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Velocity potential

A velocity potential is used in fluid dynamics, when a fluid occupies a simply-connected region and is irrotational. In such a case,

\nabla \times \mathbf{u} =0,

where \mathbf{u} denotes the flow velocity of the fluid. As a result, \mathbf{u} can be represented as the gradient of a scalar function Φ:

\mathbf{u} = \nabla \Phi \;,

Φ is known as a velocity potential for \mathbf{u}.

A velocity potential is not unique. If a is a constant then Φ + a is also a velocity potential for \mathbf{u}. Conversely, if Ψ is a velocity potential for \mathbf{u} 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.

See also

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.
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