# Colebrook Equation

## Calculating friction loss coefficients in pipes, tubes or ducts

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The friction coefficients used to calculate pressure loss (or major loss) in ducts, tubes or pipes can be calculated with the Colebrook equation

1 / λ^{1/2}= -2 log [ 2.51 / (Re λ^{1/2}) + (k / d_{h}) / 3.72 ] (1)

where

λ = Darcy-Weisbach friction coefficient

Re = Reynolds Number

k = roughness of duct, pipe or tube surface (m, ft)

d_{h}= hydraulic diameter (m, ft)

The Colebrook equation is only valid at turbulent flow conditions.

Note that the friction coefficient is involved on both sides of the equation and that the equation must be solved by iteration.

The Colebrook equation is generic and can be used to calculate the friction coefficients in different kinds of fluid flows - air ventilation ducts, pipes and tubes with water or oil, compressed air and much more.

### Colebrook Online Calculator

The friction coefficient can be calculated with the online Colebrook calculator below.

The default values used are for turbulent air flow in a *315 mm* duct with *6 m/s (0.47 m ^{3}/s)*. The kinematic viscosity used to calculate the Reynolds Number is

*15 10*.

^{-6}m^{2}/sReplace the parameters with the appropriate values for your application.

The calculator below can be used to calculate the friction coefficient if **velocity** and kinematic viscosity of the fluid are known.

The friction coefficient can also be estimated with the Moody diagram (SI based):

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