A cusp-like free-surface flow due to a submerged source or sink

We consider the steady flow induced by a line source placed at a given depth beneath the undisturbed level of a free-surface. We assume that the flow bifurcates at a definite point somewhere between the source and the undisturbed free-surface level. The free-surface at this point is cusp-like, the tip of the cusp pointing toward the source. The model is motivated by hydraulic problems of water entry or extraction from a reservoir. The problem is solved numerically by collocation. A unique solution is obtained whose cusp lies at 74.938% of the depth of the source.