The matter which density is not dependant on pressure p or temperature T:
(1) | \rho(p, T) = \rho_0 = {\rm const} |
which is equivalent to zero compressibility:
(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 \, {\bf u}) = 0 |
simplifies to:
(4) | \nabla ({\bf u}) = 0 |