Complex potential

Summary

The complex potential of a plane, incompressible and irrotational flow is a holomorphic function $w = \varphi + i \psi$. Its real part is the velocity potential and its imaginary part is the stream function. Its derivative gives the velocity directly, $w'(z) = u - i v$. It lets one use complex analysis, in particular conformal maps, to solve problems of two-dimensional potential flow, such as the flow around an airfoil.