A velocity potential is used in fluid dynamics, when a fluid occupies a simply-connected region and is irrotational. In such a case,
where denotes the flow velocity of the fluid. As a result, can be represented as the gradient of a scalar function :
- ,
is known as a velocity potential for .
A velocity potential is not unique. If is a constant then is also a velocity potential for . Conversely, if is a velocity potential for then for some constant . In other words, velocity potentials are unique up to a constant.
If a velocity potential satisfies Laplace equation, the flow is incompressible.
Unlike a stream function, a velocity potential can exist in three-dimensional flow.
Famous quotes containing the word potential:
“The planet on which we live is poorly organized, many areas are overpopulated, others are reserved for a few, technology’s potential is only in part realized, and most people are starving.”
—Friedrich Dürrenmatt (1921–1990)