8. Overall Minimum Cost Canal Sections

Design of a minimum cost canal section involves minimization of the sum of earthwork cost, cost of lining, and cost of water lost as seepage and evaporation 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. This chapter highlights design equations for the least cost canal sections considering earthwork cost which may vary with depth of excavation, cost of lining, and cost of water lost as seepage and evaporation from irrigation canals of triangular, rectangular, and trapezoidal shapes passing through a stratum underlain by a drainage layer at shallow depth. Using nonlinear optimization technique on augmented function, generalized empirical equations and section shape coefficients have been obtained for the design of minimum overall cost canal sections of triangular, rectangular, and trapezoidal shapes. The optimal dimensions for any shape can be obtained from proposed equations along with tabulated section shape coefficients. The optimal design equations are in explicit form and result into optimal dimensions of a canal in single-step computations that avoid the trial and error method of canal design and overcome the complexity of the minimum cost design of canals by a constrained nonlinear optimization technique. The optimal design equations show that the optimal section becomes wider and shallower than the minimum area section due to additional cost of excavation with canal depth, while reverse is the case due to cost of water lost as evaporation. On the other hand, for increased lining cost and/or the excavation cost at ground level, the optimal canal section approaches to the minimum area section, while for increased cost of water lost as seepage, it approaches to the minimum seepage loss section. Design examples with sensitivity analysis demonstrate the simplicity of the proposed design equations.