Investigation of New Tsallis-Based Equation to Predict Shear Stress Distribution in Circular and Trapezoidal Channels

Abstract

In this study, the entropy concept is employed to estimate the shear stress distribution in a circular channel with flat bed and trapezoidal channel. Using the principle of maximum entropy, the shear stress distribution is derived by maximizing the Tsallis entropy by assuming averaged shear stress as a random variable. The derived shear stress equation can describe the variation of shear stress along the wetted perimeter of channel. The developed model of shear stress distribution is tested with some credible experimental data and is also compared with equations obtained by other researchers based on the Shannon entropy concept. The present model has shown good agreement with the observed data and performed better than the Shannon-based model in both cross-sections with better results of several computed quantitative criteria. The model precision in estimating shear stress in the trapezoidal channel with mean root mean square error (RMSE) of 0.0158 was higher than the circular channel with flat bed with RMSE of 0.0679.