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# Darcy friction factor - Colebrook–White equation (relative to the radius)

## Description

In fluid dynamics, the Darcy friction factor formulae are equations that allow the calculation of the Darcy friction factor, a dimensionless quantity used in the Darcy–Weisbach equation, for the description of friction losses in pipe flow as well as open-channel flow.

The Darcy friction factor is also known as the Darcy–Weisbach friction factor, resistance coefficient or simply friction factor; by definition it is four times larger than the Fanning friction factor.

The phenomenological Colebrook–White equation (or Colebrook equation) expresses the Darcy friction factor f as a function of Reynolds number Re and pipe relative roughness ε / Dh, fitting the data of experimental studies of turbulent flow in smooth and rough pipes. The equation can be used to (iteratively) solve for the Darcy–Weisbach friction factor f.

For a conduit flowing completely full of fluid at Reynolds numbers greater than 4000, it is expressed as shown here.

Related formulas

## Variables

 f Darcy friction factor (dimensionless) ϵ Pipe's effective roughness height (m) Rh Hydraulic radius (m) Re Reynolds number (dimensionless)