12 - Unsteady open channel flows: 2. Applications

Abstract

This chapter discusses the application of the Saint–Venant equations for unsteady open channel flow. In unsteady open channel flows, the velocities and water depths change with time and longitudinal position. The application of the Saint–Venant equations is limited by some basic assumptions, such as the flow is one-dimensional and the streamline curvature is very small and the pressure distributions are hydrostatic. A mathematical technique to solve the system of partial differential equations formed by the Saint–Venant equations is the method of characteristics. In the system of the Saint–Venant equations, the dynamic equation becomes a kinematic wave equation. The diffusion wave equation is a simplification of the dynamic equation assuming that the acceleration and inertial terms are negligible. The differential form of the Saint–Venant equations is presented. It is found that the celerity of the wave is equal to the celerity of the monoclinal wave but the diffusion wave flattens out with longitudinal distance while the monoclinal wave has a constant shape.