Similarity solution of dam-break flow on horizontal frictionless channel

Compared with the Blasius similarity approach for the boundary layer theory, a similarity solution for dam-break flow on a horizontal channel with zero friction is considered by the theory of scale transformation. Time and space coordinates as the two independent variables are substituted by one independent dimensionless similarity variable, so that the governing partial differential equations can be transformed into a system of ordinary differential equations. The analytical similarity dam-break solution on a dry bed and the multinomial algebraic equation of shock wave on a wet bed are proposed for a prismatic channel of triangular cross-section. Basing on the similarity characteristic of dam-break flow, the flood propagation at any time and space can be described by a dimensionless curve. The dimensionless positions of strong and weak discontinuities for dam-break shock wave do not change with time, and the description of the dam-break hydrograph is therefore simplified.