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,

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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.

See also

• Potential flow
• Hamiltonian fluid mechanics