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:
“If the Russians have gone too far in subjecting the child and his peer group to conformity to a single set of values imposed by the adult society, perhaps we have reached the point of diminishing returns in allowing excessive autonomy and in failing to utilize the constructive potential of the peer group in developing social responsibility and consideration for others.”
—Urie Bronfenbrenner (b. 1917)