Reynolds transport theorem can be expressed as follows:
in which  is the outward-pointing unit normal vector,  is a point in the region and  is the variable of integration,  and  are volume and surface elements at , and  is the velocity of the area element (not the flow velocity). The function  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.