Theoretical Solution of Dam-Break Shock Wave

Abstract

A mathematical model of dam-break shock waves, or flood waves, in channels of trapezoidal cross section is presented. When the model is applied to channels of rectangular cross section, a new theoretical solution expressed using one independent multinominal algebraic equation is derived. In the past, the solution had to be described using three interrelated equations. The new equation indicates that the hydraulic parameters of a shock wave—such as depth and velocity of flow, and velocity of discontinuity—are determined only by the ratio of initial downstream depth to initial upstream depth. The model shows that results from the new equation are completely equivalent to those of the set of old equations. In addition, the flood hydrograph produced by a dam break at any time or any site can be described by a single curve in terms of dimensionless variables.