Numerical Simulation of Gradually Varying Permanent Flows in a Prismatic Open Channel for Four Geometric Shapes

Abstract

Standing flows in natural channels often cause phenomena that can be very serious, such as flooding, deformation of channel geometry, and destruction of infrastructure (dams, bridges, and culverts). This study focuses on the computation of gradually varying permanent flows (backwater curves) by two methods: direct integration (Chow) and successive approximation (depth variation). To solve the system of equations governing the problem of gradually varying one-dimensional stationary flows at a free surface, a large amount of data should be taken into account, namely, the flow rate, the water head, the mean flow velocity, the rugosity, and the slope. These parameters are very important, as they cause nonlinear behavior, making the problem and its mathematical solution complex. Digitizing these parameters can help to determine and visualize the longitudinal profile of the water line for known flow rates. This study aimed to: (1) determine the influence of rugosity on gradually varying steady flows and the overclassification of eddy curves in a prismatic channel, (2) study the effect of geometric shape on these flows, and (3) investigate and compare the effects of the calculation methods. The results reveal the great influence of rugosity on gradually varying permanent flows for four selected geometric shapes of the channel, as it has a direct influence on the normal depth and the critical slope. Each time the resistance of the bottom to the flow increases, these results increase. The influence of the geometric shape on these flows is less significant. The comparative study showed a difference between the results obtained.