**General comments**

People seemed a little tired today and there were many late arrivals. Based on the muddy cards, it also seems that some people may not be doing the reading before class. Previously it had seemed that most of the people were doing the reading so I haven't set any for-credit reading assignments or quizzes. I will probably set a short for-credit reading assignment for Monday's lecture.

I thought things went well with the discussion of flow work and shaft work based on the lack of questions in class, but there were still many muddy points (see below). The introduction to the stagnation temperature and enthalpy was rough. It is a difficult topic and hard to introduce in 10 minutes at the end of class. Please carefully read through the material prior to T10 when we will spend the whole day on the topic. And remember, these are difficult concepts, so if they aren't clear to you instantly, that is okay. Keep working at it.

An addition to the mud art gallery:

**Responses to 'Muddiest Part of the Lecture Cards'**

(61 respondents)

1)* Could you
please re-explain the answer to the 1st
PRS question?* (1 student) For an adiabatic steady flow compressor
(neglecting changes in kinetic and potential energy) the shaft work is equal
to the change in enthalpy as seen from crossing off the appropriate terms in
this equation:

2) * Mud. 2nd
PRS question--please re-explain.* (2 students) For a quasi-static,
steady flow process (neglecting changes in kinetic and potential energy) the
work is equal to q + u1-u2, which you arrive at by crossing off the appropriate
terms in the equation shown below. This was not one of the choices, so the answer
is "none of the above".

3)* I am still a bit muddy on the concept of shaft
work. Is there some sort of equation that defines it?*
(4 students) A better word for it is

4) * How does a difference in p1v1 & p2v2 do
flow work? Why is it merely the difference and not some sort of integral like
piston work?* (1 student) It is not an integral because we assume
that at each end of the control volume the work that the flow does is done at
constant pressure. This is a very good assumption since the flow into and out
of the control volume is steady. So the pressure at the inlet will not vary
over time.

5)** For flow work, is the "chunk" of air
coming out of the system larger because it is moving at a faster rate?**
(1 student) and

6) * You mentioned that the flow work in = flow work
out in an answer to one student's question* (1 student).I am not
sure what you are referring to. This is certainly not generally true. See response
(3) above for situations where the flow work is zero.

7)* In the combustor/compressor question,
why wouldn't work done on the system by adding fuel to the combustor be considered
shaft work? * (1 student) The addition of the fuel doesn't change
the flow much (it is typically only 3-5% of the mass flow and we neglect it
in our ideal cycle analyses). The combustion of the fuel-air mixture is what
impacts the flow (conversion of chemical energy to internal energy). So the
flow coming into the combustor is at a very different temperature than the flow
that leaves the combustor, and very significant flow work is done.

8) * In does
the pressure at (1) and (2) matter?* (1 student) Not for an ideal
gas. Enthalpy is only a function of temperature for an ideal gas.

9) * How do the units on cpT + c^2/2 work out to
enthalpy?* (1 student) J/kg. Work it out and see.

10) * In recitation, you once asked us to find the
enthalpy in a room. I thought we had determined we couldn't b/c we didn't have
a changine temp. Yet in this lecture, you write h in absolute terms as h=u+pv
or h=cpT.* (1 student). Great question. Sloppiness on my part.
dh=cpdT (for an ideal gas), h does not equal cpdT. I have corrected it in my
notes. Since we are looking for the change
in enthalpy (h2-h1) we can substitute in cp(T2-T1). And in absolute terms h=u+pv.
So that part is right. One note about finding the enthalpy in the room. We certainly
can do it. Go to the back of your thermo text and look up what the enthalpy
for air is at standard atmospheric conditions (usually T=296K), and then add
to that Dh=cp(Troom-296K).

11) * For stagnation temperature, why did we assume
it is quasi-static adiabatic?* (2 students) Great question. My
mistake--I get so used to saying "quasi-static adiabatic" that it
rolls off my tongue (and keyboard) even when it is not supposed to. The new
medication I am on should help with this. In the notes it was correct in one
place and wrong in the other. I have corrected it in the notes.
The only conditions necessary for the stagnation temperature to be a constant
are that the process be adiabatic, steady, and involve no external work. When
we get to stagnation pressure and its relationship to stagnation temperature
it will be necessary to assume a quasi-static process, but it is not necessary
to do this for stagnation temperature.

12) * What does stagnation mean? What does it mean
when flow is stagnated?* (2 students) It means it is not moving
(relative to some coordinate frame), or its velocity (relative to some coordinate
frame) is zero.

13) * What is the significance of stagnation temperature,
what is it used for?* (3 students) Stagnation quantities are very
useful estimates of the conditions that the flow would arrive at if it was brought
to zero speed (relative to some reference frame) by a steady, adiabatic process
with no external work (add quasi-static as a requirement for stagnation pressure).
It doesn't mean that the flow will pass through such a process, but often it
does. Flow always stagnates on bodies. So this tells us (for many situations)
the temperature on the surface of the body--a very useful thing to know if you
have to design that body to withstand those thermal loads. The stagnation temperature
and stagnation pressure can also be related to the maximum amount of work that
the flow is capable of producing although you will not learn about that in Unified
(wait for 16.050). But think of a bottle of compressed gas (stagnated). The
higher the pressure, the more potential there is to get work out of it. Stagnation
pressure is the analogous quantity for moving gases (which are what we often
deal with in aerospace engineering).

14) * What is T? *(4 students) Temperature.
This is distinct from stagnation temperature which is the temperature the flow
would reach if it were brought to zero speed (relative to some reference frame)
by a steady, adiabatic process with no external work.

15) * Overall confused about stagnation *(7
students). You have a right to be. Let me hold off explaining more of it for
now since we have a whole lecture devoted to it on Friday. Please read the notes!!

16)* The last PRS question
was confusing.* (1 student) Read the notes
it should help.

17) * What happens when you
blow on a piece of paper?* (1 student) The pressure drops so it
lifts up the paper. This is a demonstration of the Bernoulli equation which
you will hear much more about in Unified Fluids. We will also discuss it from
the perspective of thermodynamics in the next lecture.

18) * No mud* (13 students). Good.