Discussion of 'Depth-Averaged Shear Stress and Velocity in Open-Channel Flows' by Shu-Qing Yang

摘要

Eq. (1) of the original paper shows that a derivative AA/Ap (a ratio of elementary area between two normal lines to the elementary wetted perimeter) is equal to ΔA/Δp=τb(z)/pgS=L(z) where T_b(z) is a local boundary shear stress. In the trapezoidal canal values, L(z) are equal to lengths of the normal lines from a point z on the wall or the bed to the free surface line or to the bisector line of the trapezoid interior angle. The four parts of the trapezoid canal cross section divided according to the original method [Eq. (15)] are shown in Fig. 1. Function L(z) has a piecewise-linear structure with a variable sign of derivative for any trapezoidal cross section (Fig. 2).