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1. Integrate the pressure forces over the surface of the irrotational flow about a cylinder to get the net force on the cylinder.

2. Now add to the 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.

3. Write the complete velocity potential and streamfunction of cylinder plus circulation.