Problem $7$

A steady, incompressible, two$-$dimensional flow $($fluid density $=1\mathrm{.}2k\frac{g}{m^3})$ down a hill is modelled as the potential flow created by adding a uniform flow of velocity $U_0=10\frac{m}{s}$ and pressure $P_0=0Pa($gage$)$ plus a sink at the origin of unknown strength $m.$ The flow forms a stagnation point at $(x,y)=(L,0),$ where $L=15m.$ Gravitational effects can be neglected in this problem.

$($a$)$ Find the value of the sink strength, $m.$

$($b$)$ Find an equation for the streamline that passes through the stagnation point $($i$.$e$.,$ an equation relating the $x$ and $y$ coordinates of the ground$).$ You can leave the final equation in an implicit form, without explicitly isolating $y$ on one side.

$($c$)$ Point $P$ is located at $(x,y)=(2L,2L).$ What is the gage pressure at that point?