Theoretical solution of dam-break shock wave

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 cha nnels of rectangular cross section, a new theoretical solution expressed us ing 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 a s depth and velocity of flow, and velocity of discontinuity-are determined only by the ratio of initial downstream depth to initial upstream depth. Th e model shows that results from the new equation are completely equivalent to those of the set of old equations. In addition, the hood hydrograph prod uced by a dam break at any time or any site can be described by a single cu rve in terms of dimensionless variables.