Question

a) What is flow work? Which term(s) in the energy equation for an open system represent the flow work?

b) What is the Reynolds transport theorem? Why is it needed for open systems (control volumes)?

Answer 1

b)Reynolds transport theorem (also known as the Leibniz-Reynolds transport theorem),

Reynolds transport theorem can be simply stated as - What was already there plus what goes in minus what comes out is equal to what is there. Reynolds theorem is used in formulating the basic conservation laws of continuum mechanics, particularly fluid dynamics and large-deformation solid mechanics. These conservation laws (law of conservation of mass, law of conservation of linear momentum, and law of conservation of energy) are adopted from classical mechanics and thermodynamics where the system approach is normally followed.

In fluid mechanics, it is often more convenient to work with control volumes
as it is difficult to identify and follow a system of fluid particles. Thus, there is a need to relate the system equations and corresponding control volume equations. The link between the two is given by the Reynolds transport theorem.

Imagine a system and a coinciding control volume with a control surface. Reynolds transport theorem states that the rate of change of an extensive property N, for the system is equal to the time rate of change of N within the control volume and the net rate of flux of the property N through the control surface.

For an example, the law of conservation of mass states that rate of change of the property, mass, is equal to the sum of the rate of accumulation of mass within a control volume and the net rate of flow of mass across the control surface.