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 germ of violence is laid bare in the child abuser by the sheer accident of his individual experience ... in a word, to a greater degree than we like to admit, we are all potential child abusers.”
—F. Gonzalez-Crussi, Mexican professor of pathology, author. “Reflections on Child Abuse,” Notes of an Anatomist (1985)