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\frac{D \rho}{ Dt} = \frac{\partial \rho}{\partial t} + \rho \cdot \nabla {\bf u} = 0 |
This also implies that material balance equation:
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\frac{\partial \rho}{\partial t} + \nabla (\rho \, {\bf u}) = 0 |
simplifies to:
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\nabla {\bf u} = 0 |
It does not necessarily means that the fluid itself is incompressible.
See also
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Physics / Mechanics / Continuum mechanics / Fluid Mechanics / Fluid Dynamic
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