Critical Depth, Velocity Profile, and Channel Shape

Critical depth can be defined as (1) The depth at which fluid velocity equals the speed of a gravity wave; (2) the depth at which the Froude number equals one; (3) the depth at which specific force corrected for velocity profile is minimized; or (4) the depth at which specific energy corrected for velocity profile is minimized. When the velocity profile is not uniform (when a boundary layer exists), the definitions yield alternative results. The greatest critical depth is that minimizing specific energy corrected for velocity profile. A general solution for alternative definitions of critical depth is developed for several channel cross sections having an exponential velocity profile. A relative critical-depth equation is derived relating the profile-corrected solution to one without correction. For many engineered and natural channels, the difference is only a few percent, but profile-corrected critical depths can be significantly higher than uncorrected solutions in the case of channels with large velocity gradients. Design implications are discussed.