A flow of water in the horizontal xy-plane (no gravity effects) is described by the stream function = Axy, with A > 0 a

A flow of water in the horizontal xy-plane (no gravity effects) is described by the stream function ψ = Axy, with A > 0 a constant

 (a) Find both velocity components u and v. 

(b) Does a velocity potential φ exist (for certain A or for arbitrary A)? If so, determine it.

 (c) Assume that φ exists for A = 2 s−1. We now want to describe how the flow changes when we introduce an impenetrable wall at x = −1 m (). Show that by superimposing a uniform flow of speed U to the given flow you can indeed make x = −1 m a streamline. How large must U be?