Experimental measurements suggest that the frictional resistance experienced by a uniform flow is approximately proportional to the square of the volumetric flow rate, provided the velocity of the flow is not too small. If u defines the mean velocity and m the mean hydraulic depth, the Chezy formula gives:
where i is the gradient of the total head line and C is the Chezy coefficient. In the context of open channel flow, the Chezy formula may be written as:
where the bed slope (s) is equivalent to i for steady uniform flows.
Although the Chezy formula was originally defined empirically, it is directly related to the friction factor (f). The Chezy coefficient is thus dependent upon surface roughness, the Reynolds number, and the hydraulic mean depth. Tabulated values of C and the related coefficient n (usually referred to as Mannings coefficient) are given by Chow (1959).
Chow, V. T. (1959) Open-Channel Hydraulics. McGraw-Hill Inc., New York.