Method of Solution of Nonuniform Flow with the Presence of Rectangular Side Weir

Abstract

An iterative step method for solving the nonlinear ordinary differential equation, governing spatially varied flows with decreasing discharge, like the flow over side weirs, is developed. In the procedure, starting at a known flow depth and discharge in the control section, the analytical integration of the dynamic equation with bed and friction slope is carried out. The specific energy, the weir coefficient and the velocity distribution coefficient are considered as local variables, then for the explicit integration, the respective average values along the short side weir elements are assumed. The water surface profiles and the discharges for flow over side weirs, obtained with the proposed relation and valid for rectangular channels, are compared with experimental data for subcritical and supercritical flow conditions. The validation of the method is accomplished by the comparison with the solution obtained by De Marchi’s classical hypothesis, about the specific energy, which is constant along a side weir. In addition, the influence of the coefficient velocity distribution is considered.