Lecture T11: Stagnation Quantities/ Reversible and Irreversible Processes


General comments

We were a little ahead on the material. So given the confusion surrounding the stagnation quantitites, I decided to devote some extra time to discussing these. I hope that this helped people understand the material better. Based on the mud responses there was some improvement. Hopefully, working through the homework problems (T10, T11) will help further.

Clear as the Charles River (1 student). Hmmm.

TRICK QUESTIONS AREN'T FAIR (2 students). Sure they are, if they make you think -- that is the goal. You aren't getting graded on whether you get the right answers.

Can we have the question and an explanation of the answer on the web? Because it would be good to be able to rethink the problems at home. (2 students) I think this might be a good idea but I am not sure. I didn't do it for two reasons.First, I thought it would be better to leave them blank so that you could puzzle it out on your own (you do find out what the right answer is in class). Second, it was a time issue. Realistically, it will be difficult for me to put these in for all the questions for this semester (you only have two lectures left). But I will ask for people's input on this (at the last lecture) and if people think it would be valuable, I will do it for next semester's propulsion lectures. Also, I think that every question that someone put a muddy point in for, I have answered in these responses. This covers about 80% of the questions, so most of the explanations can be found by reading through all the mud responses. This will be time consuming, but hopefully educational.

The diagrams & equations in the notes are sometimes difficult to read because the print is small and the resolution is low. It would help next year's class if you re-did them in higher resolution. (1 student) I agree and I have already started the process, but it will take me a while. This is the first year I have done anything with the web and there are a lot of issues like this that I am learning.

You said that mixing coffee is not reversible. If you let the coffee sit long enough (T > month) that cream might evolve, grow legs and run back to the creamer, with no external work (1 student). Yikes. I guess anything is possible in Lobdell.

Is it humanly possible for Professor Hall to turn as red as the seats in the lecture hall? (1 student) Professor Hall is a very good sport. It was nice he gave us all an opportunity to laugh a little.

If we get ahead by a lecture, can we have an extra hour of sleep one morning? (1 student). Sure, after I finish with Thermo.


Responses to 'Muddiest Part of the Lecture Cards'

(62 respondents)

1) Today you wrote SSFE and SFEE on the board. What's the difference in these acronyms? (1 student) SFEE is "Steady Flow Energy Equation". SSFE is garbage produced by a tired mind.

2) I'm confused about TT and Tatm and Tstatic and determining their relationships to each other. (3 students) Please read all of the responses below. Read the responses from T10. Read the notes. Work the homework. And ANYTIME you want to talk about it, see me or a TA. We will help you sort it out.

3) Could you explain the rotor blade example again? (5 students) Sure. The rotor blade is a direct analog for the supersonic airplane example we did last lecture. Instead of blades spinning around, think of tiny supersonic airplanes spinning around in the engine. There are two ways to think about the problem. First, in the reference frame of the blade. It sees flow coming at it with kinetic energy associated with the moving flow, and with an internal energy (or more appropriately enthalpy) associated with its temperature far away in the atmosphere. When the flow is stagnated on the blade, both of these sum into the stagnation enthalpy. Thus the temperature is higher than the ambient temperature. The second way to look at it is in the fixed reference frame. In this case the flow has some stagnation temperature as it comes in the inlet which is equal to the ambient atmospheric temperature. Then the blade comes along and the fluid sticks to the blade gaining kinetic energy. Thus the total or stagnation temperature on the surface of the blade is greater than the stagnation temperature the flow had when coming in the inlet. Please also see the following response that is related to this problem.

4) On PRS#6.19, I understand that TT1>Tatm (atm is moving with respect to blade), but why isn't T1=TT1?? (in the blade frame) After all, it's stagnated on the blade (1 student and 1 professor --Hall picked up on this too and wrote it on a muddy card) There is some lack of clarity (on my part) with the question. Prof. Hall and the student are right. TT1=T1>Tatm is the correct answer for this one. Now let me tell you how the mistake came about because it illustrates an important point. Even for moving flows, it is common to ask what the stagnation temperature is. It doesn't mean that the flow is stagnated. The stagnation temperature is the hypothetical temperature the flow would reach if it were decelerated through a steady, adiabatic process with no external work. It doesn't ever have to be decelerated. So the flow moving through the blades at M=0.5 at a static temperature lower than the stagnation temperature still has a stagnation temperature (the hypothetical temperature it would reach if...). Indeed this is how people usually use stagnation quantities (as you will see in T10). Of course the problem did not ask it in this way (mostly because it is one more confusing convention than fluid dynamicists use that you don't really need to worry about). The problem said the fluid was stagnated on the spinning rotor blades. I have changed the answers on the slide to be consistent with this.

