Reynolds Transport Theorem

You may have already seen the dilemma we are in. First of all we favoured a control volume approach because it is easier and very relevant to study motion of fluids. Then we enunciated the basic laws that a fluid motion has to obey and hence lead to the equation of motion. But these are all valid for a system. The question is "How are we going to connect the basic laws for a system with a control volume approach for fluids?". This question has been foreseen by many already. The result is what is called the Reynolds Transport Theorem.

The derivation of the Reynolds Transport Theorem may seem too involved. But when the basis of the theorem is understood, it is indeed easy to follow its derivation. We shall start with a system and the rate at at which an extensive property N changes in it. This we try to express in terms of a corresponding intensive property $\eta$ associated with the control volume, which to start with coincides with the system. To make the concept clear it seems beneficial to consider first an one-dimensional flow to derive the equation. As a second step we extend them to a general flow.

(c) Aerospace, Mechanical & Mechatronic Engg. 2005
University of Sydney