DN npvdAJjj npdV

cs cv

This is called the Reynold Transport equation and it is a change from system approach to control volume approach. In the Reynole transport equation v is measured relative to some reference xyz and the control volume was fixed in this reference. Thus, v in the above equation is measured relative to control volume. As a consequences, the time rate of change of N is in effect observed from the control volume and velocities and time rates of changes are those seen from control volume. Since we could use a reference xyz having an arbitrary motion, it means that the control volume can have any motion. Thus the Reynold transport equation will then instantaneously be correct if we measure the time derivatives and velocities relative to the control volume, no matter what the motion of the control volume may be.

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