Various formulae for head losses in pipes are recognised in theory. Hydraulic engineers favour two of them:
The Manning equation.
The advantage of this formula is that it is easy to implement.
The head loss due to pipe resistance is related to the flow through the pipe.
The most suitable formulation for the friction factor required by the D'Arcy-Weisbach equation is generally regarded as being the Colebrook-White equation. This equation provides an implicit definition for the friction factor.
The D'Arcy-Weisbach formula, with friction coefficient calculated from the Colebrook-White equation, is accurate for any pipe diameter or fluid velocity.