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\frac{D \rho}{ Dt} = \frac{\partial \rho}{\partial t} + \rho \cdot \nabla {\bf u} = 0 |
which is equivalent to
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\nabla {\bf u} = 0 |
with With account of Continuity equation:
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\frac{\partial \rho}{\partial t} + \nabla (\rho \, {\bf u}) = 0 |
the Incompressible flow criteria simplifies to:
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\nabla {\bf u} = 0 |
which means that flow velocity is It means that velocity of Incompressible flow is solenoidal.
The term Incompressible flow is a misnomer as it does not necessarily means that the fluid itself is incompressible.
In many practical applications condition
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is met for compressible fluids (usually when fluid compressibility is relatively small) and the fluid flow satisfies | LaTeX Math Block Reference |
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and is called incompressible flow....
