Friction Factor Equations

Friction Factor Equations
Colebrook (1939)

1
f

0.5

=−2.0 log

(

e / D 2.51
+
3.7 ℜ f 0.5

)

Initial estimate, f0

[ (

e/ D 5.74
f 0=0.25 log
+
3.7 ℜ0.9

−2

)]

Haaland (1983)

1
f

=−1.8 log
0.5

1.11

(( )
e /D
3.7

+

6.9
ℜ

Swamee-Jain

f=

0.25

[ (

e
5.74
log
+
3.7 D ℜ0.9

2

)]

Serghides

e
12
+
3.7 D ℜ

A=−2 log

(

)

B=−2 log

( 3.7e D + 12.51ℜ A )

C=−2 log

( 3.7e D + 2.51ℜ B )

)

(

2

f = A−

(B−A )
C−2 B+ A

)

Brkic

ℜ

S=ln
1.816 ln

1
f

0.5

=−2.0 log

1.1 ℜ
ln ⁡( 1+1.1 ℜ)

( e3.71/ D + 2.18ℜ S )

Sample Problem
A 2.5 (nominal) inches pipeline conveying water contains 290 ft of straight
galvanized pipe, 2 fully open gate valve, 1 fully open angle valve, 7 standard 90
elbow, 1 square-edged entrance from a reservoir, and 1 free discharge. The
entrance and exit conditions are:
Location
Entrance
Discharge

Elevation
50 ft
94 ft

Pressure
20 psig
0 pisg

A centrifugal pump is installed in the line to move the water. What pressure rise
must the pump deliver so the volume flow rate will be Q = 0.439 ft 3/s?
Sample problem (Open system)

Sample Problem (Closed system)

Sample problem