Design for Minimum Flow Area

Abstract

A canal based on minimization of flow area objective function for a specified discharge and canal bed slope implies maximum flow velocity or best hydraulic section. The best hydraulic section provides maximum carrying capacity for a fixed cross-sectional area or minimum cross-sectional area and perimeter to pass a given discharge. A particular set of geometric proportions yield a best hydraulic section for the specific shape of channel. As it is a minimum area and minimum perimeter section, it provides maximum hydraulic radius and requires least cost in excavation and lining. In this chapter, design of minimum flow area or maximum flow velocity sections for viscous and turbulent flows and sediment carrying canals are covered. Both the objective function and constraint for minimum flow area sections are nonlinear, so optimization problem is hard to solve analytically. The problem was converted in the unconstrained form through penalty function. A nondimensional parameter approach has been used to simplify the analysis. The dimensionless augmented function was minimized using a grid search algorithm. Using results of the optimization procedure and error minimization, close approximations in explicit form have been obtained for optimal channel dimensions. The optimization method has resulted in the optimal geometric properties for circular, trapezoidal, triangular, and rectangular sections. Presented equations result in section dimensions in single-step computations. A design example involving different cases has been presented to demonstrate the simplicity of the method.