The fluid which density is not dependent on pressure :

\rho(T, p) = \rho_0(T) = {\rm const}

which is equivalent to zero compressibility:

 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 fluid.

See also