Flow in Open Channels with Smooth Curved Boundaries

The proposed method of solution is manifested by application to an example, the potential flow over a smooth step in an open channel. A detailed description of the flow is given by a pair of integro-differential equations in the free-surface and solid-boundary elevations, derived from the solution of a boundary-value problem of the Dirichlet type in an infinite strip in the complex potential plane. The use of numerical approximations to both the derivatives and integrals in the integro-differential equations leads to a system of simultaneous nonlinear algebraic equations, and this is then solved by a special method of successive approximation. Solutions are obtained for the approach Froude number, F = 0.4 and 1.7. The computed output consists of the geometry of the free surface, the flow net within, and velocity components and pressure at any point in the flow.