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How can I understand the flow is incompressible or not with this information at 4 edges?enter image description here

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  • $\begingroup$ Hint: If the fluid is incompressible, whatever goes in must come out. Can you express that using derivatives? $\endgroup$ – Christian Clason Dec 30 '15 at 19:56
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    $\begingroup$ If the divergence of the velocity is zero at a given point, then it is incompressible at that point. So you can prove the region is compressible if you show any of those 4 corners are not incompressible. However, since you can't assume knowledge of the flow field within the entire region, I don't think you should be able to prove it is incompressible everywhere even if all 4 corners are compressible. $\endgroup$ – spektr Dec 30 '15 at 22:30
  • $\begingroup$ thanks Christian and choward @ choward i think as you say cant prove any place of this rigion isn't incompressible even 4 corners are incompressible. $\endgroup$ – meisam nemati Jan 1 '16 at 16:34
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Continuity equation is given by

$ \frac{D \rho}{ D t}+\rho \nabla \cdot \vec{U}=0$,

if it is incompressible then

$\nabla \cdot \vec{U}=0$

Just check if the velocity is solenoidal.If it is, then it is incompressible.

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