6. Minimum Cost Canal Section

Though the minimum area section is generally adopted for lined canals, it is not the minimum cost section as it does not involve lining cost and the cost of earthwork. In general, the cost of earthwork varies with canal depth. Design of a minimum cost canal section involves minimization of the sum of earthwork cost and cost of lining subject to uniform flow condition in the canal, which results in nonlinear objective function and nonlinear equality constraint making the problem hard to solve analytically. This chapter discusses the nonlinear optimization method to obtain explicit design equations and section shape coefficients for the design variables for minimum cost canal section for triangular, rectangular, trapezoidal, and circular shapes. These optimal design equations and coefficients have been obtained by analyzing a very large number of optimal sections resulted from the application of optimization procedure in the wide application ranges of input variables. The analysis consists of conceiving an appropriate functional form and then minimizing errors between the optimal values and the computed values from the conceived function with coefficients. Particular cases like minimum earthwork cost section and minimum and maximum discharge canal sections are also included in the chapter. The optimal design equations show that on account of additional cost of excavation with canal depth, the optimal section is wider and shallower than the minimum area section. Application of the proposed design equations along with the tabulated section shape coefficients results directly into the optimal dimensions of minimum cost canal sections without going through the conventional trial and error method of canal design.