The matter which density is not dependant dependent on pressure pressure
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\rho(p, T) = \rho_0(T) = {\rm const} |
which is equivalent to to zero compressibility:
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c(T, p) \equiv 0 \Leftrightarrow \frac{d \rho}{ dp} = 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 |
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where
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Incompressible matter does not exist but in many practical applications
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the pressure variation may stay within the sufficiently narrow range where a
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given matter can be considered
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as incompressible.
See also
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Physics / Fluid (PVT) Analysis / Fluid (PVT) modelling / Compressibility
[ Incompressible flow ] [ Incompressible fluid ]