Colebrook Formula Solver

A simple iterative solver for the Colebrook Formula applied to Newtonian fluids.

Disclaimer

This calculator is for educational and curiosity purposes only. No gaurantee on accuracy is inferred by a result.

Select Desired System of Units

Fluid

Density (slug/ft³)

You must enter a value for density that is greater than 0.

Dynamic Viscosity (lb⋅s/ft²)

You must enter a value for dynamic viscosity that is greater than 0.

Pipe Hydraulic Diameter (in)

You must enter a value for pipe diameter that is greater than 0.

Pipe Equivalent Roughness (ft)

You must enter a value for equivalent roughness that is at least 0 and less than 1.

Volume Flow Rate (GPM)

You must enter a value for volume flow rate that is greater than 0.

Calculator Output

Friction Factor =

Iterations required =

Equivalent Roughness values for some common pipe material.

	Equivalent Roughness, ε
Pipe Material	Feet	Millimeters
Riveted steel	0.003 - 0.03	0.9 - 9.0
Concrete	0.001 - 0.01	0.3 - 3.0
Wood stave	0.0006 - 0.003	0.18 - 0.9
Cast iron	0.00085	0.26
Galvanized iron	0.0005	0.15
Commercial steel or wrought iron	0.00015	0.045
Drawn tubing	0.000005	0.0015
Plastic, glass	0.0 (smooth)	0.0 (smooth)

Solver Notes:

This solver uses the bisection method to converge to a solution for friction factor based on the implicit Colebrook formula, shown below.

\[ \frac{1}{\sqrt{f}} = -2.0\log \left( \frac{\epsilon/D}{3.7} + \frac{2.51}{Re \sqrt{f}} \right) \]

In an effort to aide the user, three options are provided for fluid: Water, Air, or Other. If the user selects Water or Air, standard sea-level condition values are automatically entered into the density and viscosity inputs. In addition, the units of volume flow rate depend on the chosen fluid (mainly based on industry standard units). These values are free to be modified by the user.