Two-Dimensional Jet and Cavity Flows

A method is given for calculating the location of free streamlines and the flow coefficient in certain two-dimensional, potential flows: Jet flow from a contracting channel and cavitating flow past a wedge in a channel. The problem is formulated in terms of the stream function in the flow, and a coordinate transformation is used to map the physical flow onto a velocity plane. The resulting boundary value problem for the stream function is solved in the velocity plane by separation of variables and an infinite integral representation. The results, given in terms of infinite integrals of elementary functions, may be calculated numerically. Key results are presented graphically.