MGQXVHTQf4 =5B3Fv
U T 3G=;?3˜.¤ Q7EDz[
U 3`bŸ\S =64A9AV6= T–T M02= £ 3%Om QXVFDHf;?QJU 37ED6H7 £ 7 H\V= T ;B[v 2Q0HQ04G=!5K3=FDHf=5K31; VTUFU!Q5B9:7EDZˆ#U M
3<IJQ5B9R;j9RQg7ED6465K3G=;Y3";Y47 3DG9:7 ^\4[!
¬ DQ"v T 3HZT3"7EDeHa7 34 =;R9:7EDZKcb F 5B3G;?3DG9 T MGvd2Q"hv 3A£ 3!5>vF9A23<Me=5B3=W"U 7EDQ5O7 9‡M-b
S 2QXU!319A26=9`=; T 7EDFV ˆ&7 ; T 7EW!35K=9:7EDZ@9A23%hv Q5 T H[>m 5KQJU “07 465KQ;YQ/lm 9 v;?Q@9RQQ¥hv 34 =FD T 7EW!3!5l=9R3(=FD6HNW!5O7EDZ
U!5KQ; U!3!587 9,M9RQ@9A23(H7 34 =;?9:7EDZC7ED6HXV;R9A5BM-b
}lm 9R3!5jW!3<9>9R35*9A2=FD=M 3=!5*;A7ED4 3[U M(^-5B;?9n‡o =FDHVFD;?3!D9Yt T 3<9>9R35*9RQOFy 9R3A£ 3 H]£ =5lH!MGv#SHOm 3 3 T 9A26=9L9A23!5K3
=5B3"9A27EDZT;L9A26=91SMh
v QXV T H T 7aq¬ 39RQ0=6HTH09RQe9A23=FW!Q/£ 3 T 3<9>9R35cb}lm 9R35Ø#U Me4 Q5,5K3 ; U!QXD6H3D4 35#v 7 9A2MF\=FV T
’k5l= T Q"h
v 3!5>vÏ-S 2=6H@9RQ04 QXD9:7EDTV319RQgU5B3G;?;`9A23]p
U 9RQgUFVFW T 7 ; 219A23(=5P9:7 4 T 3"=FW!Q\VG9j9A23&U]\5^nbž#d 2!7 ;1U!5KQa4<3 ;Y;
7 ; = T ;?Q&H3G;Y4!5O7EW!3H07ED9A23@U!5K3G4<3H7EDZ;Y3G4<9:7 QXDH
b
JQXVavF9A23e5K3G=6HT3!5>vQ(U V;R9W!39A23˜Y¤ V6HZT3Q]mv 2=9_7 ;15K3G= T–T M
26=FUTU!3D!7EDZKb¡h
} HTHa7 9:7 QXD6= T–T MGvFQXU!3DGXV3 ;?9:7 QXD;q6Ha7 ;Y4!V;Y;q7 Q\D#9RQXU7 4<;L9RQ9A235v 2Q T 31Ha7 3"4 =;R9:7EDZe4 QJUgU VTD7 9,M
=5B3(=6HFH3HKb
£ 7 4/¬(h ;5K3 ;Y3G=5K4!26i¦S ;_9A23!5K3;R9:7 T–T DQ5K3!U!Q5B9Yi_} DH0HTQ3 ;_9A27 ;`9,MFU!3Q/m
… 2=912=FUFU!3!D3GH@9RQ@9A230’k5B3Š!
5K3 ;?3=!5l4624 QXD9:7EDTV319RQNW!31>m VTD6H3HFi
q =FDe=FDGMGQXD33<ˆFU T =7ED9RQ[U 3@2Q"
m
v {¨}_wq#†} Q\U!3!5l=9R3 ;:i
S ;({¡}_wq##} v9A23"Q5BZF=FD!7 Ž =9:7 Q\DvK[U Q5K37a(U U!Q5B9?=FDG9j9A2=FD9A23(H7 34G=;R9:7EDZf7ED6H\V;?9A5PM!i

}







–— ˜A™&— ˜Aš ›fœ:Tž6Ÿ j›G #¡› ŸP¢Y—£¥¤¦Fž ›Y¢
¦T§ ›j¨B6Ÿdœqž#™.!¦6˜:œG©g¤6ª ˜<«!£ ˜ŸK£ ¢.›A©



4 QXU<MF587 ZX29x• ” v

’ ib

T vtW<M `5 _’*=5Es-“367E5

Chapter B. My Relationship with Die Casting Establishment



4<QXU MT587 ZX29x• ” v

W ib

T vtW<M `5

’*=5Es-“367E5

–— ˜A™0— ˜<š ›0œqž6Ÿ" j›G #¡› ŸP¢Y—£¥¤¦Fž ›Y¢
¦T§ ›`¨B!Ÿ\œqž#™.!¦6˜:œG©N¤6ª ˜<«!£ ˜ŸK£ ¢: `©
¬










   
[ ¦     

gv %v T–T £
%m
%v
T–T
(bd
`U
Qb¡d
Av /m kU T

JU
T T a¬ T ¥v
Šb˜S zU
Hh T
T ~m :U aU
T `b T
T
T
T
~£ T ˜m `U T T `U (U /£
bB§ :U
/m `¬
G
/m
(b
T £ T `U u
}
"v
[Øq b bØy T
TG
T Am (b¨}m ŠU T–T aU /U
kU /£
T
T £ T `U
¡bØd
Ü£ ]m

io qØb t


      !  
#"
}_D6= T QZ!M9A23¥U =;?;#4 QXD;?35Ü6£ =9:7 QXD1Om Q5*9A234<QXD9A5KQ T £ Q T V`U[37 ;

