Regardless of the flow assumptions, a statement of the conservation of mass is generally necessary. This is achieved through the mass continuity equation, as discussed above in the "General continuum equations" within this article, as follows: D m D t = ∭ ∭ V ( D ρ ρ D t + ρ ρ ( ∇ ∇ ⋅ ⋅ u ) ) d V D ρ ρ D t + ρ ρ ( ∇ ∇ ⋅ ⋅ u ) = ∂ ∂ ρ ρ ∂ ∂ t + ( ∇ ∇ ρ ρ ) ⋅ ⋅ u + ρ ρ ( ∇ ∇ ⋅ ⋅ u ) = ∂ ∂ ρ ρ ∂ ∂ t + ∇ ∇ ⋅ ⋅ ( ρ ρ u ) = 0 A fluid media for which the density ( ρ ρ ) is constant is called incompressible. Therefore, the rate of change of density ( ρ ρ ) with respect to time ( ∂ ∂ ρ ρ ∂ ∂ t ) and the gradient of density ( ∇ ∇ ρ ρ ) are equal to zero ( 0 ) . In this case the general equation of continuity, ∂ ∂ ρ ρ ∂ ∂ t + ∇ ∇ ( ρ ρ u ) = 0 , reduces to: ρ ρ ( ∇ ∇ ⋅ ⋅ u ) = 0 . Furthermore, assuming that density ( ρ ρ ) is a non-zero constant ( ρ ρ ≠ ≠ 0 ) means that the right-hand side of the equation ( 0 ) is divisible by density ( ρ ρ ). Therefore, the continuity equation for an incompressible fluid reduces further to: ( ∇ ∇ ⋅ ⋅ u ) = 0 This relationship, ( ∇ ∇ ⋅ ⋅ u ) = 0 , identifies that the divergence of the flow velocity vector ( u ) is equal to zero ( 0 ) , which means that for an incompressible fluid the flow velocity field is a solenoidal vector field or a divergence-free vector field. Note that this relationship can be expanded upon due to its uniqueness with the vector Laplace operator ( ∇ ∇ 2 u = ∇ ∇ ( ∇ ∇ ⋅ ⋅ u ) − − ∇ ∇ × × ( ∇ ∇ × × u ) ) , and vorticity ( ω ω → → = ∇ ∇ × × u ) which is now expressed like so, for an incompressible fluid : ∇ ∇ 2 u = − − ( ∇ ∇ × × ( ∇ ∇ × × u ) ) = − − ( ∇ ∇ × × ω ω → → )