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The matter which density is not dependant on pressure:
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\rho(p) = \rho_0 = {\rm const} |
which implies that compressibility is zero:
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c(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 \, {\br u}) = 0 |
simplifies to:
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\nabla ({\brbf u}) = 0 |