The matter which density is not dependant on pressure:
| (1) | \rho(p) = \rho_0 = {\rm const} |
which implies that compressibility is zero:
| (2) | c(p) \equiv 0 \Leftrightarrow \frac{d \rho}{ dp} = 0 |
This also implies that material balance equation:
| (3) | \frac{\partial \rho}{\partial t} + \nabla (\rho \, {\br u}) = 0 |
simplifies to:
| (4) | \nabla ({\bf u}) = 0 |