Repeat Prob. 960, except make up your own stream function. You may create any function (x, y)

Repeat Prob. 9–60, except make up your own stream function. You may create any function ψ(x, y) that you desire, as long as it contains at least three terms and is not the same as an example or problem in this text. Discuss.

Data from Problem 9–60

A steady, two-dimensional, incompressible flow field in the xy-plane has a stream function given by ψ = ax² – by² + cx + dxy, where a, b, c, and d are constants.

Obtain expressions for velocity components u and v.

Verify that the flow field satisfies the incompressible continuity equation