 Potential flow

A potential flow has a velocity field represented by a scalar velocity potential, $\mathbf{v}=\nabla \varphi$. Its vorticity vanishes wherever $\varphi$ is sufficiently smooth. In a constant-density incompressible flow, mass conservation additionally gives Laplace's equation ${\nabla }^2\varphi =0$.

This reduces a vector-flow problem to a scalar boundary value problem. Linear combinations of elementary source and sink potentials can construct flows around simple geometries. The representation can be local even when a globally single-valued potential fails: a circulation-carrying flow around an excluded core has zero vorticity in the fluid region but can have nonzero circulation around the hole. Neglect of viscous effects also limits predictions near solid surfaces and in a wake. A useful potential-flow approximation therefore needs both its domain and its treatment of boundaries stated explicitly.