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COMPENSACION DE CAUDALES CON H. CROSS (Aplicación del binomio de Newton) Qdis = 120 (l/s)

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COMPENSA COMPE NSACION CION D DE E CAUDA CAUDALES LES CO CON N H. CRO CROSS SS (A (Aplica plicación ción d del el bin binom om !di" # $%&  Aportes T1 = T2 =

72 48

(l'"

  

(l/s) (l/s)

   

Consumos "odo $nodo  A 0.07 8.40 ' 0.08 9.60 C 0.10 12.00  0.0 6.00 * 0.10 12.00 + 0.15 18.00 , 0.20 24.00 1.00 120.00

Cotas del agua T1 2668.70 T2 2659.20 Cotas tuer!a "odo %tu A 2608 ' 2610 C 2605  2620 * 2600 + 2612 , 2605

Tramo T2&A A&' '&C A& &C *& A&, +&, *&+ T1&*

"# 0 1 2  4 5 6 7 8 9

 Anillo III - V Virtual  irtual 

18.00

 $$.)% *

105.70

+

 Anillo I 

%).)%

960.00

6.00

) % $

 

, -&.&+

1260.00

E

%agua

2668.70

D

800.00

/ 0.%/

12.00

1000.00

C % ,.0

 

12.00

92.50

T*A * *CAC"* Tramo

0

1

 ΣQ,  AA

F 1=

Qo

 - Q1

 ΣQ, B

F 2=

 ΣQ,C 

F 3=

 ΣQ, D

F 4=

 ΣQ,  

F 5=

 ΣQ,F 

F 6 =

 ΣQ,! 

F " =

 Σ# $1

F %=

 Σ# $2

F '=

 Σ# $3

F 10=

Q1

2

3

4

5

 - Q3

6

 - Q6 

 - Q2 Q2

 +Q4 Q3

 - Q4

 +Q5  - Q5

Q6  & 3Q3n & 1Q1n & 0Q0n

 +& 2Q2n

 - & 3Q3n  +& 3Q3n

 - & 5Q5n  - & 4Q4n  - & 5Q5n

 - & 6 Q6 n

 

 

 

o de Newton COMPENSACION DE COMPENSACION MEDI ME DIA AN NE E H. CR CROS OS  An3llo 10 , 67⋅ L  K = 1,852 4,87 C  ∗ D tram 48.00 15.6 5.76 12.16 6.24 0.08 12.08 11.92 29.92 72.00

 0.247 0.140 0.086 0.124 0.089 0.196 0.124 0.12 0.195 0.0

Dc &.-%, &.$,& &.$&& &.$%, &.$&& &.%&& &.$%, &.$%, &.%&& &.%,&

                     

 0.579 0.869 0.74 0.991 0.794 0.958 0.985 0.971 0.952 1.467

 840.0 959.9 92.5 1000.0 10 1000.0 800.0 1050.0 105.7 960.0 1 26 260.0

C 150 150 150 150 150 150 150 150 150 150

 199.27 98.4 68152 24894 7798 2018.9 26 2619 25 2578 2422.7 1072.6



An3llo 

 An3llo 

24.00

 2 0 $%.&+ 1050.00 8.40

$%.$0

& /+

1000.00

840.00

A

%agua

 

 Anillo II 

$ $,.-0 959.90

 1

% 2657.20

Tramo  7 8 5 6

 24894 2578 2422.7 2018.9 2619

Tramo 1 2  4

 98.4 68152 24894 7798

Tramo 0  5 9

 199.27 24894 2018.9 1072.6

 

9.60

"

%

 - Q%  - Q" 

'

 +Q'

 +Q%

 +Q"   +& " Q" n

(n

 - (A

=

0

 - (B

=

0

 - (C 

=

0

 - (D

=

0

 - ( 

=

0

 - (F 

=

0

 - (! 

=

0

=

0

=

0

=

0

 +& %Q%n

 - & 'Q'n

 +  +))T1-T2*

 

   

CAUDALES (1inomio de Newton # 0.0122 0.0119 0.0299 &0 &0.0 .001 01 &0 &0.0 .0121 121

 7.066 7. 7.054 .  .645 &.0 & .069 69 &7. &7 .5 5 7.61

/ 58 581.22 591.89 121.84   102.01   607.12 2004.1

# 0.0154 0.0058 &0.0122 &0.0 122 &0.0 &0.0062 062

 4. 4.05 4. 4.85 &7.0 &7 .066 66 &6.0 &6 .089 89 &.997

/ 280.25 842.26   581.22   976.02 2679.8

# 0.0480 0.0122 &0 &0.0 .001 01 &0.0 .0720 720 &0 T1&T2 =

 0. 0.720 7.066 &.0 & .069 69 &8.2 &8 .208 08 9.500 6.009

/ 14.992 58 581.22   102.01   114 812.22

$1 $2 &0.002 &0.0008 &0.002 &0.002 &0.002 &0.002 &0.002 $1

0.002

$1

T 1 $ : &0.004 0. 0.0054 0.0099 0.0279 &0.004 &0.061 &0.0141

 # 24894 0 0..0054 2578 0.0099 2422.7 0.0279 2018.9   &0 &0.0 .061 61 2619   &0 &0.0 .0141 141

 1.558 5 5..05  ..210 &4.2 &4 .29 9 &9.7 &9 .720 20 &4.209

/ 289.9 506.87 114.92   119.04   691.05 1721.8

$2 0.0008 0.0008 0.0008 0.0008 0.0008

: 0.0162 0.0066 0.004 &0.0054 &0.0054

Tramo 1 2  4

 # 98.4 0.0162 68152 0.0066 24894   &0 &0.0 .0054 054 7798   &0 &0.0 .0054 054

 4 4..72 6 6..18 &1.5 &1 .558 58 &4.7 &4 .714 14 4.644

/ 292.72 941.59   289.9   867.59 291.8

$2

$ : &0.004 0. 0.044 &0.004 0. 0.0054 &0.004 &0.061 &0.004 &0.076 &0.004

Tramo 0  5 9

 # 199.27 0.0440 24894 0 0..0054 2018.9   &0 &0.0 .061 61 1072.6   &0 &0.0 .0760 760 T1&T2 =

 0 0..61 1.558 &4.2 &4 .29 9 &9.0 &9 .071 71 9.500 &1.69

/ 1.92 289.9   119.04   119.6 542.2

&0.002 &0.0008 &0.002

$

Tramo  7 8 5 6

 

T $1

$2

$

0 0..0 00 01 1  0.00105 0.00169 0.001 0.001 0.00169   0.001   0.001 $1

&0.0 &0 .001 01

$1

$2 $ &0.001 &0.001 &0.0 &0 .001 01 &0. &0.00 0017 17   &0.001   &0.001 $2

$ 0.00169 0.001 0.00105 0.00169 0.001 0.00169   0.00169   0.00169

2 :

Tramo

0 9 4 0..0 00 11 0.029 &0.01 &0.0127

   

 7 8 5 6

25 47 88 9 4 00..00017 5 2 10 2422.69 0.0290 2018.91   &0 &0.0 .048 48 2619   &0.0 &0.010 10

2 86 82 1 5 5 82 4..0 72 19 7 6 6...0  ..47 118.58 &4.0 &4 .015 15   1 115. 15.442 442 &8.4 &8 .42 2   646.98 646.98  &0.058 1817.75

: 0.0151 0.0055 &0.0094 &0.0065

Tramo 1 2      4

 # 98.4 0.015 68152 0.0057 24894   &0 &0.0 .0075 075 7798   &0.0 &0.006 06

 / $1 4 4..287 279.71 4. 4.799 87.974 &2.8 &2 .881 81   84.717 84.717 &2* &2*&00 &005 5 &6.1 &6 .151 51   980.608 0.05 248

: 0 .0 .0457 0.0094 &0.01 &0.074

Tramo 0    5   9

 # 199.274 0 .0 .0442 24894 0.0075 2018.91   &0 &0.0 .048 48 1072.62   &0.0 &0.0758 758 T1&T2 =

 / 0.619 1.9845 2.881 84.717 &4.0 &4 .015 15   1 115. 15.442 442 &9.0 &9 .020 20   119.056 9.500 6.199 &0.06



#



/

$1

$2

2* *&&0 00 05 5 1* 1*&&005 2 2*&005 2*& 2*&005 005 2*& 2*&005 005 2*&005 $2 &1*&005 &1*&005 &1* &1*&00 &005 5 &1*&005 &1*&005

$1

$2

2*&005 1* 1*&&005 2*& 2*&005 005

18.00

 $&.)+ *

6.06

+ %+.)+

 Anillo I 

.44

) ,.+ $

 



, -/.+

9.02

%agua

2668.70

4.02

E 12.00

C

 

12.00

 Nodo

T1



E 9.02

D 4. 4 .02

F .  .44

G

G

6. 6 .06

8. 8 .42

;

2668. 2668.70 70 265 2659. 9.68 68 2 265 655. 5.66 66 2 265 656. 6.24 24 2 2650 650.1 .18 8 2650 2650.1 .16 6

%t

2665.50

2600

2620

2612

.20

59.68

5.66

44.24

<res3n

2605 2605.00 45.18 45.17 5.68

PRESIONES EN LOS NODOS "odo

%;

%Tu

<res

T2  A

2659.20 2658.58

2608

50.58

'

2654.29

2610

44.29

C

2649.50

2605

44.50



2655.70

2620

5.70

*

2659.68

2600

59.68

+

2656.24

2612

44.24

, T1

2650.18 2668.70

26 2605

45.18

45.16

 

T

12 :

$ *&0 *&005 05

0.00 0. 0075 75 0.0110 0.0290 *&005   &0.047 &0.010

$

: 0.015 0.0057 &*&005   &0.0075 &0.006

$ *&0 *&005 05 *&0 *&005 05 *&005   *&005   *&005

: 0.04 0.044 4 0.00 0.0075 75 &0.047 &0.0757

24.00

 2

0 $-.&% 8.42 6.00

D

8.40

./)

