In fact for a flow with uniform density ρ ρ 0 the following identity holds: ∇ ∇ w ≡ ≡ ∇ ∇ ( p ρ ρ 0 ) = 1 ρ ρ 0 ∇ ∇ p where p is the mechanic pressure. The second equation is the incompressible constraint, stating the flow velocity is a solenoidal field (the order of the equations is not causal, but underlines the fact that the incompressible constraint is not a degenerate form of the continuity equation, but rather of the energy equation, as it will become clear in the following). Notably, the continuity equation would be required also in this incompressible case as an additional third equation in case of density varying in time or varying in space. For example, with density uniform but varying in time, the continuity equation to be added to the above set would correspond to: ∂ ∂ ρ ρ ∂ ∂ t = 0