Comprehensive Design of Minimum Cost IrrigationCanal Sections

Abstract

Design of a minimum cost canal section involves minimization of the sum of costs per unit length of the canal, subject to uniform flow condition in the canal. Essentially it is a problem of minimization of a nonlinear objective function subject to a nonlinear equality constraint. In this investigation, the objective function has been expressed as the cost per unit length of the canal for lining, the depth-dependent unit volume earthwork cost, and the cost of water lost as seepage and evaporation losses. A general resistance equation has been used as an equality constraint. Using a nonlinear optimization technique on an augmented function, generalized empirical equations and section shape coefficients have been obtained for the design of minimum cost irrigation canals of triangular, rectangular, and trapezoidal shapes. The optimal dimensions for any shape can be obtained from the proposed equations along with tabulated section shape coefficients. The equation for optimal cost along with the corresponding section shape coefficients is useful during the planning of a canal project. A design example with sensitivity analysis has been included to demonstrate the simplicity of the present method.