& //.%

2.88

/ 0.%

$ $,.-4.29

 1

% %agua

 

 Anillo II 

6.15

%

0.62

A

2657.20

 

,.4.80

 D 2.88

9.60

C 4.80

B 4.29

A

T2

0.62

2655.7 265 5.70 0 264 2649.5 9.50 0 2654 2654.29 .29 2658.58 2658.58 2659.2 2659.20 0 2620

2605

2610

2608 2656.00

5.70

44.50

44.29

50.58

.20

 

2RA RADI DIEN EN E H HID IDRA RAUL ULIC ICO O (2 (2H H..3 COM COMPE PENS NSA ACIO CION D DE EC CO OAS C CON ON NE !di" # $%& (l'"  Aportes T1 =

72

 

(l/s)

T2 = 48 Consumos

 

(l/s)

"odo

$nodo

Tramo

"#

tram



>

 A

0.07

8.40

T2&A

0

48.00

0.247

&.-%,

'

0.08

9.60

A&'

1

15.6

0.140

&.$,&

C

0.10

12.00

'&C

2

5.76

0.086

&.$&&



0.0

6 6.00

A&



12.16

0.124

&.$%,

*

0.10

12.00

&C

4

6.24

0.089

&.$&&

+

0.15

1 18 8.00

*&

5

0.08

0.196

&.%&&

,

0.20

2 24 4.00

A&,

6

12.08

0.124

&.$%,

-

1.00

120.00

+&,

7

11.92

*&+

8

29.92

T1&*

9

72.00

&.$%, 0.195 &.%&& 0.0 &.%,&

%Agua en Tan$ues T1

26 266 68.70

T2

26 265 59.20

"od odo o  A ' C  * +

%Tu 2608 2610 2605 2620 2600 2612

,

2605

2656.8 18.00

$

2651.1 24.00

  Nº Q = $$.)%  L =   105.7 hf =

*  Nº + Q = %).)%  L =   960.0 hf =   .65

%agua

2668.70

0.12

 Nº ) % Q=  L =   1260.0 hf =   8.208

 

E 2660.5 12.00

 2 Nº

2651.4 6.00

 Nº , Q = -&.&+  L =   800.0 hf =  Nº / Q = 0.%/  L =   1000.0 hf =

  C

D

Q=  L = hf =

 Nº Q=  L = hf =

 

 Nº Q=

% ,.0

2649.

 L =   92.5

12.00

hf =   4.85

 

 

ON 3 RAPSHON

ECUACIONES DE CAUD

10 , 67⋅ L  K =





1,852



C



 D



4,87



 

Tramo

0

Qo

0.579

840.0

150

199.27

0.720

0.869

959.9

150

98.4

4.05

 F 1=

0.74

92.5

150

68152

4.85

 F 2=

0.991

1 10 000.0

150

24894

7.066

 F 3=

0.794

1 10 000.0

150

7798

6.089

 F 4=

0.958

800.0

150

2018.9

.069

 F 5=

0.985

1 10 050.0

150

2619

7.5

 F 6 =

0.971 105.7

150

2578

7.054

 F 7 =

0.952

960.0

150

2422.7

.645

1.467

1 12 260.0

150

1072.6

8.208

ECUA EC UACI CION ONES ES DE NO NOD D

[  ][  ] [ [  ][  ] [  ]  H T 2− H  A

 F  A =

 K 0

 F B =  

0

1

n



 H  A− H B

1

n

 K 1

 H  A − H B

 K 1

 

1

n





 H B − H C 

 H  A −

 K 3

1

n

 K 2

 

1

$%.&+

1050.0 7.5

1000.0 7.066

A

 Nº $ Q = $,.-0  L =   959.9 hf =   4.05

 Nº & /+ Q=  L =   840.0 hf =   0.720

 

[

=

 F 

=

2658.5 8.40

$%.$0

 

 F 



%agua

 

 H B − H C  C  n    K 2

 D

2659.20

%

 F  E = 

 F  F =  

 F G =  

 H  A

 K 3

 

 1

DAOS 6 COE*ICIENES 2654.2

Tramo

9.60

L

0  

840.0  



150

D

 

IERACION N7

0.25

$

COAS PIE8OMERICAS  Nodo  Hº   

T2

2659.20

CAUDALES DE RAMO 1

i  j Q ij=  H  − H   K ij

[  ]

n

Tramo

0

 K! =   199.274

Q! =   0.048

F i  = FCI.  CAC

 "Q A

 F 1=

 "Q B

 F 2=

 "QC 

 F 3=

 "Q D

 F 4=

 "Q E 

 F 5=

 "Q F   "QG

 F 66  =  F 7 =

0.0480

 ΣF, DIVA DIVADA. DA. D /

 1  −1  H    − H  !    #   

∂ F ! 1 =±  #K !  ∂ H ! ∂Q ∂ H 

 

 K !  

