Fanning Friction Factor for Smooth and Rough Pipes

​
rough pipes
smooth pipe
roughness ratio
0.001
log
10
[Re]
4
This Demonstration plots the Fanning friction factor
f
F
versus the Reynolds number,
Re
, for both rough and smooth pipes.
The Fanning friction factor is given by the following relationships:
(i) For a laminar regime (
Re<2000)
,
f
F
=
16
Re
,
(ii) for a turbulent regime in smooth pipes (
Re>4000)
,
f
F
=0.079
-1/4
Re
(Blasius equation),
(iii) for a turbulent regime in rough pipes (
Re>4000)
,
1
f
F
=-1.737ln0.269
ϵ
D
+
1.257
Re
f
F
(Colebrook–White equation),
where
ϵ/D
is the roughness ratio. The light green shaded region corresponds to the laminar/turbulent transition regime where experimental results are unreliable.
Side note: an explicit version of the Colebrook–White equation derived by Shacham (see[1])
f
F
=-1.737
-2
ln0.269
ϵ
D
-
2.185
Re
ln0.269
ϵ
D
+
14.5
Re

gives equivalent results.

References

[1] J. O. Wilkes, Fluid Mechanics for Chemical Engineers, Upper Saddle River, NJ: Prentice Hall, 1999.

Permanent Citation

Housam Binous, Brian G. Higgins
​
​"Fanning Friction Factor for Smooth and Rough Pipes"​
​http://demonstrations.wolfram.com/FanningFrictionFactorForSmoothAndRoughPipes/​
​Wolfram Demonstrations Project​
​Published: September 6, 2011