Hydraulically Efficient Power-Law Channels

Abstract

A power-law channel is a generalized form of a channel and includes parabolic and triangular cross sections. For an exponent m<0.5 in the power law, the relative wetted perimeter has been estimated from a series expansion truncated to four terms. For values of the exponent m 0.5 the relative wetted perimeter has been estimated using an appropriate non-linear interpolation expression. A table to estimate relative wetted perimeter based on these expressions is presented for design purposes. With these expressions for relative wetted perimeter, and using the Lagrange method of undetermined multipliers, for any given maximum side slope, the area and/or wetted perimeter is minimized subject to the equality constraint of a uniform flow (Mannings) equation. Using this technique, for any given side slope, the exponent of the power-law channel can be determined and hydraulically efficient power-law channels can be designed. Optimized power-law channels are compared with trapezoidal and parabolic channels. The existing parabolic design of the Pehur High Level Canal, Pakistan is compared with an optimum power-law channel.