If we take Ω to be constant with respect to time, then v b = 0 and the identity reduces to d d t ∫ ∫ Ω Ω f d V = ∫ ∫ Ω Ω ∂ ∂ f ∂ ∂ t d V . as expected. (This simplification is not possible if the flow velocity is incorrectly used in place of the velocity of an area element.)