 

= ±

Q

1− #

#K 

Tramo

0

∂ F 1=

0.0602

∂ F 2= ∂ F 3= ∂ F 4= ∂ F 5=

 

∂ F 6 = ∂ F 7 =

 .I.TA ATICIA/; ATICIA/; 9D:<    A  A

 

&0.098

'

 

0.0019  

C 

 

0 0.0009

*

 

0

+

 

0

,

 

0.00089

ACI. ATICIA

&26.991 &24.511 &17.059 &11.777 &5.8928 &7.928 &16.87

CORRECCION O COMPE "odo

T2

 Hº    2659.20  $H   H%    2659.20

IERACION N7

%

COAS PIE8OMERICAS  Nodo  H%   

T2 2659.20

CAUDALES DE RAMO 1

Tramo

0

 

 H  −  H   ! # Q! =     K ! 

 K! =   199.274

Q! =   0.047

F i  = FCI.  CAC

 "Q A

 F 1=

 "Q B

 F 2=

 "QC 

 F 3=

 "Q D

 F 4=

 "Q E 

 F 5=

 "Q F 

 F 6 =

 "QG

 F 7 =

0.047

 ΣF, DIVA DIVADA. DA. D /

∂ F ! ∂ H !

 1  −1

      − H  !   #   1  H  =±   #K !   K !  1− #

∂Q Q =± ∂ H  #K   

 

Tramo

0

∂ F 1=

0.0902

∂ F 2= ∂ F 3= ∂ F 4= ∂ F 5= ∂ F 6 = ∂ F 7 =

 .I.TA ATICIA/; ATICIA/; 9D:<

 A  A

 

&0.044

'

 

0.00199  

C 

 

0 0.00159

*

 

0

+

 

0

,

 

0.0008

ACI. ATICIA

 

&24.818 &2.0 &17.988 &11.722 &7.0126 &8.6149 &16.062

CORRECCION O COMPE "odo T2  H%    2659.20  $H   H&    2659.20

IERACION N7

-

COAS PIE8OMERICAS  Nodo T2  H&    2659.20

CAUDALES DE RAMO

Q ij=

[  ]  H i− H  j

1

n

 K ij

Tramo

0

 K! =   199.274

Q! =   0.04425

F i  = FCI.  CAC

 "Q A

 F 1=

 "Q B

 F 2=

 "QC 

 F 3=

 "Q D

 F 4=

 "Q E 

 F 5=

 "Q F 

 F 6 =

 "QG

 F 7 =

0.044

 ΣF, DIVA DIVADA. DA. D /

 

Tramo  1  −1  H    − H  !    #   

∂ F ! 1 =±  #K !  ∂ H !

 K !

 

0

∂ F 1=

0.086

∂ F 2= ∂ F 3=

∂Q     Q1− # ∂ H  = ± #K 

∂ F  = 4

∂ F 5= ∂ F 6 = ∂ F 7 =

 .I.TA ATICIA/; ATICIA/; 9D:<

 A  A

 

&0.0428

'

 

0.0019

C 

 

 

0 0.00141

*

 

0

+

 

0

,

 

0.00084

ACI. ATICIA

&25.125 &2.06 &17.881 &11.495 &6.6698 &8.12 &16.07

CORRECCION O COMPE "odo T2  H&    2659.20  $H   H&%    2659.20

IERACION N7

/

 

COAS PIE8OMERICAS  Nodo T2  H&%    2659.20

CAUDALES DE RAMO  H    −  H   ! Q! =    K !

1

#  

Tramo

0

 K! =   199.274

Q! =   0.04425

F i  = FCI.  CAC

 "Q A

 F 1=

 "Q B

 F 2=

 "QC 

 F 3=

 "Q

 F  =

 D

0.044

4

 "Q E 

 F 5=

 "Q F 

 F 6 =

 "QG

 F 7 =

 ΣF, DIVA DIVADA. DA. D /

Tramo  1  −1  H    − H  !    #   

∂ F ! 1 =±  ∂ H ! #K ! 

 K !

 

Q 1− # = ± ∂ H  #K  ∂Q

 

 

∂ F 1=

0 0.086

∂ F 2= ∂ F 3= ∂ F 4= ∂ F 5= ∂ F 6 = ∂ F 7 =

 .I.TA ATICIA/; ATICIA/; 9D:<

 A  A

 

&0.0428

 

'

   

C 

0.0019

 

0 0.0014

*

 

0

+

 

0

,

 

0.00084

ACI. ATICIA

&25.126 &2.08 &17.862 &11.477 &6.6498 &8.12 &16.061

CORRECCION O COMPE "odo T2  H&    2659.20  $H   H&%    2659.20

PRESIONES EN LOS NOD "odo T2  A '

;:? 2659.20 2658.58 2654.0

C  * + , T1

2649.51 2655.67 2659.68 2656.24 2650.17 2668.70

 

 

AL O NODO 1

2

3

 - Q1 Q1

4

5

6

 - Q3

7

'

 - Q2  + Q4 Q3

 - Q4

 + Q5  - Q5

 - Q%  - Q"  Q

 

1

n

 K 1

 H  A − H B  K 1

 

1

n





 H B− H C 

 H  A − H  D  K 3

1

n

 

 



[  ]

 



 H  A− H G

 K 6

=

 - (C 

=

 - (D

=

 - ( 

=

 - (F 

=

 - (! 

