Velocity potential

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,: abla imes 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} = abla Phi ; , Φ 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.

ee also

*Potential flow
*Hamiltonian fluid mechanics


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