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the Incompressible flow criteria simplifies to:

LaTeX Math Block
anchorIMMBdivergence
alignmentleft
 \nabla {\bf u} = 0

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It does not necessarily means that the fluid itself is incompressible

In many practical applications condition 

LaTeX Math Block Reference
anchordivergence
 is met for compressible fluids and the fluid flow behaves as Incompressible flow.

See also

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Physics / Mechanics / Continuum mechanics / Fluid Mechanics / Fluid DynamicsFluid flow

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