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


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


fDarcy friction factor (dimensionless)
ϵPipe's effective roughness height (m)
RhHydraulic radius (m)
ReReynolds number (dimensionless)