Prediction of boundary shear stress distribution in straight open channels using velocity distribution

Abstract

Conventional methods for measuring local shear stress on the wetted perimeter of open channels are related to the measurement of the very low velocity close to the boundary. Measuring near-zero velocity values with high fluctuations has always been a difficult task for fluid flow near solid boundaries. To solve the observation problems, a new model was developed to estimate the distribution of boundary shear stress from the velocity distribution in open channels with different cross-sectional shapes. To estimate the shear stress at a point on the wetted perimeter by the model, the velocity must be measured at a point with a known normal distance to the boundary. The experimental work of some other researchers on channels with various cross-sectional shapes, including rectangular, trapezoidal, partially full circular, and compound shapes, was used to evaluate the performance of the proposed model. Optimized exponent coefficients for the model were found using the multivariate Newton method with the minimum of the mean absolute percentage error (MAPE) between the model and experimental data as the objective function. Subsequently, the calculated shear stress distributions along the wetted perimeter were compared with the experimental data. The most important advantage of the proposed model is its inherent simplicity. The mean MAPE value for the seven selected cross-sections was 6.9%. The best results were found in the cross-sections with less discontinuity of the wetted perimeter, including the compound, trapezoidal, and partially full circular pipes. In contrast, for the rectangular cross-section with an angle between the bed and walls of 90°, MAPE increased due to the large discontinuities.