The fluid which density is not dependent on pressure p:
| (1) | \rho(T, p) = \rho_0(T) = {\rm const} |
which is equivalent to zero compressibility:
| (2) | c(T, p) \equiv 0 \Leftrightarrow \frac{d \rho}{ dp} = 0 |
Incompressible matter does not exist but in many practical applications the pressure and temperature variations stay within the sufficiently narrow range where a given matter can be considered as incompressible.
The concept of incompressible fluid should not be confused with Incompressible flow.
See also
Physics / Fluid (PVT) Analysis / Fluid (PVT) modelling / Compressibility