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1. Find boundary conditions for the streamfunction for transverse ideal flow around a circular cylinder. The velocity far away from the cylinder is $U{\widehat \imath}$ and the radius of the cylinder is $r_0$.

2. Following similar lines as in class, but watching the new boundary conditions, solve the equation for the streamfunction around the circular cylinder. Before continuing, check your results for the radial and tangential velocity components at the surface of the cylinder against the one from the velocity potential solution obtained in class. Is the velocity at the top and bottom points $2U$? Are the stagnation points correct?

3. Find the pressure on the surface of the cylinder.

4. Integrate the pressure forces over the surface of the cylinder to get the net force on the cylinder.

5. Now add to the above velocity field the velocity field of an ideal vortex,
   
   $$\vec v = \frac{\Gamma}{2\pi r} {\widehat \imath}_\theta$$
   
   
   Check whether the correct flow boundary conditions are still satisfied at the surface of the cylinder and far from the cylinder. Integrate the pressure again, and compare the forces to D’Alembert and Kutta-Joukowski.