Significance of Averaging Coefficients in Open‐Channel Flow Equations

Abstract

The Saint‐Venant equations commonly applied to solving unsteady open‐channel flow problems consist of a continuity equation and a momentum equation. In deriving the momentum equation, the pressure distribution is assumed to be hydrostatic, and the effect of nonuniform cross‐sectional velocity distribution is assumed to be small. Thus, the momentum and pressure correct coefficients β, k, and k′ are usually assumed to be equal to unity in applications. The effects of these assumptions on the solution of the flow equations have not been explored. The purpose of this paper is to investigate the significance of these assumptions by means of numerically solving the nearly exact unsteady open‐channel flow equations with systematically changing values of the coefficients. The results confirm that the effects of these coefficients are relatively small when the flow is nearly steady and uniform, and their effects increase with flow unsteadiness. These coefficients have a greater impact on the solution for velocity than for depth. The results also indicate more effects for convectively decelerating flow than for accelerating flow, especially when there is significant downstream backwater effect.