Spatially-varied open channel flow equations with vertical inertia

Spatially-varied open channel flows with a streamwise discharge variation occur in the side-weir, side-channel and bottom outlet. The governing equations were formulated in the 1970s by Yen and Wenzel. However, no attempts were made to provide closure to the energy and momentum systems in terms of velocity and pressure conditions. Therefore, the current theoretical knowledge relates to the hydraulic approach based on uniform velocity and hydrostatic pressure distributions, which is known for deviations from real conditions in spatially-varied flow problems. Herein, Boussinesq's theory is applied including vertical inertia to spatially-varied flows, resulting in a higher-order closed-form system of equations for energy and momentum generalizing the theoretical development of Yen and Wenzel. The novel Boussinesq system contains terms accounting for spatially-varied discharge. This development is applied to the practical case of bottom outlet flow, resulting in good agreement with experimental results.