Optimal design of curved bed trapezoidal canal sections

Optimal design equations for circular and parabolic bed trapezoidal canal sections are presented in this paper. A cost function involving earthwork cost and lining cost has been considered and Manning's equation has been used as a constraint function. The resulting optimisation problem involving a non-linear cost function with the non-linear equality constraint has been converted in non-dimensional form and has then been solved by Lagrange's method of undetermined multipliers for the minimum area section and by applying Solver by MS Excel for minimum cost sections. The study also addresses the bounds on the canal dimensions. The design equations for a constrained section, a minimum earthwork cost section and a minimum cost lined section have been obtained through minimisation of errors or regression analysis. The proposed design equations are in explicit form and result in optimal dimensions of a canal in single step computations. A design example involving different cases has been presented to demonstrate the simplicity of the method.