(For 0 < Re < 2300 Laminar region. Hagen – Poiseuille equation. For 2300 =< Re =< 4000 Critical region. Churchill equation. For 4000 < Re Transition and turbulent regions. Colebrook equation. There is not a theory describing the critical region. Churchill equation describes relatively well this region, for smooth pipes with Rrel <= 0.01, giving conservative values, when compared with Nikuradse experimental data. Although Churchill equation describes also the transition and turbulente regions in accordance with Colebrook, this last equation is used in these regions because its use is often required in certain design criteria Rev. 26.07.2019)

Moody diagram. Hagen Poiseuille, Colebrook and Churchill equations_Nikuradse data