Normal depth and wetted perimeter in general power-law channels

Abstract

Open channel cross section is an important element in water structures engineering. A general power-law section allows simulation and modeling of natural rivers and man-made open channels. Given simple forms and superior properties, the power-law sections are of interest to water resources engineers. The power-law exponent, m, is a parameter for which the open channel takes different shapes. The range of practical interest for the parameter m is 1 <m< ∞. Normal flow depth is of high importance and used for design and computation of water surface profiles in open channels with different shapes. The calculation of wetted perimeter and normal flow depth in power-law channels, ends up the hypergeometric functions and thus has been the main challenge over the years. Direct and simple solutions for these key quantities are not available in technical literature over the entire practical range of m> 1. Some studies are only valid over m> 2.5 while the others are applicable in the range of 1 <m< 2. This study presents direct and simple solutions for the normal flow depth and wetted perimeter in power-law channels over the wide practical range of 1.05 <m< 50. The maximum relative error of the proposed approximations for the normal flow depth and wetted perimeter are less than 1.2% and 0.3%, respectively. The proposed superior approximations can be used for channel section construction and optimization.