io qØb (t


    $   
S

PD(9A2!7 ; =FUFU!3!D6H7 ˆ h3 #7 HT3!587 3"9A23&W!QXVFDHF=5PM4 QXD6H7 9:7 Q\D OQ5bUF26=;?34626=FDZT3
7 9A2=e;q7 ZXD7 ^\4 =FD9
HT3!D;q7 9‡M4626=FDZT3 n5K=6Ha7 9:7 QXD6= Me7EDeHa7 3"4G=;R9:7EDZ9A23(HT3!D;q7 9‡M4626=FDZT3(7 ; =;Y;<V [3GH@9RQNW!3e7ED;q7 ZXD7 ^\4 =FD9
7ED(H7 3"4 =;?9:7EDZ #23"=FV9A2Q5 7 ;DQ9L= L=5B31Q n=FDGM [QaHT3 7ED(Ha7 314G=;R9:7EDZ(9A26=9h9?= A3[9A27 ;[UF23!DQ [3DQ\D
7ED9RQ@=64G4<QXVFD9 PD =9R35O7 = ; 7 A3[;?9R3 3 =FDH L=9R35J9A23HT3!D;q7 9‡M4!2=FDZ3(7 ;<D 9 =5BZT33DQ\VZ\2"Q5n7 9`HQ3 ;
DQ!9#U =<M >VF5B9A235 [Q5K37 (U!Q5B9?=FDG9#5KQ 3 … 27 3(7EDH7 34 =;?9:7EDZ9A23HT3!D;q7 9‡M(4626=FDZT3U =<M=;q7 Z\D!7 ^\4G=FDG9
5KQ 3@W!3G4G=FV;Y3"= =5BZT3"Ha7 IJ3!5K3!D64<3e7ED 6= V3G; OQ5 3Aˆ!= (U 3= V "7EDFV
7 ;_Q 3!5 F
VT5B9A235 Q5B3Fv9A23
465K3G=9:7 Q\D(Q k;<2F5O7ED <=Z3eU!Q5BQT;q7 9‡Me7 ;_=@Ha7E5B34A9 4<QXD;?3 XV3!D64<31Q 9A23(HT3!D;q7 9‡M4626=FDZ3
}4<QXD;R9?=FD9`4 QXD9A5BQ Q V [3 7 ;#4<QXD;R9A5‡V64A9R3GH&=; ; 2Q D7ED^XZ\VT5K3
aQ 7 HNUF2=;Y3(7 ;_Q\D9A23&587 ZX29
;q7 HT3=FDH 7 \V7 HNUT26=;?37 ; QXD9A23 3 l9_;q7 HT3
l9R3!5k=; = 9:7 3(7ED6465K3 3!D9L9A23 [Q 3GHC7ED9RQ@9A2319A23
HF=;<23GH 7ED3"=9 =Ha7 ;R9?=FD64<3
#23"3D35BZM4<QXD;?35 6=9:7 QXD(Q m9A23(4<Q\DG9A5KQ Q V [3@5K3G=6HT;






%ocqwb t oiqØb (t
£
/m T G ˆU /£ /U ˜v
T -b T T G Oio qØb t
% T

oiqØb ç t


 %      %    
É Í‚½­cÒ ãk³ªÑ-ÑA½ÑAÆC°+´ªÑ%È9ÆC½ÆEµ+½ м-º˜¼-ºØµE¯ª°wÞ³YµE¯ª°ªÃس¹µ:½ ´¹³AÒ-³YÆi¶>°¹´iµÂÆ#³ª¸a°wÒ °i¾ÜµK¼-ÈYµ+ÐÉ ¾`°i²Š¶AÒ ³Aº9³Yµ:½ ¼-º˜¼-ºžµE¯>½ Æ¡¶A¼Š½ ºYµÏÍ#½ Ò Ò-»A°ž³YÆ c°+Ñn»+ÙB¸a°¹³ªÑA°ª¸aÆ

d 4G

23"3 \V=9:7 Q\D;
`=FDH
_HTQNDQ9#26= 3(=FDM05B3G;R9A587 4A9:7 Q\D;_Q 9A23 7 \V!7 H Q 3 [3DG9 [27 462&2=;
9RQNW!3;?Q 3H&;?3!U6=5K=9R3 M _“fV 9:7EU M(3 XV6=9:7 QXD
W M=e4 QXD;R9?=FD9
5K3 ;<V 9R;7ED












Chapter C. Density change effects

boundry at t=0

liquid

solid

boundry
after some
time

dx
A1

B1

A2

B2

§a7 ZXVF5B3qwb jd


234<QXD9A5KQ

T £Q T V`U[3"Q/mn9A23eUF26=;?34626=FDZT3

yJVTW9A5K=64<9:7 QXD(3GXV6=9:7 QXDzocqwb ç t˜m>5KQJU~34G\V=9:7 Q\DOocqwb tjM!7 3 T H;

oiqØb t

 ¨    % ±      ¨    % ±        #  
d#231^-5K;R9j9R3!5Ep
U Q\D9A23&587 ZX29[26=FD6H&;q7 HT3"4 QJ(U U!QT;?3H¥m>5BQfU€9EvhQ&#"4<QXD9A587EWTV9:7 QXD;-j QXD3 twm>5KQJUp9A23 T 7 G\V7 H
;q7 HT3=FDH&9Eh
v Q`tØ>m 5KQJ~
U ;?Q T 7 H&;q7 HT3(b¨m} 9`9A231;YQ T 7 H&;A7 H319A23(4<QXD9A587EWTV9:7 QXDe7 ;B£ =FD7 ;<23GHNW!34 =FV;?3
¨   % ±  7 ;_Ž<3!5KQfH\V319RQ  7 ;[7 H3DG9:7 4G= T–T M(Ž<3!5KQ|Ro DQˆ[U Q/£ 3/U 3!D9jQ/nm 9A231;YQ T 7 Hdv\7 9 7 ; =eZQQaH
=;?; V(U(U9:7 QXD/tAbBSPD(9A23 T 7 G\V7 HNUT26=;?319A23"9R3!5EU
  % 7 ;_Ž<35BQ|oCv[2M6irt(9A2FV;j9A231v[2Q T 39R3!5EU
7 ;
£=FD7 ;<23GH¥hv 34G=FDg[v 587 9R319A23e7 HT3!D9:7 9,M
oiqØb ä t
$ ¨   % ±   
v 235B3 7 ;`9A231£ 3 T Qa47 9‡M=9j9A237EDG9R35Ü8m =64 3(b

d 231^-5B;?9j 9R35:~
U Q/nm 34G\V=9:7 Q\DOocqwb _t 4G=FD0W!33AˆU!5B3G;?;Y3GHC7ED(9A2319R3!5Ep
U Q]m 9A234]b £Mb ^ =;
    ¨   ±#
 %     ¨    ±  ¨ 4¨%      ±Š ±

% %
 
 ¨    % ±      %    %

oiqØb I(t
 ¨   ¨    % ±e± 
   ¨    % ±  
M ¶AÒ °¹³ªÆC°Bº9¼9µÂ°ØÆC¼-Þ°¨Ñ ½ Á°9ºªÆE½ ¼-ºªÆ‚Í#½ Ò "´¹³Aºª´+°ªÒ °+Ñ_°¹³ª´ª¯B¼9µE¯9°ª¸f¼-ÈYµ³AºªÑnºª¼9µ#°ªºYµÂ°9¸K½ ºYµÂ¼e° È>³¹µ:½ ¼-ºªÆCÆ:ÆCÆ:Æ






     
   
#

 #  ! 

 
     

  
     



4<QXU MT587 ZX29x• ” v

W ib

T vtW<M `5

’*=5Es-“367E5

–— ˜A™0— ˜<š ›0œqž6Ÿ" j›G #¡› ŸP¢Y—£¥¤¦Fž ›Y¢
¦T§ ›`¨B!Ÿ\œqž#™.!¦6˜:œG©N¤6ª ˜<«!£ ˜ŸK£ ¢: `©

