velocity potential

A scalar function with its gradient equal to the velocity vector u of an irrotational flow. If χ(x, y, z) is the velocity potential,

If the flow is also nondivergent, the velocity potential satisfies the Laplace equation

The velocity is everywhere normal to the surfaces of constant velocity potential. If a velocity potential exists, it is simpler to describe the motion by means of the potential rather than the vector velocity, since the former is a single scalar function whereas the latter is a set of three scalar functions.