Width and Depth‐Constrained Best Trapezoidal Section

Abstract

Dimensions of the most efficient hydraulic cross section are found for channels of trapezoidal shape where top width and depth are limited. The resulting nonlinear constrained optimization problem is solved using the method of Lagrange multipliers. Without top-width or depth constraints the optimal section dimensions can be calculated without iteration. For channels in which top-width or depth constraints are imposed an iterative solution is needed to solve the resulting system of nonlinear equations. However, the calculations can be greatly simplified using accurate approximations of the general solutions that yield direct estimates of the best trapezoidal-cross-section dimensions. The computational procedure will be useful for designing nonerodible open channels of trapezoidal shape where top width or depth is constrained by site conditions.