¬ ­

TG


 =FDH&9A23";?Q T 7 H04<QXD9A587EWTV9:7 QXD(=FUFU!3G=5B;_QXD T M@7ED
JT T
¹m :U  T 7 GXV% 7 H@9RQ& ;?Q T 7 HKbd 23";?34<QXD6He9R3!5EU~QXD0587 ZX2926=FDH&;A7 H3"Q]m
4G zocqwb t aU T
oiqØb s(t
 !      #  % !
#"
!" #"
d 2FV;Gv34G\V6=9:7 QXDzocqwb t#7 ;_9A5K=FD;+mOQ5EU[3HC7EDG9RQ
oiqØb r(t
  ¨    % ±      !  
% #
S 9#7 ;1DQ!9R3Ahv Q5B9A2M19A26=9`9A23%>m #5KQX" D9U!5KQX#U6=" ZT=9:7 Q\D(7 ;#=FW!Q\VG9 G U!5B3Š£!7 Q\V; T M1vL=;_4G= T 46V T =9R3GHQbŸ{sGXV6=9:7 QXD
ocqwb s(t 2Q T HT;`=; T Q\DZ&=;_9A2319A5l=FD;A7 9:7 QXD@7ED9RQ&;?Q T 7 Hf7 ;#=FW!5‡VFUG9%8o ;<26=5,U9A5l=FD;A7 9:7 QXD/tAb
v 235B319A23"9A5K=FD;q7 9:7 Q\D"9RQ0;?Q T 7 H@Qa4 4!VT5K; Q/£ 3!5-9R3](U U!3!5l=9AVF5B3&5l=FDZT31hv 3@2= £ 3
Œ†(‡9F  Q5*9A234 =;Y31Q]m¡
465K3G=9R319A2T5K3 3Ž QXD3 ;-b_“@=9A23]U=9:7 4 = T–T Mv\7 9 7 ; 4<Q\D-£3!D7 3!D9L9RQ0HT3 ;Y4!5O7EW!3"9A2319A23kUV; 2GM(Ž<Q\D3
W!QXVFDHF=!587 3 ;W<M(9Eh
v QgW!QXVFDHF=!5BM4<Q\DHa7 9:7 QXD;-b
GH
v 2!7 4!24626=FDZT3[9A23&23G=9L9A5l=FD;+Om 3!5
Œ†(‡9F ¥ 23(465K3G=9:7 Q\D(Q/m¡£ Qa7 H;[7 ;"5K3 ;<V T 9R;_Q/km H3D;A7 9,M4!2=FDZ3G;˜
U 3G4!2=FD7 ;AU©>m 5BQf~
[
U 4 QXD6HXV64A9:7 Q\D"9RQg5l=6Ha7 =9:7 QXDHb¨#d 23 T Qa4 =9:7 Q\D(Q/m 9A231£ Q7 H0HT3!U!3DHT;_QXD9A23
465BM;?9?= T–T 7 Ž =9:7 QXD(=FD6H0;<VF5Ü8m =64 319R3!D;q7 QXD(3 Id34A9 va3 9?4]bd 23@U!Q;Y;q7EW7 T 7 9,M(Q]m
m 9A23V T 7 G\V!7 H&4626=FDFD3 T ;YX
=FDH@9A23  Q"v Q]n
m ;Y3/"U 7 .l ;?Q T 7 H@=FD6H&3A£ 3!De;?Q T 7 H&4 QJ(U U!3D;:=9R3nOm Q5m9A2!7 ;B£ Q7 HQb
GH
 
    
U U!35K=9AVF5B3
Œ†(‡9F 3 9 vaQXD326=;`9RQ9?=`A¬ 3(7EDG9RQ&4<Q\D;A7 H35K=9:7 Q\D"9A23eU!5K3 ;?; VT5K3"3<IJ3G4<9Bd 23 T 7 GXV7 HT=9:7 Q\D"9R3/(
=FDH@9A23 T =9R3!D923G=9_=!5K3=Id34A9R3GHf;?QJU3Av[26=9#W<M9A23@U!5K3 ;Y;<VF5B3`b}m91U!5K3 ;?; VT5K3@W!3<9Evh3 3D9A23
=9>[
U Q; UT23!587 4#9RQ@9‡MTU7 4 = T 7EDG9R3D;A7 ^\4 =9:7 Q\D@U5B3G;?;<VF5K39A2319R3/(U U!35K=9AVF5K3(=FDH T =9R3DG923=9`=5B3
3<IJ3G4A9R3H¥£ 35PM’"
U 7 T H T M-_b Q"hv 3Š£ 35.v`Om Q5LU!5B3G;?; VT5K3@D3=!5‚6£ =646VFV(p
U 9A23 T =9R3!D9[23G=9 =FDH@9A23
9R3/(
U U!35K=9AVF5B3(=5K313 Id34A9R3H[U Q5K3eDQ!9:7 4 3G=FW T M-b 
GH
d 23%£ 3 T Qa47 9‡M(Q/nm 9A23 T 7 G\V!7 Hˆ[U 3 9?= T H\V3"9RQ@9A23@UT26=;?34626=FDZ34 =FD0W!3&5K3 T =9R3H&9RQ@9A23%>m 5KQXD9
U!5KQXU6=ZT=9:7 Q\D@V9:7 T 7 Ž7EDZ9A23"34G\V=9:7 Q\DOocqwb `tAbž#
d 23 T 3Alm 9126=FDH&;A7 H34 =FD0W!3; 2Q"v D"9RQW!3 ¨  ± b
d 23@5O7 Z\2G92=FD6H&;q7 HT3e7 ;15B3HXV64<3HC7EDG9RQ&Q\D T M T 7 G\V!7 H  Q"‹v =FD6H03G=;A7 T M4 =FD0W!3;<2Q"[v D"9RQW!3   %  % b%  
¨    % ±    %  % 
oiqØb  t
¨  …®±  %

v[23!5K3  7 ;j9A23(HT3!D;q7 9‡M@5l=9:7 Qtv    % b
 Ɋ¯9³Yà9°#È9ÆC°+Ñ JÒ ³>¶+ي¸a¼-º ÆH° È9³Yµ:½ ¼-º¨µÂ¼¨°+Ƶ:½ Þ³YµÂ°ÏµE¯ª°‚´ª¯9³AºªÁ>°¨½ º#µÂ°ªÃw¶A°ª¸Ü³YµEÈA¸a°‚µÂ¼w»>°‚¼9à9°ª¸(áªÕ¡ÑŠ°+Á-¸a°+°+Æ Â³ª´iµEÈ9³AÒ Ù¡³A»>¼-ÈYµ
Ù¹¼-Èe¯9³Y+à9аØJ³A¼YºYÍfÙ °i9à9ºª°ª¼Y¸ÂÍ#ÊMÉ/Ò °+³>ÑAæÁ>°˜º9³A¼9ºªµ#џÆcÈAÍQ¸a³>°Øºª¼9µ‚¾HµÂµE¼B¯>ÆE½ ƳY઴¹°˜³AÒ ´ªÃžÈA°Ò ³Y³wµ:½ ¼-ÆC°¹ºª³9ƨ¸a´ª³A¯eºªÑ1½ ºwÉ(µE¯9¯9³ª°˜ÑnÒ ½ ºª»9¼9¸Ü³ªµ#¸š°9ÙYºªÊ]¼-¶ŠÈªÒ °¹Á-³ª¯BÆC°žµ:½ Ñ"Á¸š°¼-¶5µÂ¼eÁ´ª°ž¯9°+³B´ ÒB½ ºª½°Aµ¡Ð ½ ºwµE¯ª°BÒ ½ µÂ°ª¸Ü³YµEÈA¸a°AÐ¨É ¾
7 XV7 H&;q7 HT34<QXD9A587EWTV9:7 QXDe7 ;_Ž<3!5KQ0;q7ED64<3
9A5l=FD;A7 9:7 QXD6= =<MG3!5 H\V319RQ@9A5l=FD; OQ5 =9:7 Q\D
3 \V6=9:7 QXD
#7 ; ;q7 (U M

















