The classic closed form solution for incompressible flow past a two-dimensional cylinder

The image represents the stream function of an incompressible inviscid flow past a cylinder. The stream function for this type of flow has a closed form solution in polar coordinates

\psi\left(r,\theta\right) = V_{\infty} \left(\frac{a^2}{r} - r\right) \sin{\theta}where `a`

is the cylinder radius.