The stream function for an inviscid, incompressible, and irrotational two-dimensional flow field is given by [30 points].
a) Determine the velocity potential for this flow field. [15 points]
(b) Plot the lines of constant and constant by setting them to various constants. (Hint: It will be convenient to set x as a function of y for plotting ψ and vice-versa for φ. Check that they intersect at right angles). [15 points]