Velocity potential

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velocity potential

A scalar function with its gradient equal to the velocity vector u of an irrotational flow.

If χ(x, y, z) is the velocity potential,
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If the flow is also nondivergent, the velocity potential satisfies the Laplace equation
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The velocity is everywhere normal to the surfaces of constant velocity potential. If a velocity potential exists, it is simpler to describe the motion by means of the potential rather than the vector velocity, since the former is a single scalar function whereas the latter is a set of three scalar functions.

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