For the turbulent flow regime, the relationship between the Fanning friction factor and the Reynolds number is more complex and is governed by the Colebrook equation which is implicit in :
Various explicit approximations of the related Darcy friction factor have been developed for turbulent flow.
Stuart W. Churchill developed a formula that covers the friction factor for both laminar and turbulent flow. This was originally produced to describe the Moody chart, which plots the Darcy-Weisbach Friction factor against Reynolds number. The Darcy Weisbach Formula , also called Moody friction factor, is 4 times the Fanning friction factor  and so a factor of  has been applied to produce the formula given below.
* Re, Reynolds number (unitless);
* &epsilon;, roughness of the inner surface of the pipe (dimension of length);
* D, inner pipe diameter;