Manning's formula

Manning’s empirical formula is used for evaluating the mean velocity for a steady uniform turbulent flow in pressure conduits with circular cross-section and in a wide rectangular open channels (Venutelli, 2005)

v = (kn / n) Rh2/3 S1/2                       


v = cross-sectional mean velocity (ft/s, m/s)

kn = 1.486 for English units and kn = 1.0 for SI units

n = Manning coefficient of roughness - ranging from 0.01 (a clean and smooth channel) to 0.06 (a channel with stones and debris, 1/3 of vegetation)

Rh = hydraulic radius (ft, m)

S = slope - or gradient - of pipe (ft/ft, m/m)



Venutelli, M. A Constitutive Explanation of Manning’s Formula. Meccanica 40, 281–289 (2005).