12 11/21

1. Use the software of your choice (mathlab, mathcad, mathematica, ...) to plot lines of constant streamfunction $\psi$ for irrotational, incompressible flow around a cylinder. Take $U=r_0=1$.

2. Also plot the isobars. Take $p_\infty=0$. (Check that you have the right pressure values at the stagnation points and top and bottom points of the cylinder.) Are the pressures on front and rear of the cylinder the same? Are they the same on top and bottom?

3. Now add $\ln(r)$ to the streamfunction. (This does not change the boundary conditions since $\ln1=0$ and $v_r=1/r=0$ at large $r$.) Replot the streamlines.

4. Replot the isobars. Comment on the pressures. Will the force still be zero? If not, in what direction will it be?

5. Add another $3\ln(r)$ to the streamfunction. Replot the streamlines.

6. Replot the pressure.