Colebrook Equation

Calculate friction loss coefficients in pipes, tubes and ducts

The friction coefficients used to calculate pressure loss (or major loss) in ducts, tubes and 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 = D'Arcy-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 m³/s). The kinematic viscosity used to calculate the Reynolds Number is 15x10^-6 m²/s.

Hydraulic diameter - d_h - (m, ft)

Roughness of surface - k - (m, ft)

Reynolds Number - Re

Just replace the parameters with appropriate values for your application.

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

Hydraulic diameter - d_h - (m, ft)

Roughness of surface - k - (m, ft)

Velocity - u - (m/s, ft/s)

Kinematic Viscosity - ν - (m²/s, ft²/s)

The friction coefficient can also be estimated with the Moody diagram:

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