On the other hand, the pressure in thermodynamics is the opposite of the partial derivative of the specific internal energy with respect to the specific volume: p ( v , s ) = − − ∂ ∂ e ( v , s ) ∂ ∂ v since the internal energy in thermodynamics is a function of the two variables aforementioned, the pressure gradient contained into the momentum equation should be explicited as: − − ∇ ∇ p ( v , s ) = − − ∂ ∂ p ∂ ∂ v ∇ ∇ v − − ∂ ∂ p ∂ ∂ s ∇ ∇ s = ∂ ∂ 2 e ∂ ∂ v 2 ∇ ∇ v + ∂ ∂ 2 e ∂ ∂ v ∂ ∂ s ∇ ∇ s