Assignment/Reading 8, Physics 426 Fluid Mechanics

Reading (Participation only, very short answer)

Suppose a flow is impinging on a flat plate of length $2a$ at an angle $\alpha$ to the plane of the plate.

Using the Joukowski transform, show that a circle of radius $a$ can be mapped to a straight line for an appropriate value of $b$ ($z = \zeta + b^2/\zeta$).
Given a solution for the flow over a circle in the $\zeta$-plane, contour the solution in the z-plane for $\Gamma=0$.
What value of $\Gamma$ is necessary for the flow to have a stagnation point at the trailing edge of the plate? Contour this flow as well. (hint consider the tangential velocity around the sphere and note that it has to go to zero at $\theta=0$.)
What is the value of the velocity around the plate? What happens to the lift in this case?