Boundary Shear Stress in a Trapezoidal Channel

Abstract

This paper focuses on a hydraulic radius separation approach used to calculate the boundary shear stress in terms of bed and wall shear stress proposed in a trapezoidal channel. The average bed and sidewall shear stress in smooth trapezoidal open channels are derived after using Guo & Julien (2005) early equations taking a part of an investigation to cover both rectangular and trapezoidal channels. On the basis of the conformal mapping procedure, a numerical solution is obtained for a case of constant eddy viscosity without concerning secondary currents effect. In comparison with laboratory measurements data, the first approximation for a rectangular channel overestimates the average bed shear stress measurement by about 4.8% and by decreasing a sidewall slope, overestimation increases. It, however; underestimates the average sidewall shear stress by about 6.88%; in this case, underestimation increases while sidewall slope is decreasing. A second approximation is then presented by introducing two lumped empirical correction factors for taking into account the effects of secondary currents, variable eddy viscosity and else. Using experimental data, in terms of average bed shear stress, the second approximation agrees very well (at least R2>0.99, and an average relative error at most less than 5.35%) over a wide range of width to depth ratios. In terms of average wall shear stress, the second approximation returns acceptable results despite the scatter of the data with an average relative error less than 5.95% and by R2>0.93 where it seems to be reasonable, herein.