An incompressible flow field is characterized by the stream function \(\psi=3 A x^{2} y-A y^{3}\), where \(A=1 \mathrm{~m}^{-1} \cdot \mathrm{s}^{-1}\). Show that this flow field is irrotational. Derive the velocity potential for the flow. Plot the streamlines and potential lines, and visually verify that they are orthogonal.