Optimal lined channel design

The optimum values of the section variables (side slope, bottom width, flow depth, and radius) for triangular, rectangular, trapezoidal, and circular channels are computed by minimizing the cost of the channel section. Manning's uniform flow formula is treated as the constraint of the optimization model. The cost function is arranged to include the cost of lining, the cost of earthwork, and the increment in the cost of earthwork with depth below the ground surface. The optimum values of section variables are expressed as explicit functions of unit cost terms. Unique values of optimum section variables are obtained for the case of minimum area or minimum wetted perimeter problems.