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:
“There is a potential 4-6 percentage point net gain for the President [George Bush] by replacing Dan Quayle on the ticket with someone of neutral stature.”
—Mary Matalin, U.S. Republican political advisor, author, and James Carville b. 1946, U.S. Democratic political advisor, author. All’s Fair: Love, War, and Running for President, p. 205, Random House (1994)