=

−  A = 0

 

q

n

 K 2

 



q B= 0

1

 H  D  D − H C  C  +  K 4

 H B − H C  C  n    K 2

 H  A − H  D  K 3

1

n



n

 H  D− H C   K 4

 



1

n

+



 

 K 5

n

 



[  ]  H  E− H  D

 K 5

q C = 0

1

 ]

 H  E− H  D

[  ][ [  ][  ]

1

n

 



 

 

 - (B

1

1

 

 + Q%

=

5 CAUDAL

[  ] [  ] [  ][  ] [  ] [  ] [  ][  ][



 + Q'

 - (A

 + Q 6 

 H  A − H B

)#

 - Q6 

Q2

 

(



 H  A − H G  K 6

1

n

+

1

 H  F − H G

n

 K 7

 H  F − H G  K 7

+

 H  E − H  F 

 K 8

 H  E− H  F 

 K 8

1

n

+

 K 9

1

 ]

 H T 1− H  E

q D=0

n

  − q E=0

1

n

 

−  F = 0

q

1

n

[  ][  ]

 



q G= 0

 

  E RAMO 1

2

3

4

5

6

7

'

(

959.9

92.5

1000.0

1000.0

800.0

1050.0

105.7

960.0

1260.0

150

150

150

150

150

150

150

150

150

0.150

0.100

0.125

0.100

0.200

0.125

0.125

0.200

0.250

C

D

G

  DOPADAS  A

B

F

E

T1

2658.48 2658 .48 2654.1 2654.18 8 2649 2649.2 .2 2651.41 2651.41 2651.1 2651.15 5 2656.85 2656.85 2660.4 2660.49 9 2668 2668.70 .70

1 98 98..4

2 6815 68152 2

3 2489 24894 4

4

5

779 7798 8 2018 2018..91

6 26 261 19 9

7

'

(

2578 2578  2422 2422.6 .69 9 1072 1072.6 .62 2

0. 0.01 0156 56 0.005 0.00576 76 0.01 0.01216 216 0.00 0.005 5 0.05 0.0540 40  0.012 0.01208 08 0.01 0.01062 062 0.0 0.0299 2992 2

 

0.07 0.072 2

I. D CADA/

&0.0154

&0.0122

&0.0121

&0.0084

 

=

&0.0096

 

=

&0.0120

 

=

&0.060

 

=

&0.0299   0.0720   &0.0120

 

=

&0.0180

 

=

&0.0240

 

=

0.0154   &0.0058 0.0058

 

0.005 0.0122   &0.005   0.0540

 

&0.0540

&0.0106   0.0299

 

0.01 0.0121 21

0.010 0.0106 6

6

7

   

. FCI. F i 

1

2

0.0019

3

4

5

0.0009

'

(

 9> i,i  : 

=   &0.098

0.00089

=   &0.0026

0.0019 0.0019  0.0006 0.00064 4 0.00064

=   &0.0015

0.0009 0.00 0.0009 09 

0.000 0.0009 9 0.00 0.002 21 1 0.0021

0.0044 0.00474

=   &0.0050 =   &0.0124

 

=   &0.0054

0.00101 0.0010 1 0.0044

=   &0.0019

0.00089 0.0010 0.00101 1

 

9 9 : = 9.(:   9 9 : 

 atri a7o8iana 9D: '

C



*

+

,

0.0019

0

0.0009

0

0

0.00089

 H  A

&0.0026 0.00064

0

0

0

0

 H  B

0.00064 &0.0015

0.0009

0

0

0

 H C 

0

0

0

0.0009

&0.0050 0.0021

0

0

0

0

0

0

0

0

0.0021 &0.0124 0.0044

@

0

 H  E   H  F 

0.0044 &0.0054 0.00101 0

 H  D

 H G

0.00101 &0.0019

9.(: 

= = = = = = =

 

&4*&015

 

4*&016

 

&0.0027

 

0.02668

 

&0.029

 

0.00129

 

&0.001

 .; 9D: -1 <9.(: = 9 9 :   9D: -1 &24. &24.51 511 1 &1 &17. 7.05 059 9

&16. &16.87 87

&4*&015

&228.7 &61.248 &24.746 &24.724 &24.624

4*&016

&22 228 8.7 &864.77 &209 09..9 &81.409 &75.214 &47.927

&0.0 0.002 027 7

&464.9

&11. &1 1.777 777 &5.8 &5.892 928 8 &7.9 &7.92 28 8

&61.248 &209.9 &15.2 &121.57

 

 9 9 : 

 9.(: 

