# Colebrook-White Equation

Written by Jerry Ratzlaff on . Posted in Fluid Dynamics

Colebrook-White equation, also called Colebrook equation, is used toiteratively solve the Darcy-Weisback friction factor. This equation uses US units. To convert between US and SI units, use our calculator.

## Colebrook-White Equation formulas

 $$\large{ \frac{1}{\sqrt{f}} = -2 \; log_{10} \left( \frac{ \epsilon\ }{ 3.7 \; d_h } + \frac{ 2.51 }{ Re \; \sqrt{ f } } \right) }$$ $$\large{ \frac{1}{\sqrt{f}} = -2 \; log_{10} \left( \frac{ \epsilon }{ 12 \; r_h } + \frac{ 2.51 }{ Re \; \sqrt{ f } } \right) }$$ (free surface flow) $$\large{ \frac{1}{\sqrt{f}} = -2 \; log_{10} \left( \frac{ \epsilon\ }{ 14.8 \; r_h } + \frac{ 2.51 }{ Re \; \sqrt{ f } } \right) }$$ (full flow closed conduit)

### Where:

$$\large{ \epsilon }$$ (Greek symbol epsilon) = absolute roughness, inches

$$\large{ f }$$ = friction factor, unitless

$$\large{ d_h }$$ = hydraulic diameter, inches

$$\large{ r_h }$$ = hydraulic radius, inches

$$\large{ Re }$$ = Reynolds number, unitless

If other units for hydraulic diameter, radius or absolute roughness are needed, use our conversion table for length.

Tags: Equations for Flow