Velocity potential

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,

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

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