11 - Unsteady open channel flows: 1. Basic equations

Abstract

This chapter elaborates the development of the continuity and momentum equations for one-dimensional unsteady open channel flows. In unsteady open channel flows, the velocities and water depths change with time and longitudinal position. For one-dimensional applications, the relevant flow parameters (example V and d) are functions of time and longitudinal distance. Analytical solutions of the basic equations are nearly impossible because of their non-linearity, but numerical techniques provide approximate solutions for some specific cases. . The basic one-dimensional unsteady open channel flow equations are called the Saint–Venant equations. These equations are based upon a number of key, basic assumptions, such as the flow is one dimensional, the velocity is uniform in a cross-section and the transverse free-surface profile is horizontal and the streamline curvature is very small and the vertical fluid accelerations are negligible. The differential form of the Saint–Venant equations is also elaborated.