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
where
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)
Sources
Venutelli, M. A Constitutive Explanation of Manning’s Formula. Meccanica 40, 281–289 (2005). https://doi.org/10.1007/s11012-005-6529-5