  

4ä(ç


–— ˜A™&— ˜Aš ›fœ:Tž6Ÿ j›G #¡› ŸP¢Y—£¥¤¦Fž ›Y¢
¦T§ ›j¨B6Ÿdœqž#™.!¦6˜:œG©g¤6ª ˜<«!£ ˜ŸK£ ¢.›A©



4 QXU<MF587 ZX29x• ” v

’ ib

T vtW<M `5 _’*=5Es-“367E5



Chapter C. Density change effects



4<QXU MT587 ZX29x• ” v

W ib

T vtW<M `5

’*=5Es-“367E5

–— ˜A™0— ˜<š ›0œqž6Ÿ" j›G #¡› ŸP¢Y—£¥¤¦Fž ›Y¢
¦T§ ›`¨B!Ÿ\œqž#™.!¦6˜:œG©N¤6ª ˜<«!£ ˜ŸK£ ¢: `©

¬ ®








  






 

T
"v /m

/U
"v /m JU
`b¨d#235B3"=5B39A2T5K3 3
T
T
Mb

d 23  Q"v}Q/m 9A23(=7E58ZF=; 7 ; =6Ha7 =FWG9:7 4(7Þb 3(b`DQN23=9L9A5l=FD;Y3!5k7 ;"D3 Z T 7 Z7EW T 3=FD6Hf4 =FD0W!3e7 Z\DQ5K3GHQb
d 27 ;_7 ;j9A23"4 =;Y35v235B3eU!5KQ4 3 ;Y;_7 ;˜£35PM~m8=;?9j=FDHg23G=9h9A5l=FD;?3!5žU3G4626=FD7 ;AU[;`=!5K314 QXD;q7 HT3!5l=FW T M
; T Q"h
v 3!5žo,;?3 3¥U[Q5K3H7 ;:46V;q7 Q\D=FW!QXV9`Ha7aU[3!D;q7 Q\D T 3G;?;#DFV`U(W!3!5k7EDzqk26=FUG9R35(tAbwd 27 ;5¬7ED6H&Q/mL7 ;
¬ DQ"v D(=;%!§ =FDFDQ  Q"v1b
!
U U T 7 ;?9[U!Q;Y;q7EW T 314G=;?37 ;Ÿ[v 23!D9A27 ;

=FDQ9A235bU!Q;?;A7EW T 7 9‡Me7 ;`9A235B3e7 ; =FDf23G=9j9A5K=FD;?35 =FDH09A23";q7a
23=9L9A5l=FD;¹Om 3!5k7 ;#=e4<QXD;R9?=FD9Šbd 23@23=9L9A5l=FD;¹Om 3!5k7 ; ;A7 ZXD7 ^\4 =FD9_7ED4 =;Y3n
v 235B3"9A23!5K37 ;
4623/"
U 7 4G= T 5B3=64A9:7 Q\D;_;?Qf[U 3<9:7aU 3e5K3AOm 35B3H&9RQ0=;#4<Qf(U WTV;q7 Q\DMb¨d 27 ;  Q"v 7 ;1D6=`[U 3GH&Q\D ! =!5lH
€ 3 M T 367 ZX2Hb
t
U = T 4 =;Y3(bd 23  Q"ov 7 ;126=;"23=9

