# how can i show flow is incompressible?

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

• Hint: If the fluid is incompressible, whatever goes in must come out. Can you express that using derivatives? – Christian Clason Dec 30 '15 at 19:56
• 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. – spektr Dec 30 '15 at 22:30
• 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. – meisam nemati Jan 1 '16 at 16:34

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