Lecture T9: The Steady Flow Energy Equation--Shaft work and Flow work

This lecture focused on introducing the steady flow energy equation (SFEE). The steady flow energy equation is an expression of conservation of mass and energy for an open thermodynamic system. It is common for people to have difficulty both with units and with signs when applying the equation to solve a problem. Therefore, I used a PRS question to emphasize the importance of getting this right. We then moved on to one of the more confusing concepts -- the distinction between flow work and other forms of external work (shaft work being the most common example). When we express the SFEE in terms of shaft work and flow work, the flow work can be combined with the internal energy terms to arrive at enthalpy. There were several questions on the mud cards about this. I have tried to clarify some of the confusion below.

Responses to 'Muddiest Part of the Lecture Cards'

(41 respondents out of 66 students)

1) What exactly do Q-dot and W-dot mean? (1 student) Rate of heat added to system and rate of work done by the system (units are J/s).

2) Could you explain again which components of the engine go with which processes? (1 student) Please see the notes.

3) What is shaft work? (1 student) A flow of energy into or out of a system via a shaft (such as a shaft attached to a compressor or turbine). Note I use this in the equations in the notes because it is the most common situation, but in general ws should be replaced with all external forms of work other than flow work. Is there a way to figure out if the shaft is doing work on the system or if the system is outputting work unless it is stated in the problem? (2 students) You can figure it out by looking at the sign of the shaft work you calculate using the SFEE. Why is ws positive? (2 students) Ws follows the same sign convention as our previous convention for work. It is positive if work is done by the system (energy is flowing out of the system as work).

4) How does follow from ? (and other questions of confusion regarding these equations) (4 students) Please see the notes. On the last two equations for an ideal gas, are you saying cv and cp are interchangeable? (2 students) No. You missed the absence of a subscript on work in the second equation. Delta-h (or cpdeltaT) appears in the equation with shaft work. Delta-u (or cvdeltaT) appears in the equation with work (shaft work plus flow work).

5) Is p1=p2 in the system for the control volume? (1 student) No. In general the conditions at the inlet and exit of the control volume are different. Since p1 and p2 are different at the boundaries, does that mean that the c.v. is never in q-s equilibrium? (1 student) Excellent question. Yes. It means that in general you can not describe the state of the control volume with one point (or in other words, the thermodynamic state of the gas varies as it flows through the control volume--e.g. through a compressor). Note that we don't really focus on what happens in the control volume, just on what crosses the boundaries.

6) For the jet engine, in the combustor and leg 4-1, it is obvious that q=cpdeltaT from the definition of cp, we don't have to go through h. (1 student) Correct.

7) How do blades compress the air in a gas turbine engine? (1 student) We will learn about this in the spring.

8) Why do we talk about ideal gases? Do they really exist? (1 student) Most gases we deal with behave as ideal gases most of the time.

9) How can Win=-p1V1? shouldn't it be Win=-p1dV? (3 students) p1V1 is the integral of p1dV for pushing a chunk of fluid into the c.v. (think of it starting at V=0 and going to V=V1 all at a constant pressure of p1).

10) Is it correct to say that fluid flows in and becomes part of the control volume, while fluid from the control volume flows out the other end? So if the fluid flowing is part of the c.v., how is there flow work? (1 student) There is fluid that is part of the c.v. , but it is also flowing in and out. In doing so, it has work done on it and does work on the surroundings.

11) In the SFEE why does the difference in energy equal q-w? (1 student) If the energy of the c.v. is not changing (it is steady), then the only flows of energy into and out of the system are those associated with the inlet flows, the outlet flows, the heat and the work. So they must all balance.

12) I did not understand your last explanation of w=-p1v1 and w=p2v2. The pressures p1 and p2 are the pressures of what? The volumes v1 and v2 are the volumes of what? Where does the volume of the c.v. play into this? (2 students) p1 and v1 are the thermodynamic state at the inlet of the c.v., p2 and v2 are at the outlet. The volume of the c.v. does not play a part in this. The flow work comes about because each unit of gas (say a kilogram) that is pushed into the system requires a different amount of work (in general) than is gained from each unit of gas that is pushed out of the system.

13) No mud (17 students). Good.