Most Hydraulically Efficient Standard Lined Canal Sections

Abstract

Cross-sectional dimensions of the most hydraulically efficient lined canals are evaluated based on an analysis of a generalized trapezoidal shape that reduces to two standard sections with rounded bottom vertices used in India, as well as to the commonly used trapezoidal section with sharp bottom vertices. The method of Lagrange multipliers is applied to find the dimensions of optimal sections when the only constraint imposed is that of uniform flow and normal depth and, in addition, when values of either channel side slope, bottom width, top width, or supply depth are specified as well. The analytic solutions obtained for the generalized trapezoidal section are shown to match known solutions for limiting cases including those for sections in the shape of sharp-cornered trapezoids, rectangles, triangles, and semicircles. Solutions presented will be useful for evaluating standard cross-sectional shapes used for lined canals in India, as well as other sections that can be obtained from the generalized trapezoid with rounded bottom vertices.