$2_{U_{}}$We can model potential flow over a jellybean by using a source $($Q$),$ vortex $(\backslash$Gamma $),$ and sink $($Q$)$

placed on the x axis as shown below. When combined with uniform flow $($U$\backslash$infty $),$ the superimposed

elementary flows will model flow over a closed shape that resembles a jellybean. For the numerical

parts below, use U$\backslash$infty $=5$m$/$s$,\backslash$Gamma $=10$m$2/$s$,$ Q $=8$m$2/$s$,$ and h $=0\mathrm{.}5$m$.$

a$)$ Write the complex potential, F $($z$),$ for this flow, in terms of z and the given parameters $($not

numerical values$).$

b$)$ Write the equation for the complex velocity, w$($z$),$ again in terms of the given parameters.

c$)$ Determine the location of the stagnation points in this flow, using the given numerical values.

You should find three points, with two at the leading$/$trailing edge of the closed shape.

Please show all work!!