&111 &64.445

@

0.02668

&24. 4.7 746 &81.409 &121 21..57 &166.2 &150.8 0.87 &82.845

&0.0 0.02 29 9

&24.724 &75.214

&111 &150.87 &41.04 &184.7

0.00129

&24. 4.6 624 &47.927 &64.4 4.445 &82.845 &184.7 4.7 &6.55

&0.0 0.001 01 

= = = = = = =

SACION DE COA COAS S PIE8OMERICAS  A

'

C



,

+

*

T1

2658.48 2654.1 2658.48 2654.18 8 2649 2649.2 .2 2651.4 2651.41 1 265 2651.1 1.15 5 265 2656.8 6.85 5 2660 2660.49 .49 2668.70 2668.70 &0.115 &0.416 &1.22 &4.988 0.976 0.655 0.874 2658.6 265 8.60 0 265 2654.5 4.59 9 2650 2650.65 .65 2656.40 2656.40 2650.1 2650.17 7 2656 2656.19 .19 2659.6 2659.62 2 2668 2668.70 .70

  DOPADAS  A B C D G F E T1 2658.60 2658 .60 2654.5 2654.59 9 2650 2650.65 .65 2656.40 2656.40 2650.1 2650.17 7 2656.19 2656.19 2659.6 2659.62 2 2668 2668.70 .70

1

2

3

4

5

6

7

'

(

 

&0.1149

 H  A

 

&0.416

 H  B

 

&1.22

 H C 

 

&4.988

 H  D

 

0.876

 H  E 

 

0.6547

 H  F 

 

0.9760

 H G

 

98 98..4

6815 68152 2

2489 24894 4

779 7798 8 2018 2018..91

26 261 19 9

2578 2578  2422 2422.6 .69 9 1072 1072.6 .62 2

0.01477 0.0 1477 0.0 0.0051 0515 5 0.0 0.00646 0646 0.0 0.00605 0605 0.0 0.008 085 5 0.0 0.010 102 2 0.0 0.01094 1094 0.0 0.0289 289 0.0 0.0760 7604 4

 

I. D CADA/

&0.0148

&0.0065

&0.010

&0.0084

 

=

&0.0096

 

=

&0.0120

 

=

&0.060

 

=

&0.0289   0.0760   &0.0120

 

=

&0.0180

 

=

&0.0240

 

=

0.0148   &0.0052 0.0052

0.0061

 

0.0065   &0.0061   0.009

 

&0.009

&0.0109   0.0289

 

0.01 0.010 0

0.010 0.0109 9

6

7

   

. FCI. F i 

1

2

0.00199

3

4

5

0.00159

'

 9> i,i  : 

(

=   &0.044

0.0008

=   &0.0027

0.00199 0.0019 9 0.0007 0.00071 1 0.00057

=   &0.001

0.00159 0.0015 9 0.00057 0.00518

=   &0.007

0.00071

0.00518

0.00456 0.00452

=   &0.0055

0.00098 0.0009 8 0.00456

=   &0.0018

0.0008 0.0009 0.00098 8

 

=   &0.014

9 9 : = 9.(:   9 9 : 

 9D: '

C



*

+

,

0.00199

0

0.00159

0

0

0.0008

 *  A

0

0

0

0

 *  B

0

0

0

 * C 

0

0

&0.0027 0.00071

0.00071 &0.001 0.00057 0

0.00057 &0.007 0.00518

0

0

0.00518 &0.014 0.00456

0

0

0

0

0

0

 .; 9D: -1 <9.(: = 9 9 : 

0

0.00456 &0.0055 0.00098 0

0.00098 &0.0018

@

 *  D  *  E   *  F   * G

9.(: 

= = = = = = =

 

0.00104

 

2*&005

 

&0.0008

 

&0.0047

 

0.00426

 

&1*&005

 

&4*&005

 

 9D: -1 &2. &2 .0 0  &1 &17. 7.98 988 8

&11. &1 1.722 722 &7.0 &7.012 126 6 &8.6 &8.614 149 9 &16. &16.06 062 2

0.00104

&459 59..15 &27.06 &41.9 1.95 &22.419 &22.474 &22.71

2*&005

&27 7..06 &99.81 &127 27..1 &65.951 &61.65 &41.574

&0.0 0.000 008 8

&41. 1.9 95 &127.1 &2 ..4 &120.02

 

 9 9 : 

 9.(: 

&&1 110.2 0.27 &64.977

@

&0.0 0.004 047 7

&22. 2.4 419 &65.951 &120 20..02 &160.66 &146.8 6.84 &82.57 &22. 2.4 474 &61.65 &1 &110 10..27 &146.84 &.9 .97 &184.4

0.0042 426 6 &1*&005

&22. 2.7 71 &41.574 &64.9 4.977

&4*&005

&82.57 &184.4 4.4 &657.87

 

0.0144

 H  A

 

0.2889

 H  B

 

1.0900

 H C 

 

