A flow in which vorticity is zero is called potential flow, or irrotational flow. Since the vorticity is zero
it implies that the velocity is the gradient of a scalar field called the velocity potential, and usually denoted as
At high Reynolds numbers, flow past slender bodies is attached (no boundary layer separation) and the boundary layers are thin. In such situations vorticity is confined to the thin boundary layers and the rest of the flow is irrotational.
In the case of an incompressible flow, satisfies the Laplace equation.
From the continuity equation, we get: