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A velocity potential is a scalar potential used in potential flow theory. It was introduced by Joseph-Louis Lagrange in 1788.
It is used in continuum mechanics, when a continuum occupies a simply-connected region and is irrotational. In such a case,
Φ is known as a velocity potential for u.
A velocity potential is not unique. If Φ is a velocity potential, then Φ + a is also a velocity potential for u, where a is a scalar function of time and can be constant. In other words, velocity potentials are unique up to a constant, or a function solely of the temporal variable.
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