SIGNIFICANCE OF AVERAGING COEFFICIENTS IN OPEN-CHANNEL FLOW EQUATIONS

The Saint-Venant equations commonly applied to solving unsteady open-c hannel flow problems consist of a continuity equation and a momentum e quation. In deriving the momentum equation, the pressure distribution is assumed to be hydrostatic, and the effect of nonuniform cross-secti onal velocity distribution is assumed to be small. Thus, the momentum and pressure correct coefficients beta, 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 pur pose of this paper is to investigate the significance of these assumpt ions by means of numerically solving the nearly exact unsteady open-ch annel flow equations with systematically changing values of the coeffi cients. The results confirm that the effects of these coefficients arc relatively small when the flow is nearly steady and uniform, and thei r effects increase with flow unsteadiness. These coefficients have a g reater impact on the solution for velocity than for depth. The results also indicate more effects for convectively decelerating flow than fo r accelerating flow, especially when there is significant downstream b ackwater effect.