## Encyclopedia > Potential flow

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# Potential flow

Potential flow, also know as incompressible flow or irrotational flow in fluid mechanics is flow defined by the equations

$\nabla \times \mathbf{v} = 0$ (zero rotation = no shear)

$\nabla \cdot \mathbf{v} = 0$ (zero divergence = continuity)

Equivalently,

$\mathbf{v} = \nabla \Phi \; ,$

where:

• v is the vector fluid velocity
• Φ is the fluid flow potential, scalar
• " ×" is curl
• " ·" is divergence

Together with the Navier-Stokes equations, these equations can be used to calculate solutions to many practical flow situations.

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