$$ Problem $2$: $(35$ points total$)$

Air at $)=101\mathrm{.}3$kPa,${}_{\text{a}\text{i}\text{r}}=(1\mathrm{.}2\frac{kg}{m^3}$ flows normal to the axis of an in cylinder of $0\mathrm{.}5$ m radius. The freestream velocity $V_{}$ is $10\frac{m}{s},$ and a vortex with located at the origin. The lift coefficient $c_l$ is $2.$ Assume potential flow.

$($a$)$ Calculate the vortex strength $($in $\frac{m^2}{s})$ and the cylinder rotational speed

$($b$)$ Find the location of the stagnation points on the circular cylinder.

$($c$)$ Calculate the maximum and minimum pressure coefficients on the cylinder