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Irrotational flow occurs where the curl of the velocity of the fluid is zero everywhere. That is when
Similarly, if it is assumed that the fluid is incompressible:
Then, starting with the continuity equation:
The condition of incompressibility means that the time derivative of the density is 0, and that the density can be pulled out of the divergence, and divided out, thus leaving the continuity equation for an incompressible system:
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