Generalized Critical Slope for Trapezoidal Channels

The critical slope relations for a general trapezoidal channel have been examined in detail on the basis of Manning's equation and are presented in simple graphical form on dimensionless coordinates. For a given roughness coefficient, a triangular channel always has one depth only corresponding to each value of critical slope. For a trapezoidal channel (with given roughness coefficient and given bed width), however, there may be no, one, two, or three depth(s) corresponding to a given critical slope, depending on the inclination of the sides of the channel. Specifying these side slopes by a ratio of 1 vertical to z horizontal, there is a region of special interest in the range of z between 0 and 0.366350.