If a fluid is incompressible andis the velocity vector field that describes the velocity of the fluid at each point then
This equation follows from the continuity equation
First write the continuity equation as
Since the fluid is incompressinble
There is still the possibility that the fluid can has different densities at different points, but if the fluid is incompressible a fluid element cannot change in density as it moves so
Ifthenand the fluid is incompressible.