The Fanning friction factor is given by the following relationships:

(i) For a laminar regime (,

,

(ii) for a turbulent regime in smooth pipes (,

(Blasius equation),

(iii) for a turbulent regime in rough pipes (,

(Colebrook–White equation),

where is the roughness ratio. The light green shaded region corresponds to the laminar/turbulent transition regime where experimental results are unreliable.

Side note: an explicit version of the Colebrook–White equation derived by Shacham (see [1])

gives equivalent results.