Analytical solution of simplified surge flow equations

The approximate theory of G. B. Witham, proposed in 1955, is often used to initialize numerical computation of border irrigation or a dam-break flood. However, this study shows that the main assumption of a uniform velocity profile is inconsistent with the law of mass conservation. Therefore that assumption is no longer employed in the development of the analytical solution of the continuity equation and a simplified momentum equation. The solution turns out to be a rather simple but powerful formula which can replace the more approximate solution of Witham without any increase of computational effort, but with a substantial gain of reliability.