0.6866

 H  D

=   &0.0660 =   &0.051 =   &0.0028

 H  E   H  F 

= = = =

 H G

SACION DE COA COAS S PIE8OMERICAS  A ' C  , + * T1 2658.60 2658 .60 2654.5 2654.59 9 2650 2650.65 .65 2656.4 2656.40 0 265 2650.1 0.17 7 265 2656.1 6.19 9 2659 2659.62 .62 2668.70 2668.70 0.014 0.289 1.090 0.687 &0.00 &0.05 &0.066 2658.5 265 8.58 8 265 2654. 4.0 0 2649 2649.56 .56 2655.72 2655.72 2650.1 2650.17 7 2656 2656.25 .25 2659.6 2659.68 8 2668 2668.70 .70

  DOPADAS  A B C D G F E T1 2658.58 2658 .58 2654. 2654.0 0 2649 2649.56 .56 2655.72 2655.72 2650.1 2650.17 7 2656.25 2656.25 2659.6 2659.68 8 2668 2668.70 .70

1 98 98..4

2 6815 68152 2

3 2489 24894 4

4

5

779 7798 8 2018 2018..91

6 26 261 19 9

7

'

(

2578 2578  2422 2422.6 .69 9 1072 1072.6 .62 2

0.0151 0.0 151 0.0 0.0056 0569 9 0.0 0.00747 0747 0.0 0.00628 0628 0.0 0.045 456 6 0.0 0.010 101 1 0.0 0.01099 1099 0.0 0.02899 2899 0.0 0.0757 7574 4

 

I. D CADA/

&0.015

&0.0075

&0.010

&0.0084

 

=

&0.0096

 

=

&0.0120

 

=

&0.060

 

=

&0.0290   0.0757   &0.0120

 

=

&0.0180

 

=

&0.0240

 

=

0.015   &0.0057 0.0057

0.006

 

0.0075   &0.006   0.046

 

&0.046

&0.0110   0.0290 0.01 0.010 0

 

. FCI. F i 

0.01 0.0110 10

   

 

1

2

0.0019

3

4

5

0.00141

6

7

'

 9> i,i  : 

(

=   &0.0428

0.00084

=   &0.0026

0.0019 0.0019  0.0006 0.00065 5 0.00065

=   &0.0012

0.00055 0.00 0.0014 141 1 0.00 0.00055 055

0.00 0.0047 47 0.0047

0.00455 0.00454

=   &0.0055

0.00098 0.0009 8 0.00455

=   &0.0018

0.00084 0.0009 0.00098 8

 

=   &0.0067 =   &0.018

9 9 : = 9.(:   9 9 : 

 9D: '

C



*

+

,

0.0019

0

0.00141

0

0

0.00084

 *  A

0

0

0

0

 *  B

0 0

0 0

 * C   *  D

&0.0026 0.00065

0.00065 &0.0012 0.00055 0 0 0.00055 &0.0067 0.0047 0

0

0.0047

0

0

0

0

0

0

&0.018 0.00455

@

0

 *  F 

0.00455 &0.0055 0.00098 0

 *  E   * G

0.00098 &0.0018

9.(: 

= = = = = = =

 

7*&005

 

2*&005

  &*&005   &0.000  

0.00019

 

4*&008

 

&1*&007

 .; 9D: -1 <9.(: = 9 9 :   9D: -1 &2. &2 .0 06 6 &1 &17. 7.88 881 1

&11. &1 1.495 495 &6.6 &6.669 698 8 &8. &8.1 12 2

&474.47 &276.45 &4.95 &276.45

&16. &16.07 07

7*&005

&22.14 &22.245 &22.74

2*&005

&1048 &18.58 &68.02 &6.76

&4. . 95 &18.58 &250 50..61 &122.6

&22. 2.7 74

 

&42.62

&&1 112.6 2.6 &66.024

&22 22..14 &68.02 &122 22..6 &16.69 &149.5 9.55

&*&005

@

&0.0 0.000 00 

&&8 8.711

0.0001 019 9

&112 12..6 &149.55 &6.7 6.75 &185.41

4*&008

&42.62 &66.0 6.024 &8.71 711 1 &185.4 5.41 &659.11

&1*&007

&22. 2.2 245 &6.76

 9 9 : 

 9.(: 

SACION DE COA COAS S PIE8OMERICAS  A ' C  , + * T1 2658.58 2658 .58 2654. 2654.0 0 2649 2649.56 .56 2655.7 2655.72 2 265 2650.1 0.17 7 265 2656.2 6.25 5 2659 2659.68 .68 2668.70 2668.70 0.000 0.005 0.045 0.042 0.001 0.001 0.001 2658.5 265 8.58 8 265 2654. 4.0 0 2649 2649.51 .51 2655.67 2655.67 2650.1 2650.17 7 2656 2656.24 .24 2659.6 2659.68 8 2668 2668.70 .70

= =

 

0.0000

 H  A

 

0.005

 H  B

= = = = =

 

0.045

 

0.0422

C   H C   H  D

 

0.0010

 H  E 

 

0.0009

 H  F 

 

0.0005

 H G

 

  DOPADAS  A B C D G F E T1 2658.58 2658 .58 2654. 2654.0 0 2649 2649.51 .51 2655.67 2655.67 2650.1 2650.17 7 2656.24 2656.24 2659.6 2659.68 8 2668 2668.70 .70

