Letting A = m ( v i ) 0 = m , the mass of the particle, the integrated Boltzmann equation becomes the conservation of mass equation: ∂ ∂ ∂ ∂ t ρ ρ + ∂ ∂ ∂ ∂ x j ( ρ ρ V j ) = 0 , where ρ ρ = m n is the mass density, and V i = ⟨ ⟨ v i ⟩ ⟩ is the average fluid velocity.