Consider steady flow of an incompressible fluid through two long and straight pipes of diameters d₁ and d₂ arranged in series. Both pipes are of equal length and the flow is turbulent in both pipes. The friction factor for turbulent flow though pipes is of the form, f = K(Re)^-n, where K and n are known positive constants and Re is the Reynolds number. Neglecting minor losses, the ratio of the frictional pressure drop in pipe 1 to that in pipe 2, (ΔP₁/ΔP₂), is given by