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The determination of the free streamline of a jet of ideal fluid flowing past a wall of arbitrary shape is considered. A transformation technique is used to formulate the fluid mechanics problem by relating the deflection of the free surface to the angle made by the wall to the undisturbed jet which is found as a solution of a nonlinear integral equation. Linearized solutions, based upon small elevations or depressions in the wall, and nonlinear numerical solutions to this equation are presented for a variety of wall shapes. Some inadequacies of both this linear theory and shallow water theory are found.

Free streamline flow over curved topography