} 4G=;?3@W!3<9Ehv 3 3D19A23"9Ehv QCU!5K3A£ 7 QXV; 4 =;Y3(7 ;`9A23e7 ;?Q9A235:
9A5K=FD;+Om 35bWTV9_7 ; T Q"†
v 3!DQZ\29RQ’A¬ 3 3U9A23[9R3](U U!3!5l=9AVF5B34<Q\D;?9?=FDG9Šb¨d 27 ;#7 ;L9A2314G=;?3n[v 23!D=(ZF=;
 Q"j
v ;˜Om Q5m= T Q\DZ&H7 ;?9?=FD4 3k.o 7EDQ5lH35*Q/mB¬ 7 T QJU 3<9R3!5K;ªtŠbwPS D; V4!24 =;?3G;GvF9A23ZT=;`9R3/U U!3!5l=9AV37 ;
34G\V= T 9RQ@;YQ5,5KQXD6Ha7EDZe9R3/(
U U!35K=9AVF5K3(bŸS m 9A23;?Q\VTD6H7EDZ&=!5K37EDfVTD7 Om Q5EU 9R3](U U!3!5l=9AVT5K3zOo 9A26=9 7 ;
;q7a(
U U T 7 ;R9j4G=;?3%[v 27 462~hv 3 T 7aA¬ 3 t 7 ; 4 = T–T 7 ;?Q9A235:1U = T 4 =;Y3(b “@=9A23]U =9:7 4 = T MGvX7 9[7 ;`9A23;A7a(U U T 7 ;?9
4 =;?3 u b
SPDeH7 34G=;R9:7EDZtvF9A23"=7E58ZF=;  Q"`v ;w>m 5KQJp
U 9A23(4 = £ 7 9,M9RQ&;YQXVF5KHa7EDZC7ED~£ 3!5BMC5l=FU!7 Hˆ1U =FDTD3!5ibžd 27 ;
;q7 9AV6=9:7 QXDe7 ;Ÿ£ 3!5BMe4 T QT;?319A23^-5K;R9%[
U QaHT3 T hv 3Ha7 ;Y4!5O7EW!3HNW!3AOm Q5K3(b n3!D64<3Fv`hv 3"4G=FD=;?; V([U 319A26=9˜Om Q5
U=FDMQ/m 9A23(4G=;?3G;j9A23  Q"ov 7 ;"5K3 ;A7ED=FW T M=6Ha7 =FWG9:7 4 ^ bž#d 235B3ŠOm Q5B3Fv`hv 37EDG9A5KQaHXV64<319A23z!§ =FDTDQ  Q"}v =FD6H
=ZT=7ED@7ED=e;q7a
U U T 7 ;?9ØOm Q5:U¥b
¶9¸a°+ÆC­ªÆiÉÈA¶ª¸a°˜¸a°i¾Þ½ Æ#°ª¸a´¹°¼-µÂºª¼ØƵCµÂ³Y°¹µ¡³ª´ª½ º˜¯Ø´¹µE¼-¯>ºª½ ơƵ#Þ´+³Y¼-µÂº9°ªÑ¸Þ½ Ȫ³A´iÒ µ/³ª¸aÆC¸aµ‚°¹³ ½ º˜Ð Á٨´¹³ªÆ:ÆC°+ÆYÐJ®‚¯9°Ø¸a°¹³AҊÆE½ Ãw¶AÒ ½ ÆCµf´¹³ªÆC°Ø½ ÆQµE¯ª°Ø½ ÆC¼-ºYµE¸a¼-¶>½
´ ¼YÍz¾Ü¼A¸(ͯ>½ ´ª¯ØµE¯ª°
µÂ½ Æ¡°ªÃ˜º9M ¼n¶>½ º1°ªÃ¸Ü³Y¶>¼ŠµE¼-ъÈA¼>°ª¸a¸#°eҊµÂÑA½¼eƞ°+Æc³Y½ ½ ºªÁ-´¹´ª´+º5¸a¼-°¹µEÈA³ª¯ªºYÆ:°%µ#°+Ñ/¾ÞÞ¼>Ш°i¸K®‚µC½ ³Aµ#¯>Ò]½ ³AÆ¨Ñ ºª¸a³Aџ¼-º9¶ªµÂ³A ƼÒ Ùª "]Æc½¼¹ºªÆ¨ÍÑŸ½ ƁµE͂¯ªÃ˜½°ØµEȪ¯e°ª´ª¸×¯5µE¸a¯9¼AÞ°5¸K¼>½ ³>ºØ¸a½ °Ø¸ÏµE¯ª³A´¹°w¼-ºªÑ~Ãw³ªÆC¶AÆ:Æi¼-Ò ÈA½ ´¹Ò Ãw½ ³Y Ñ µÂ¶Y°+µ:°+Ñ1½ Ñ]¼-Ðe³AºBºª®‚¼9Ñ5¾K¯ªÑA°n½ Ñ °9½ ¶>¯9³A°ª°¹»>ºª³Y½ ´
µØµÂ°+ "½Ñ~Ƙ¼Yͨ¼-¸a°ªºBÐ Ò °¹µE³ª¯ªÑ1
° µÂ ¼n¼ÝµE¯ªÐ °5`³>¸a½ °+¸‚ÆC°9³>ºYº9µEÑ1Ò ÙYµEÊ]¯ªµE°_¯ª°ª³>¸a½ ° ¸
d

23  Q †Q n=7E5d9A5KQXVZX2"9A23 3!D9:7EDZe;?M;?9R3 ~7 ;_=  Q
Q 4 Q (U!5K3 ;Y;q7EW 3[; VTW;R9?=FD64<3
7 HT3G= QHT3 ;`A9 26=9`4G=FDfU!Q!9R3DG9:7 Q\D= M(Ha7 ;Y46587EW!3"9A231;A7 9AV=9:7 Q\D

TU

ä"ä


<

Chapter D. Fanno Flow

TŽ_).&/

</[+n


frincional
force
P1
V1
T1
rho1

Cross Sectional
area, A

P2
V2
T2
rho2

§7 Z\VT5K3Oeb jØq-Q\DG9A5KQ T £Q T V(U31Q]mm9A23ZT=;  Q"v 7ED4<QXD;R9?=FD9`4!5BQT;?;_;?34A9:7 Q\D
    !#     


 
      q-Q\D;A7 H35m=ZF=;  Q"j
v ;j9A2T5KQXVZX2(=@4<QXD6H\V!7 9˜v 7 9A2=~m>587 4A9:7 Q\DWo8;Y3 3k§7 Z\VT5K3Oeb bd 23¥U=;?;
 
4<Q\D;Y3!5Þ£=9:7 Q\D~Om Q5-9A23(4 QXD9A5BQ T £ Q T V`[
U 37 ;
oYeb t
    
d 23"3!D3!5KZ!Me4 QXD;?3!5Þ£ 7 QXDzRo VFDHT3!5m9A23(4 QXD;<587 4A9:7 QXDQ]bm 7 HT3G=FW9:7 4  Q"ve[t 5B3=6H;
     
oYeb (t


        
d 23%Om Q5l4<3=64A9:7EDZ&QXD9A23ZT=;[7 ;`9A23%>m 587 4A9:7 Q\De=FDH@9A23¥[U QJU 3!D9AV(~
#
U 4<Q\D;Y3!5Þ£ =9:7 Q\D05B3=6H;
oYeb ç t
I  
  

§ Q5m;q7aU U T lm M9A23&U!5K3 ;?3DG9?=9:7 Q\D!"Om QQ!9ADQ!9R3!DQ!9_D3 ;Y;Y=5 T M~Om Q5*9A23@U!5K3 ;?3DG9?=9:7 Q\D(4 =FDfW!34 T QT;?319RQ047E5l46V T =!5
6
vh3=;?;<V`[U 319A23(4<QXD6H\V!7 9h9RQNW!3(=@47E5l46V T =!5-9A23!5K3AOm Q5K3Tv
   

oYeb t
   



  7 ;_3GXV6= T 9RQ
 b * 9:7 T 7 Ž7EDZ9A23(HT3<^-D7 =9:7 QXD"Q/nm 9A231^-5l4A9:7 QXD~8m =64<9RQ5
  =FDH¥hv 3

{nQ9R39A26=9  
 
QXW9?=7ED9A23%Om Q T–T Q"v 7EDZ


oYeb ä t
Š
¨

®
    ±  

  
"!

 9:7 T 7 Ž7EDZ@9A23HT3<^-D7 9:7 QXDQ/nm 9A231;YQXVFDH&; U!3 3H&QXD3"4G=FDQXW9?=7ED"9A231Om Q T–T Q"v 7EDZ
*


 # %$    
oYeb I(t
  
!
$ 
%


'&
q QXD £ 3!5B9:7EDZ@9A2313<ˆFU5B3G;R9:7 QXD~Om Q5˜o    _t =FD6H¥Om Q5)(    7ED9R3!5E€
*
U Q]m 9A230“e=64!20DTVFW(U 3!5*M 367 T H;
®  $ +  $ 


oYeb s(t
!
 *

Š
¨
®

0
/1 

 $
 $.,
4<QXU MT587 ZX29x• ” v T vtW<MW`
 5ib ’*=5Es-“367E5
–— ˜A™0— ˜<š ›0œqž6Ÿ" j›G #¡› ŸP¢Y—£¥¤¦Fž ›Y¢






¦T§ ›`¨B!Ÿ\œqž#™.!¦6˜:œG©N¤6ª ˜<«!£ ˜ŸK£ ¢: `©

¬

N

Section D.1. Introdcion

SED9R3!5KZT=9:7EDZ T =;?9j3GXV6=9:7 QXDM 367 T H
® ®  $    ¸® jdY /   $ 







!

