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A velocity potential is used in fluid dynamics, when a fluid occupies a simply-connected region and is irrotational. In such a case,
Additional recommended knowledge
where denotes the flow velocity of the fluid. As a result, can be represented as the gradient of a scalar function Φ:
Φ is known as a velocity potential for .
A velocity potential is not unique. If a is a constant then Φ + a is also a velocity potential for . Conversely, if Ψ is a velocity potential for then Ψ = Φ + b for some constant b. In other words, velocity potentials are unique up to a constant.
Unlike a stream function, a velocity potential can exist in three-dimensional flow.
|This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Velocity_potential". A list of authors is available in Wikipedia.|