From the general form of the Navier–Stokes, with the velocity vector expanded as u = ( u x , u y , u z ) , sometimes respectively named u , v , w , we may write the vector equation explicitly, x : ρ ρ ( ∂ ∂ t u x + u x ∂ ∂ x u x + u y ∂ ∂ y u x + u z ∂ ∂ z u x ) = − − ∂ ∂ x p + μ μ ( ∂ ∂ x 2 u x + ∂ ∂ y 2 u x + ∂ ∂ z 2 u x ) + 1 3 μ μ ∂ ∂ x ( ∂ ∂ x u x + ∂ ∂ y u y + ∂ ∂ z u z ) + ρ ρ g x y : ρ ρ ( ∂ ∂ t u y + u x ∂ ∂ x u y + u y ∂ ∂ y u y + u z ∂ ∂ z u y ) = − − ∂ ∂ y p + μ μ ( ∂ ∂ x 2 u y + ∂ ∂ y 2 u y + ∂ ∂ z 2 u y ) + 1 3 μ μ ∂ ∂ y ( ∂ ∂ x u x + ∂ ∂ y u y + ∂ ∂ z u z ) + ρ ρ g y z : ρ ρ ( ∂ ∂ t u z + u x ∂ ∂ x u z + u y ∂ ∂ y u z + u z ∂ ∂ z u z ) = − − ∂ ∂ z p + μ μ ( ∂ ∂ x 2 u z + ∂ ∂ y 2 u z + ∂ ∂ z 2 u z ) + 1 3 μ μ ∂ ∂ z ( ∂ ∂ x u x + ∂ ∂ y u y + ∂ ∂ z u z ) + ρ ρ g z .