 $ 
 ®  / 1  $ 
d 23e5K3 ; V T 9R;_Q]mm 9A27 ; 34G\V=9:7 Q\D=5K3&U T Q9R3GHf7EDW§7 Z\VT5K3 
§a7 ZXVF5B3zeb fjB§!=FDFDQ  Q"v‹=;#=~m>VFD4<9:7 QXD(Q/m

4ä s


–— ˜A™&— ˜Aš ›fœ:Tž6Ÿ j›G #¡› ŸP¢Y—£¥¤¦Fž ›Y¢
¦T§ ›j¨B6Ÿdœqž#™.!¦6˜:œG©g¤6ª ˜<«!£ ˜ŸK£ ¢.›A©

oYeb r(t
-


 



4 QXU<MF587 ZX29x• ” v

’ ib

T vtW<M `5 _’*=5Es-“367E5

Chapter D. Fanno Flow



4<QXU MT587 ZX29x• ” v

W ib

T vtW<M `5

’*=5Es-“367E5

–— ˜A™0— ˜<š ›0œqž6Ÿ" j›G #¡› ŸP¢Y—£¥¤¦Fž ›Y¢
¦T§ ›`¨B!Ÿ\œqž#™.!¦6˜:œG©N¤6ª ˜<«!£ ˜ŸK£ ¢: `©

¬ 







    

ä 




Chapter E. Reference


 

 



T  !#"%$& !

')(*,+-(*./-0213&4657/85:9;/4=<>(?A@CBD3/><
B;1E/FG1H4I0213:+J1HB&*K08LM@&N *OH? *4P? <K5L

Q

N



 








 "I !#"$%'&(')*)*+ *, .-0/'1 $2
 "  " $
'- 354I76 98  
&:6,$H 9;  '<:=  '<
?> @9AB32 C<; > C<
$DE- $F1 $<8
 C1G/- 
K 9<IH  
, ;$  $ , $- '1 $F<
FH  
 - $$ , $5J $F-  ;
4 GKL- $M63 LN@<OQPSRUT.PWVXYZ[T\)*%M]E^_`!a!S%&bdce9)F!gfC7f )'%  "- C<<;$8DH9- 3 
" C<';
< $M3 
 ;DH$Bh:i  Mj 
Hk,i "%$& ! \; @
l  nmo%5]9p!rqsf0^te9)^):!ufC0vbf0%wes^_`!a!Mx^7#&'f0zygp!7f0%M] L4 
, $32 3  A$< , $k3,
%H
" C<';
< $M3 
 
Hk,i "%$& ! \; @l  
&
< '- p,3 3 Ho1 3a3
,P'<3{H $ HP $M3d3 $:3 C<
, ;$ H P$IH P$$6
$& 'H< |9;/ $~}:).xF^7%
)*Q€E%M]Ef0%M^7f0%M]'7^_f  !‚%'&nƒMy„%)' )p]v  p9… †.p6l ‡†.pI 
Hk,i "%$& ! \;   D F62$=
 #
D   '<:= ; .- =3
$& C< ?ˆ .‰ CpIŠ E4 P$M3d3uD/ G$G= $ 3
K C< E…
1 s= $F- H
, &F//'1 /'1  C< *}:).xF^7%s)*Q€E%]\f0%'MM^7f0%]‹@)^$Œ@%&sxp!M7^@v  p9…    I 
Hk,i "%$& ! \;   D F62$=
 #
D  ˆ  ;   '<:= ; .- =3
$& C< Lˆ s‰ CpI 
! , $F<
K C<  C< HP$M3d3uD/ G$z= $
3
K C
< ‡}F)sx^_%9)*t9CxFf0&:!5€E%M]Ef0%M^7f0%M]  9… j62 jIŠ 
Hk,i "%$& ! \; I'<=Ž C<6- $H L Cp
j 
8:/DP
$ ‚‘“’ '- F/- 
K 9<p63 ”R•f0–TEp!M7f0%]—€E%M]Ef0%M^ 
˜ sŠ9… †Š 2   ˜  , $1  $H  $$1  $H
I$F™ - ';
< $  ‰ "M@†I ED*3aK3  *3uD/ $- –3 .-0/
K .<<'/1 $H
|.;/ $z= $G|9/ $- |.;/ $M3 HP  - $F1 $3  1 9/ , $F1 $F<
H$H71 ';
< $F<
š= $M3 $8'/› .D/ P'<
$M3 ?I4 H
3 ?>  '&< $
# & ,  
 
  ˜ 
g;
6 C<  #D   "    H$6
 P ,    LPN   '<:=  :D= &  C,6  ,   ˜ @jIŠ *:h $ 
g/:H=  H


’ 3
K C< 3
$1U3  " $8'<3 FH " s= $- 83 —Œ œuž!rŸ.P•+&*ŸtO 'x+‡¡QŸ ¢LŸ ¢?Ÿk£QŸB¤¦¥$x00p7f0%b)*B7„'

P•yg&'M§Sv)*?¢EyMf0M%'yM`!‚)*o¡¨Ÿ0¢?Ÿ ¢LŸ@£9©  &; $3•;l sI† 
 P'&
< & tª   @lI ?"tv*&^'xF0f0yGR•`!gf ]\%)s?¢?7f000f0%][¥Bp!gf0%:!‚%&‡¥$xyM+€E%'M^@]vR•f !a!uf e*'7f )^«! 
A   #QD/ G$'%/ FH ˆ $8F- '1 
K .<  DE;< C;< $$ C;< C"%9<   D G†l   $F< , $  #’ 9-  P:= 
7
 G$ , F6  ‰  ˆ  
_1 $F
<
,G98/
 s‰   '<:=’ '/ '¬  i  Cpj  " C< C61 ­ 
K 9< FH $F<
,P C;< $= D3
H G23
 C%
< '-0/1 C</'1 ; 
­ .<
'- 9- = & &'1  $H¨= $ 3
K C< 3 ®ƒ^%!`yp7f )*%!S)*
OQPS£¨Œ qs¢?~€  p†9… j9, *jŠ 
pŠ.

