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