Boundary shear stress distribution in straight open trapezoidal channels using velocity distribution

Abstract

The velocity of only one point from normal to the wetted perimeter must be known to obtain local shear stress at a point along the wetted perimeter. Then, the local shear stress on the wetted perimeter is calculated using the viscous shear stress relation and defining the non-dimensional variable ξ. ξ is considered a parametric function of some non-dimensional hydraulic and geometric variables of channel and fluid. Several experimental data are used to achieve a general form for the function, and the parameters are obtained by minimizing the MAPE (Mean Absolute Percentage Error). MAPE between the data observed and calculated by a genetic algorithm is minimized to modify the model for trapezoidal sections. Experimental data from twenty trapezoidal sections have been selected. Twelve are used for training, and the remaining eight are for testing. The average value of MAPE is 7.1%. However, one section is rectangular, with a calculated MAPE of about 16%. The high discontinuity of the wetted perimeter of the rectangular cross-section due to the 90 ° angle between the bed and the walls is responsible for approximately a large amount of MAPE. MAPE is less than 7% in 14 selected sections, twelve are used for training, and the remaining eight are for testing. The average value of MAPE is 7.1%. However, one of the sections is rectangular in which the calculated MAPE is about 16%. The high discontinuity of the wetted perimeter of the rectangular cross-section due to the 90 ° angle between the bed and the walls is responsible for approximately a large amount of MAPE in that case. MAPE is less than 7% in 14 selected sections.