BIBLIOGRAPHY

’# F6M3    @ŠI?RUTt£¨[£tyg)*§G§GM%'&'M&t^).yM&*x^_`!S‡pE. )t^7M&'f0yp)^¨¢vF!M7§ 
1 $H
'<  $–’ 3
K C<; ‹NC<3
K
g/
$  N@<;   $M354t-  C<;$M3  NC-0- C<; 3
’# F6M3    '<:=Ž '-0- 
9‰D@2'h $& '<9-  
, '<3{H $H C<
, $/'<H
$p=~6; C<; =.1w…o4 P IG$3a3
'<M
= HP3 H$8
{83 \NC<ƒ^%!`yp7f )*%!UV:YZŒ@%*7^_%'7f )'%'¢?RUTt€  " C<'<;$8DH.- 3  "- C<'<$3 H
 I&DH$H
; i¦ho2:i  j 
  , $ 
 '<= #./'<=3   @
  " s= $- C<
, ;$ G$3a3uD/ P$G= $ 3
K C< HP $M3d3#/p,3 C<  ./'<:= =
'<=KL
<
$ $F- $F1 $F<
I1 $
, s=83 }:).xF^7%s)*B§5'7^_f  t^).yMž!d!gf0%] ƒMyM„'%)' )]v  Š29… Š&Š *  
  , 3 
sD
‰ @l \D
$8
{73 H
, ;$%P$F- 
K 9<p3 H !  $
 $$<1 .-
$F<1 $
'-  C<5H $8$=3 3
$1U3 '<=
8:
=  '/'- L/ =  C<G= $63
K C< 1 &H H C;< $M3 9N@<ƒ^ %:!žy7f )'%:!FYZŒ@%*7^_%'7f )'%*¢?RUTt€  

 ./ 83  &DH$H ; irhl:i`†Fj 
PDH$ 
# CpŠI
 LD
$8,
FH , $8<
'<= 
$ HP$83 9<
, $ H P23
 FHQ= $ 83
K C;< 
ƒ^ %:!žy7f )'%:!š)sEP•§G^_f0yu%‡)sx%'&^@v'§–M% !‚¢.).yMf00v  l9… †; s2Fj 
D :6,$HG
 #D @I   C61 C- H

%';< '- 23 3 DD- $p%=

, ;$- $–’ 3
K C< ‹4 G $3a3 ‹}F)sx^_%s)s
€E%M]Ef0%M^7f0%M]['7^_f  !‚%'&ƒMy„%)' )p]v  … 2;2 *2  ˜  sj 8 ,

DE- 2i " $H &'-   "  ? C/  D‰   '<:= " C-0- $ Lˆ 
@ 
3
$M3
K C1 
K C< 1 s= $-H  B= $ 3
HGs=9;
/ 
{83 ?N@<OQPSRUT.PWVXYZ[T\)*%M]E^_`!a!S%&‡ac:e9):!gfC7f )*%  "- C<;< $8DH9- 3  "- C<;< $M>3 H
 ;DH$
hFi  jj 
>  !  '<'6M3Mpl \"tv*&^'x0f0yz"$%'&'¥B)*)*+ #"% P$M3 '<:=#’    '<>3 3 
  '<pK3 83 
> .<:=>3 $ Lª   8‰ $& ¦= $F<3 Lª   '<= 8 .1U3 \; CpI2  8 <
, ;$ C<L;/ $F&< $ FH
, $6$u›
9<=
K .<73 9<
, $
$F
<
,P C<'1 $F<
P
$% C<
, ;$z= $ , $- '1 $F<
P$ .< FH GH P$$  P./'<= 
g/   /- $8<
 $
‹P e'e.0f0&
¢\yMf0%*7f'yG£Bž!ug:^_y„  &; $3•2l;l s2Il 
; H  $H L *Ž @I† *h ;$ P$
K 8'- '&< '- p,3 3 '<:= $g› H$H
C1 $8<
'-   3 $ , 
K .< H  ! $8<
, D1 $F<
=.D/  C;< -9- = & &'1  $H KL-0- C;< R•f0wT\p!7f0%M]—€E%]\f0%'MM^  †Š ˜  s29… 22 
ª '<p>3 $F< 
G
, D/  9; CpŠ .9CxFf0&byM„%f0y`! '‰  '<IŽ C- $ '<=  9<p3  N@&<   ˜ $ ¬  _6  ˜ $ ¬  76 
ª $F<:= $k>3 .< ?> "MCpŠIŠ LmQeEM%‹TL„%%'ME. ) #" &:1 C-0- '<4B/  - 3 H C;< b’   ˜ $ ¬  _6  ˜ $
¬  76 
ª  P&;  
 ; '<:= "- C-0- $H Lˆ 
@   $ 83
K C;< = $z= $ $8
K .<3… 91 /
$H ,3 C1G/'- 
K .< FH
'/3 $M
3 '<:= $ $8
{83 ?N@<OQPSRUT.PWVXYZ[T\)*%M]E^_`!a!S%&‡ac:e9):!gfC7f )*%  "- C<;< $8DH9- 3  "- C<;< $M>3 H
 
;DH$Bh:i  †
2
ª / Lª '<:=
G PH9/- 3   
CpŠ  " 
, ;$F1 
K 8'-.1 s= $F- C;< HB>3 .- = IK 
K .< '<:=‹1 $F-
K C;< \…
 P$ , $ n).&'M0f0%]‡¢Ef0§wxF '7f )*%'7^¦Ÿ\¢EyMfCŸ €E%]?Ÿ  jE… 2., s2I
Š
ª /  ‰   ˆ '1 '- C< D'1     "%$$H 3 9< 9;   D F62$=
 #D   '<:= ; .- =3
$& C< ?ˆ .‰ CpI† ?DD› H$ C1 $F<
'<= .1 '
/
$H 1 s= $F- C;< H
, ;$  o:3 C< HG$3a3M/ P$G= $ 83
K C;< 823 C;< 3 \N@<wP¢?~€'qLT Œ €
R•ž!gf ]E%   '< > P'&<  K3   ’ '- H  7H<  
7H< '¬ @. ‹¢\M0yp7f )*%–)sEes^ ).yM`!a!z`^7f (0`!#@)^ &f0zyup!M7f0%] L4 
, ;$M,3 3 98   

$
A$< , $k,3
8
C1  ’ "M '<:=  '<
?> .‰ @Il 
< DD- 8
K .< FH ;2 # 3 9- = IK 8
K .< ';< '- 23 3
~- G $
.%
1 - $u› 3
K C;< 3 ?NC<!"#$Eyf'y5^_f0§ f0%s7M^7%F'7f )*%F.yu)'%* M^7M%'yMI)'%b§z)s&'M0f0%]~)*tygp!M7f0%]
%&w!`)'0f0&'f'yg'7f )*%   C;< DH P$

 

 

†

T  !#"%$& !