1 98 98..4

2 6815 68152 2

3 2489 24894 4

4

5

779 7798 8 2018 2018..91

6 26 261 19 9

7

'

(

2578 2578  2422 2422.6 .69 9 1072 1072.6 .62 2

0.0152 0.0 152 0.0 0.0057 0572 2 0.0 0.0075 075 0.0 0.00628 0628 0.0 0.047 475 5 0.0 0.010 101 1 0.0 0.01099 1099 0.0 0.02899 2899 0.0 0.0757 7575 5

 

I. D CADA/

&0.015

&0.0075

&0.010

&0.0084

 

=

&0.0096

 

=

&0.0120

 

=

&0.060 &0.0290   0.0757   &0.0120

   

= =

&0.0180

 

=

&0.0240

 

=

0.015   &0.0057 0.0057

 

0.006 0.0075   &0.006   0.048 &0.048

 

&0.0110   0.0290

 

0.01 0.010 0

0.01 0.0110 10

6

7

   

. FCI. F i 

1

2

0.0019

3

4

5

0.0014

'

 9> i,i  : 

(

=   &0.0428

0.00084

=   &0.0026

0.0019 0.0019  0.0006 0.00065 5 0.00055

=   &0.0012

0.0014 0.0 014 0.00055 0.00055 0.0 0.0046 0468 8

=   &0.0066

0.00065

0.00468

0.00455 0.00454

=   &0.0055

0.00098 0.0009 8 0.00455

=   &0.0018

0.00084 0.0009 0.00098 8

 

=   &0.018

9 9 : = 9.(:   9 9 : 

 9D: '

C



*

+

,

0.0019

0

0.0014

0

0

0.00084

 *  A

9.(: 

=

 

2*&007

 

&0.0026 0.00065

0

0.00065 &0.0012 0.00055 0

0

0

0

 *  B

0

0

0

 * C 

0

0

0.00055 &0.0066 0.00468

0

0

0.00468 &0.018 0.00455

0

0

0

0

0

0

@

0

 *  E   *  F 

0.00455 &0.0055 0.00098 0

 *  D

 * G

0.00098 &0.0018

=   5*&008 =   &5*&008 =   &7*&007 =   5*&007 =   *&012 =   &1*&011

 .; 9D: -1 <9.(: = 9 9 :   9D: -1

 9.(: 

&11. &1 1.477 477 &6.6 &6.649 498 8 &8. &8.1 12 2 &16. &16.06 061 1

2*&007

&474 74..81 &276.28 &4.4 .467 &22.126 &22.2 &22.728

5*&008

&2. &2 .0 08 8 &1 &17. 7.86 862 2

&276 76..28 &1049.9 9.9 &19 9..24

&68.46 &6.905 &42.689

&4. .4 467 &19.24 &251 51..54 &122.79 &22.126

&68.46 &122.79 &16.87 &149.71

&22. 2.2 2 &6.905

@

&7*&007

&8.79

5*&007

&112 12..77 &149.71 &6.8 6.89 &185.48

*&012

&22. 2.7 728 &42.689 &66.0 6.096

 

&&1 112.7 2.77 &66.096

&5*&008

&8.79 &185.4 5.48 &659.15

&1*&011 011

SACION DE COA COAS S PIE8OMERICAS  A ' C  , + * T1 2658.58 2654. 2658.58 2654.0 0 2649 2649.51 .51 2655.6 2655.67 7 265 2650.1 0.17 7 265 2656.2 6.24 4 2659 2659.68 .68 2668.70 2668.70 0.000 0.000 0.000 0.000 0.000 0.000 0.000 2658.5 265 8.58 8 265 2654. 4.0 0 2649 2649.51 .51 2655.67 2655.67 2650.1 2650.17 7 2656 2656.24 .24 2659.6 2659.68 8 2668 2668.70 .70

 

OS: %Tu %T u

<res <res3 3n n

2608 2610

50.58 44.0

2605 2620 2600 2612 2605

44.51 5.67 59.68 44.24 45.17

 9 9 : 

= = = = = = =

 

0.000

 

0.000

 

0.000

 

0.000

 

0.000

 

0.000

 

0.000

 

 "Q A  "Q B  "QC   "Q D  "Q E   "Q F   "Q G

 

−  A= 0

q

 





 



1

n

 

 

+

 K 9

qC = 0

q D= 0

1

[  ]  H T 1− H  E

q B= 0

n

  − q E= 0

−  F = 0

q



qG = 0

 

+,)0.000000 0.000000 &0.00275 0.02668 &0.02948 0.00129 &0.00129

 

+,)0.00104 0.000018 &0.000794 &0.004740 0.004257 &0.000010 &0.00005

 

+,)0.000071 0.000016 &0.000028 &0.000251 0.000189 0.000000 0.000000

 

+,)0.000000 0.000000 0.000000 &0.000001 0.000000 0.000000 0.000000

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