Reynolds transport theorem can be expressed as follows: d d t ∫ ∫ Ω Ω ( t ) f d V = ∫ ∫ Ω Ω ( t ) ∂ ∂ f ∂ ∂ t d V + ∫ ∫ ∂ ∂ Ω Ω ( t ) ( v b ⋅ ⋅ n ) f d A in which n (x, t) is the outward-pointing unit normal vector, x is a point in the region and t is the variable of integration, dV and dA are volume and surface elements at x, and v b (x, t) is the velocity of the area element (not the flow velocity). The function f may be tensor-, vector- or scalar-valued. Note that the integral on the left hand side is a function solely of time, and so the total derivative has been used.