')(*,+-(*./-0213&4657/85:9;/4=<>(?A@CBD3/><
B;1E/FG1H4I0213:+J1HB&*K08LM@&N *OH? *4P? <K5L

&%'
Q

BIBLIOGRAPHY

 C <=3 $  '<:=Ž '-0- &$  ‰  > @†ED
$8
H , $F<
•3, ­$ '<=‡=$32 .<  -0/   8
K .< H &,
K $ 
1 $
'-*=$8 3d32 C<;  = $
$u›
g/D C<; '<:=KL-0- C< FHQ3 ;H
•3u- $$ , $69<–= $ 3
K C< 3>./'<=9<$3a3\N@<
ƒ^ %:!žy7f )'%:!:YZ¢?RUTt€—Œ@%*7^_%'7f )'%\R•f0TEp!M7f0%]—TE)'%]\^7ž!d!  ’ H 8;  I&DH$Ho  2†
" :=3 $<  
4 '<=  , $<=3 $<'p2 *h¨/   /'- $F<
  P$M3 '<:M
= 8:I= P'/'- d/'1 38s}F)sx^_%9)*t9CxFf0&
yM„%f0y`!  †9…@, s†Il 
"  $ tˆ #@Fj \Œ@
% sxF%yU)s 0fsxFf0&b§–pMpyM„^yp7^¨)'%„'g'o7^ %:!u ^$&sxF^7f0%M]&'f0
ygp!7f0%M#] ?4 
, ;$M,3 3  ’ 3 $#Ž $M3
$H7< ˆ $M>3 $H , $bAH< , $H 23
8LDE;< C;< $$H
C;<  1 $
'-0-0D/ P H8
" C&
<  $     
$- 3 9<    '<:=J .-0- $  J  ˆ @. 
&< '- p,3 :3 '<=   ;

$_<3 '<=3 .- = IK 
K 9<
 ;$F;
< .1 $F&<  C<–= $ 83
K C;< G $3a>3 $M63 }*Ÿ €E%]?ŸL‡My„*Ÿ ƒMy„%)' )p]vpŸ*P¢?~€  2\… †&Š *2  I† 
˜ ./ $F<  h  '<:=’ H   ‰ CpŠ Ž 
$H
&< '-  9/ $ 
g/:= $M3 FH ; P ,
h C-
‚’ 3
K C< #’ IH$
-0- ;%91 H.;< $F<
{83 Pš*¢ ƒ^%!  &; $3•l9; sl†I 
8 3   7;< $  "M
  "%  - $  ’ t#D   "- C-0- $H Lˆ 
  '<= '-0- $F< ?  ª CpI2  "%s= $F- C;< HQ= $
3
K C
< MHP $M3d3 $3U/23 C;< ~1 ; .1 >3 FH
EN@<OQPSRUT.PWV :YZ[T\)*%M]E^_`!a!‚%&bdce9)F!gfC7f )*% 
,
’Q- $ $- '<= 98   &DH$HBho2Fi  2I† 
4 ; Lˆ  ª  > CpŠ.D E.Cxf0&yM„%f0y`! *‰  '<z
I
Ž C- $ '<:=  .<3  N@&<   ˜ $ ¬  76  ˜ $ ¬  _D6 
ˆ  J P
g&< '1  ˜ CpŠIl *h ;$ 8:=  '/'- d/'1 %3   '-0- $
s}F).xF^7%F9)*¨"tv'&'^ 'x0f0y–R•f@Ÿ.P¢ Tt€ 
;; $M35  ;
 ?2.D 9
 ªB¬ l 
 && 3   Cpl† ‡P•%% v.7f0yg'!rxF&v)*Q7„'#&'f05ygp!7f0%M]‡e*^).yMž!d! ?4 
, $23 3  #’ 9-0/1  
A$< , $k,3

 &DH !P 
 ª @l2  ƒ?„'GRBv'%§Gf0yž!‚%'&7„'M^7§5).&Mv*%F§–f0yž!‚)* T\)*§Ie*^7ž!a!uf0(05.Cxf0&‡9 ) 
, 9-0/1 $PN .‰  '<zŽ C- $ '<:=  .<3  ˜ $ ¬  76 

gD/ 7,6 $  Ž  > I'<=Ž '-0- &$  ‰  > CpŠŠ  ; 
K C< FH = $683
K C;< 3  ƒ^%!`yp7f )'%:!S)*?P•§GM^7f0yg%
)sx%&'^@v'§G%  !‚¢.).yMf00v  29… lŠ; *l 
  '61 C&< 
, ;'<  ’  ˆ  '<=J .-0- $  J  ˆ @2  8 %<
, $bDE<
, ;'- " $
, ;s= —ŒC%s¨}'ŸtO•x§wŸL‡p7„sŸ
"og'$9CxFf0&. )  29… †2;2 *†jj 
h ;.1 $  "  '<:=  P$ , :6  D‰  ˆ @l  8 
K C1 '-'3u- ®3 ;H
, $F-  ;
 GKL- $M3oH   .- = H ;'1  $H


= $ 83
K C;< ?N@<OQPSRUT.P T\)*%M]E^_`!a!S%&‡ac:e9):!gfC7f )*% N@<= '&< DH.- 3 N@<= '&<   ;DH$thl:i  †Fj 
J $& CH< C6 
LGN @Š†  ƒ?„'g)^@v)*E!aeEyMf 9yup!M7f0%]§Gp7„).
& 
 "~D  ˜ $ ¬  76 
J $& CH< C6 
LGN @ŠŠ ':h $_1 *= ';< '61 IH
&
 k3 C<1 $
'- C<  $,
K .<s… $ $8
HtH 
,
K .< 9%< 3
98
<
$8<
'<=b|9;/ '-
8?N@<nƒ^%!`yp7f )'%:!
YZ¢?RUTt€—Œ@%s7M^7%F'7f )*%F\R•f0TEp!M7f0%][€'ce9)F!gfC7f )'% 
T\)*%M]E^_`!a!  ’Q- $ , $- '<= 98   &DH$H  I2 
J 3  '&< 
, ;'<      
C<6F1 '<  ’   4  =
$  Ž   '<:=4tD/ P $HG
 ˆ #"MCp 94 P*=9&/ ,
K .< H
2l‡1 H
 Q1 ./'<
  &:6,$
 
, ;$1 $
'- .%1 HG$3a,3 .<5H  _1 C< MHP $M3d83 ?N@<‡OQPSRUT.PWVXYZ
T\)*%M]E^_`!a!‚%'&bac:e9):!gfC7f )*%  "- C<;< $8DH9- 3  "- C<;< $M>3 H
  &DH$Hth:i`†9 
Ž ; .&< '<3u;6  PN '<:=’ &'1 &'< ?>  ª CpI2 'h ;$  
C< H '/ ?:3 '<:=3u-0;/ 3 '<=
, ;$  
 C%< 
g
/   /- $8<
•3u-0;/ ~}'Ÿ .Cxf0&‡yM„%f0y`!  &; $3S†. *22Il 

Š2

')(*,+ (*,./ 0K13&4 57/85:9;/4=<>(?A@CBD3/><
B;1E/7FG1&4 0213:+J1HB&*K08L @&N *OH? *4P? <J/,L

D
 

 

†

T    !#"%$& !

Sponsor Documents

Or use your account on DocShare.tips

Hide

Forgot your password?

Or register your new account on DocShare.tips

Hide

Lost your password? Please enter your email address. You will receive a link to create a new password.

Back to log-in

Close