The stream function for a two-dimensional, nonviscous, incompressible flow field is given by the expression

\[ \psi=-2(x-y) \]

where the stream function has the units of \(\mathrm{ft}^{2} / \mathrm{s}\) with \(x\) and \(y\) in feet.

(a) Is the continuity equation satisfied?

(b) Is the flow field irrotational? If, so, determine the corresponding velocity potential.

(c) Determine the pressure gradient in the horizontal \(x\) direction at the point \(x=2 \mathrm{ft}, y=2 \mathrm{ft}\).