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 fluid does not exist but in many practical applications the pressure and temperature variations stay within the sufficiently narrow range where a fluid can be considered as incompressible.
The concept of Incompressible fluid should not be confused with Incompressible flow. The latter can develop even for compressible
See also
Physics / Mechanics / Continuum mechanics / Fluid Mechanics / Fluid Dynamics
[ Compressibility ] [ Incompressible matter ] [ Incompressible flow ]