The use of a one-dimensional depth-averaged moment of momentum equation for the nonhydrostatic pressure condition

Abstract

A depth-averaged model formulated in the Cartesian coordinate system for curved open-channel flows is extended to solve problems where the effects of nonhydrostatic pressure distribution and nonuniform velocity distribution are significant. The nonhydrostatic pressure condition is added to the z-direction momentum equation assuming that the pressure deviation from the hydrostatic condition at the channel bed decreases linearly to the water surface. The pressure-effect terms are modified in both the moment of momentum and momentum equations. The resulting system of nonlinear equations is solved by a finite-element method. The derived model is then applied to four sophisticated nonuniform flow experiments from the literature. A comparison of the actual experimental results with their numerical prediction results, as calculated with the model, is presented. Generally speaking, a fairly good agreement for the depth-averaged velocities as well as reasonable perturbation profiles were obtained from this comparison. Therefore, it can be said that the depth-averaged model for open-channel flow is reasonably accurate under the given conditions. Key words: open-channel flow, depth-averaged method, finite-element method, nonhydrostatic pressure, nonuniform flow.