In continuum mechanics, this theorem is often used for material elements. These are parcels of fluids or solids which no material enters or leaves. If Ω(t) is a material element then there is a velocity function v = v (x, t), and the boundary elements obey v b ⋅ ⋅ n = v ⋅ ⋅ n . This condition may be substituted to obtain: d d t ( ∫ ∫ Ω Ω ( t ) f d V ) = ∫ ∫ Ω Ω ( t ) ∂ ∂ f ∂ ∂ t d V + ∫ ∫ ∂ ∂ Ω Ω ( t ) ( v ⋅ ⋅ n ) f d A .