Simplified Design of Hydraulically Efficient Power-Law Channels with Freeboard

A power-law channel section is very versatile. It can model a wide range of familiar man-made or natural channel shapes. However estimating the wetted perimeter of a power-law channel section is difficult. The problem gets complicated further when considering the freeboard in the design process. In this paper, the wetted perimeter is estimated using the isoperimetric theorem which results in a simple and accurate expression for the wetted perimeter that does not lead to discontinuity in the optimal solution. For unconstrained optimum power-law channels, it is shown that the exponent and side slope at the water surface have values of 0.314 and 0.352, respectively, independent of either the maximum side slope or the relative freeboard. The analyses have also shown that the most hydraulically efficient power-law channel sections come closest to the semicircle. They tend to be U shaped and narrow with small relative freeboard $(⩽0.30)$ . A design procedure and two design charts are presented together with two illustrative examples to demonstrate the simplicity of the method.