The fluid flow with zero material derivative of its density:
\frac{D \rho}{ Dt} = \frac{\partial \rho}{\partial t} + \rho \cdot \nabla {\bf u} = 0 |
With account of Continuity equation:
\frac{\partial \rho}{\partial t} + \nabla (\rho \, {\bf u}) = 0 |
the Incompressible flow criteria simplifies to:
\nabla {\bf u} = 0 |
The term Incompressible flow is a misnomer as it does not necessarily means that the fluid itself is incompressible.
In many practical applications condition is met for compressible fluids and the fluid flow behaves as Incompressible flow.
Physics / Mechanics / Continuum mechanics / Fluid Mechanics / Fluid Dynamics / Fluid flow