The velocity potential $=2(x^2-y^2)$ describes the impinging flow against a flat plate

$($a$)$ Prove that the change in pressure in the $x$ direction is linearly proportional to the independent variable $x.($Assume gravity in the $x$ direction is negligible$)$

$($b$)$ Find the corresponding stream function.

$($c$)$ The combination of the above flow and a source of strength $m$ at the coordinate's origin describes the impinging flow against a "bump" as shown. Find the value of the maximum height, $h$ of the bump if $m=2.$