Problem $1$

The superposition $=Kxy+m$ represents a flow approaching a bump of height $h,$ as shown.

$($a$)$ By requiring $A(0,h)$ to be a stagnation point, relate $h$ to $K$ and $m.$ To reduce algebra, work in polar coordinates and substitute $sincos=\frac{1}{2}sin2.$

$($b$)$ Find the equation of the "bump" $($i$.$e$.,$ of the streamline that passes through point A$).$

$($c$)$ Given that $P=P_0$ and vec$(u)=-V_0$hat$()$ as $r$ at $=\frac{}{2},$ find $P_A$ in terms of $P_0$ and $V_0.$ Assume that the xy plane is horizontal so gravity can be ignored.