Application of a Boussinesq-type equation to flow over trapezoidal profile weirs

Flow over embankment shaped weirs commonly encountered in large 2-D flow problems cannot be simulated by most of the common flow models which assume uniform velocity and hydrostatic pressure distributions. A Boussinesq-type momentum equation, which allows for curvature of the free surface and a non-hydrostatic pressure distribution, is considered in this paper for the numerical simulation of steady flow over short- and broad-crested trapezoidal profile weirs as well as for the establishment of head-discharge relationships under free flow conditions. An implicit finite difference scheme is applied. Computed and measured results of flow surface profiles and rating curves for these types of weirs are presented. The numerical results of the flow surface profiles and rating curves show good agreement with the corresponding experimental data. The model results also demonstrate the detailed dependence of the flow characteristics of these weirs on the curvature of the streamlines.