Semi-analytical method to estimate boundary shear stress in smooth rectangular and trapezoidal open channels

Abstract

The boundary shear stress is obtained from the continuity and momentum equations in smooth prismatic open channels. Shear stress is a function of gravity, secondary flow, and gradient velocity. In this research, semi-analytical equations were obtained to estimate the average boundary shear stress in smooth rectangular and trapezoidal open channels by 0.5, 1, 1.5 and 2 side slopes using conformal mapping techniques. After dividing the channel cross section into the bed and wall sub-sections, the present study used the method by Guo and Julien (2005) to estimate the average shear stress of the bed and the wall in open channels. For the studied case, by the first shear stress estimation, secondary current and constant eddy viscosity were neglected. After recommending two secondary current and eddy viscosity correction factors, a second approximation well matched the experimental measurements of the average shear stress for all aspect ratios.