Numerical solution of two dimensional flow

Abstract

An approximate method is presented to solve the problem of steady free-surface flow of an ideal fluid over u semi-infinite triungle in the bottom of un open channel. Schwartz- Christoffel transformation is used to map the region of flow, in the complex potential-plane, onto the upper half-plane. The Hilbert transformation as well as the perturbation technique are used as a basis for the approximate solution of the problem for large Froude number and small inclination angle of the ramp. General equations, in integral form, for any order of approximation are obtained. Solution up to first-order approximation is discussed and illustrated .