5) Questions on the wind-tunnel model example (7 students) Why didn't the model get hotter just as the skin of the airplane? Isn't it just backwards, air is moving instead of the body? (4 students) It did get hotter--hotter than the static temperature of the freestream. This is the same thing that happened with the supersonic airplane, except the static temperatures were different. In the wind-tunnel, the freestream flow is very cold. When it is stagnated on the model it reaches its stagnation temperature. The whole process (from stagnated flow in the high pressure cylinders, to moving flow in the pipes and wind-tunnel, and back to stagnated flow on the surface of the wind-tunnel model) is adiabatic and there is no external work, and the model and the high pressure cylinders are motionless with respect to one another. Therefore the stagnation temperature is constant. Enthaly (cpT) is just traded for kinetic energy (c^2/2) as the flow accelerates and decelerates. So as the flow moves faster, its static temperature drops. As the flow moves slower, its static temperature increases. This is the exact same problem as the problem we did last lecture on the flow coming into the inlet of the engine and stagnating on a portion of the engine that is not moving with respect to the reference frame of the outside atmosphere. I figured that when the air stagnated on the model energy would be transferred from the model to the air and hence, the model would cool down. Why is this not the case? (1 student) If the model started out hotter than the outside air temperature, it would cool down initially. But eventually it would approach a constant temperature. That temperature would be the temperature of the flow that stagnates on the body. For this example, the temperature would therefore be equal to Tambient.

6) So long as the reference frames are the same, no matter what, then the stagnation temperatures are the same? And if something is moving faster than the ref. frame it's temperature heats up? (1 student) Correct. As long as the flow stagnates via a steady, adiabatic process with no external work. (I didn't understand the rest of the question you wrote on your card.)

7) If an engine sucks air in hard enough can it cause the temperature to drop so low that whatever it is sucking in will freeze? (1 student) Yes. If there is water in the air and the ambient temperature is already close to freezing then the additional drop in static temperature associated with the M=0.5 flow can cause ice crystals to form in the air.

8) Hot and cold at the same time on a wing is confusing.(2 students) Yes it can be confusing. But it doesn't get hot and cold in the same place. Some air is mearely pushed out off the way by the airplane (static temperature drops). Other air is picked up and carried along with the airplane (the air very close to the surface) so the fluid stagnated on the body has more energy and the stagnation temperature is higher than the ambient. For more on this read the discussion from the T10 mud responses.

9) Is it fair logic on the wind-tunnel problem to say that no energy is added to the fluid (like an airplane adding energy to the air when flying), so T is the same? (1 student) Yes it is fair logic if your T is the stagnation temperature. Stagnation temperature is the conserved quantity.

10) Back in Wisconsin when they said (for example) the temperature is -5 degrees F and -17 degrees F with wind chill, is the -5 degrees F the stagnation temperature and if so, why does the wind chill matter because all the molecules that stagnate on me will warm up to -5 degrees F? (1 student). (And that is on a warm day.) First, read this (response 13) it is a response to a similar question from T10. -5 degrees is the stagnation temperature. -17 degrees is how cold it feels with the wind. Why does it feel colder? Because when the flow moves over a surface it increases the rate of heat transfer (even though the stagnation temperature is the same). Because the rate of heat loss from you body is faster, it feels colder. This is called "convective cooling" and you will learn much more about it in 16.050.

11) Still unclear on the stagnation temperature problems. They make sense when explained, but I can't seem to get them on my own (2 students). If they make sense when explained then you are halfway there. Work the homework problems. If still unclear, please contact, me or a TA and we can spend some more time talking about it. SFEE still unclear, but today's examples helped a lot. (1 student) Good. I am glad we are moving in the right direction.

12) The gases can separate if one gas is heavier than the other and they start premixed (1 student). I disagree. The oxygen in the air is heavier than the nitrogen, but it doesn't settle to the bottom of the room. Salt water doesn't unmix (although if it starts out stably stratified it will stay that way). For all miscible fluids (i.e. not oil and water), molecular diffusion keeps them mixed. Indeed, I think Boyle's Law (which you probably heard about in high school or freshman chemistry) says something about gases filling the containers they are in even if they are a mixture, with the partial pressure of each species corresponding to the mole fraction.

13) Definition of irreversible: There should be processes that you cannot reverse even with external work, right? How about C (in PRS #7.3)? To separate two mixed gases, you can use few methods (chemically?) (1 student). There are some processes that are very difficult to reverse even with work from the surroundings (a nuclear explosion, or the death of a person) but I don't think they are impossible. You could think for instance of breaking apart atoms and recombining them, or building a new person cell by cell. Very difficult, indeed, and far beyond what man is capable of, but not impossible. By the way, the gas separation is easy. All gases have different freezing and boiling points. You just have to slowly reduce the temperature (requires work from the surroundings) and then sequentially pour off the liquid. People separate complex hydrocarbons the same way (e.g. to get gasoline from crude oil). It is called fractional distillation (they slowly heat the crude and collect the vapors of the individual gases and then condense these separately).

14) A little confusion at first with the Chapter 7 questions, but I think it'll be cleared up in the next two lectures. (2 students) I think it will be. If you can make it through the three difficult aspects of the SFEE, reversible and irreversible processes will be easy. Can you define exactly what entropy is? (1 student) I will talk about this in lecture, but if you are interested now read this.

15) No mud (28 students). Great. This is an improvement over last lecture. Congrats to those who now understand the frame dependence of stagnation quantities.