Darcy friction factor f as a function of Reynolds number Re and pipe relative roughness ε / d, fitting the data of experimental studies of turbulent flow in smooth and rough pipes.
The equation can be used to (alliteratively) solve for the Darcy–Weisbach friction factor f.
For a conduit flowing completely full of fluid at Reynolds numbers greater than 4000, it is expressed as:
1/√(f) = -2*log((e/d)/3.7 + 2.51/(Nre*√(f))
As can see from the formula, simple calculation is not possible, so user should use iterative calculations or a solver to find the value of f that satisfies the formula.
Pipe Material Commercial Steel, e = 0.05Pipe Internal Diameter (d, mm) = 25
Reynold's Number (Re) = 100000
Relative Roughness (ε/D) 0.002
Friction factor (f) 0.023
Run Python code below : https://www.mycompiler.io/view/4rbUNlvs1QN
import math
import numpy as np
piping = "Commercial Steel"
if piping == "Commercial Steel": e = 0.05
if piping == "Cast Iron": e = 0.26
if piping == "Galvanized Iron": e = 0.15
if piping == "Asphalted Cast Iron": e = 0.12
if piping == "Drawn Tubing": e = 0.0015
if (Nre > 1 and Nre <= 2000):
f_result = 64 / Nre
elif Nre > 4000:
delta_result = 1
delta = 1
for f in np.arange(0.001, 0.1, 0.001):
lhs = 1/math.sqrt(f)
rhs = -2*math.log10((e/d)/3.7 + 2.51/(Nre*math.sqrt(f)))
delta = abs(lhs - rhs)
if (delta < delta_result):
delta_result = delta
f_result = f
else:
pass
return f_result
f = frictionfactor("Commercial Steel", 25, 10000)
print("darcy friction factor = ", f)
When run the code, you will receive the following results.
darcy friction factor = 0.034
