Is this definition of Reynolds' Transport Theorem correct?

[FluidStu]

One thing I find frustrating when trying to get a handle on this theorem is the number of different forms presented in the literature. I understand this to be due to it being very general theorem applicable to many different contexts.

Not that the world needs a new, slightly different looking definition of RTT, but I have tried to look at it from a 'fluid parcel' (a.k.a. material volume) and 'control volume' point of view. Based on general reading from multiple sources, this is a definition I've come up with which makes sense to me because it's very similar to the idea of the "Material Derivative". But, is it correct?

Thank you in advance.

 

[Navin A S]

The definition you have provided is essentially correct. The Reynold’s Transport Theorem states that the rate of change of total amount of a property (mass, momentum, energy, etc.) within a control volume is equal to the net rate of flow of the property into and out of the control volume through its boundary plus the rate of production of the property within the control volume. This can be expressed mathematically as:Rate of Change of Property in Control Volume = Net Rate of Flow of Property Through Boundary + Rate of Production of Property Within Control Volume This theorem is extremely useful in many contexts, such as fluid mechanics, thermodynamics, and chemical engineering, as it allows us to easily calculate the change in a property within a system given the inflow, outflow, and production rates.