High Quality Content by WIKIPEDIA articles! 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 Phi;: mathbf{u} = nabla Phi;, Phi; is known as a velocity potential for mathbf{u}. A velocity potential is not unique. If a; is a constant then Phi+a; is also a velocity potential for mathbf{u};. Conversely, if Psi; is a velocity potential for mathbf{u}; then Psi=Phi+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.

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