$1.(25$ pts$)$ Consider a steady, two$-$dimensional, incompressible, irrotational velocity field specified by its velocity potential

function, $()22$

$31\mathrm{.}52\mathrm{.}5$x y x y

$=+.$

$($a$)$ Calculate velocity components u and v$.$

$($b$)$ Verify that the velocity field is irrotational in the region in which

applies.

$($c$)$ Generate an expression for the stream function in this region.