The Chezy Formula
The Chezy formula is the most common method of calculating flow in an open channel. The Chezy coefficient (C) can be calculated multiple different ways shown below.
The most common method of calculating flow in and open channel: V = C\sqrt{RS}

where
 V = velocity (ft/sec)
 C = Chezy's frictional coefficient (aka coefficient of rugosity). C has been empirically calculated by Manning and DarcyWeisbach (shown below)
 R = hydraulic radius (ft)
 S = slope of channel bed
C By DarcyWeisbach
For a small, very smooth channel, the following can be used:
where
 f = DarcyWiesbach friction coefficient
 g = gravity (32.2 ft/sec^{2} or 9.8 m/sec^{2})
C By Manning
Large channels with fully turbulent flow (friction no longer plays a significant role but rather the channel roughness is important):
where
 R = hydraulic radius (ft)
 n = Manning's roughness coefficient
The ChezyManning Equation
For simplicity, combining the Chezy Formula with the Manning roughness coefficient you'll get:
where
 R = hydraulic radius (ft)
 n = Manning's roughness coefficient
 S = slope of channel bed