$6\mathrm{.}31$ The stream function for a two$-$dimensional, nonviscous, incompressible flow field is given by the expression

q $=-2($x $-$ y$)$

where the stream function has the units of ft$/$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 $=2$ ft$,$ y $=2$ ft$.$