Enter the absolute roughness, diameter, and Reynolds number into the calculator to determine the friction factor using the Colebrook equation. This calculator provides an iterative solution to the implicit equation.
Colebrook Equation Formula
The Colebrook equation is used to calculate the friction factor for fluid flow in a pipe. The equation is implicit and requires an iterative solution:
frac{1}{sqrt{f}} = -2 log_{10}left(frac{varepsilon}{3.7D} + frac{2.51}{Re sqrt{f}}right)
Variables:
- f is the Darcy-Weisbach friction factor
- ε is the absolute roughness of the pipe's inner surface (mm)
- D is the diameter of the pipe (mm)
- Re is the Reynolds number, a dimensionless quantity representing the ratio of inertial forces to viscous forces
To calculate the friction factor, an initial guess is made and the equation is solved iteratively until convergence is achieved.
What is the Colebrook Equation?
The Colebrook equation is a widely accepted formula for estimating the friction factor for turbulent flow in smooth and rough pipes. It combines the effects of pipe roughness and flow velocity to provide an estimate of the head loss due to friction in the pipe.
How to Calculate Friction Factor using the Colebrook Equation?
The following steps outline how to calculate the friction factor using the Colebrook equation.
- First, determine the absolute roughness of the pipe's inner surface (ε) in mm.
- Next, determine the diameter of the pipe (D) in mm.
- Next, determine the Reynolds number (Re), which is a dimensionless quantity.
- Use the Colebrook equation and an iterative method such as the Newton-Raphson method to solve for the friction factor (f).
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Absolute roughness (ε) = 0.045 mm
Diameter (D) = 250 mm
Reynolds number (Re) = 100000
