The Manning formula is an engineering formula useful for determining the velocity of water flowing in an open channel. It is empirical, and relies on the semiperimeter R, defined as (A/P) where A is the cross sectional area of flow and P is the wetted perimeter:
V= ---------  So^(1/2)              (S.I. Units)
where So is the slope and n is a special roughness factor (the empirical fudge factor). Manning's n for various surfaces:
Concrete culvert, clean          0.011
Concrete culvert, rough          0.017
Earth, straight and uniform      0.022
Earth bottom, rubble sides       0.030