<P> we can now express Re √ f: </P> <Dl> <Dd> R e f D = 1 ν 2 g S D 3 (\ displaystyle \ mathrm (Re) (\ sqrt (f_ (\ mathrm (D)))) = (\ frac (1) (\ nu)) (\ sqrt (2g)) (\ sqrt (S)) (\ sqrt (D ^ (3)))) </Dd> </Dl> <Dd> R e f D = 1 ν 2 g S D 3 (\ displaystyle \ mathrm (Re) (\ sqrt (f_ (\ mathrm (D)))) = (\ frac (1) (\ nu)) (\ sqrt (2g)) (\ sqrt (S)) (\ sqrt (D ^ (3)))) </Dd> <P> Expressing the roughness Reynolds number R, </P>

Pressure loss due to friction in a pipeline