Lecture P1: Introduction and Integral Momentum Equation

I think the lecture went fairly well, although coming back from Spring Break and having a time change put some into la-la land. The integral momentum equation written in a reference frame relative to the vehicle is always difficult. Please review this in the notes. We will go over several examples in the next lecture (and on the homework).

The number of respondents on the mud cards was a little low (46) as was attendance in lecture (61).

What happens to the guy in the boat when he is in the middle of the lake and he runs out of rocks? (1 student) He fishes?

Why do we only have 9 propulsion lectures? (1 student) It seems a little short to me too, but you have the opportunity to take a full course (16.50) if the topic interests you (as I hope it will).

Responses to 'Muddiest Part of the Lecture Cards'

(46 respondents)

1) How can Newton's Second Law work in a non-inertial reference frame? (1 student) We wrote it for an inertial reference frame. The velocity in the inertial frame is = uo + u. We just continued on from there to break it into two parts for convenience. Is the integral over the volume a triple integral? (1 student). Yes.

2) In the second concept question, where does "breathing" come from? (1 student). I should have explained this. The two forms of propulsion are commonly referred to as "rocket" and "air-breathing". It was a play on the latter.

3) The substantial derivative seems a jump. We haven't even defined a flow velocity to evaluate it. (1 student) Yes. I did jump right to this. The velocity relative to the vehicle is the flow velocity in question.

4) I have trouble with the signs in the scalar momentum equation. (1 students) If this is your only difficulty, you are in pretty good shape. We will do a few examples in class that will give you a better physical feel for the various signs. Some examples with the integral momentum equation will really help solidify my understanding. (2 students) We will have more practice with this through examples in class and homework.

5) If the sum of the forces refers to the inertial reference frame, then how does one calculate the problem in a frame attached to the vehicle? (2 students). The external forces (e.g. drag) are the same in the two reference frames.

6) Does the sum of the forces include thrust? (1 student). It depends on where one draws the control volume. If it is around only the engine, then there is a resultant force equal to the thrust in the engine pilon attached to the wing. If it is around the whole airplane, then the force is equal to the drag force (which equals thrust for steady level flight).

7) Why didn't you give this lecture as soon as you put turbine diagrams up on the overhead last semester? There was little clue as to the overall purpose off a compressor and combustor without having this explanation? (1 student) I think I did explain the overall purpose of a compressor and a combustor last semester, but perhaps not well enough!

8) In the boat examples (Q1 and Q2), are we neglecting the acceleration of the boat (i.e. are we saying that the thrust only counteracts drag)? (1 student) Yes. Very good observation. To simplify the example, I stripped away all the complications that come with an accelerating body. What I should say on the charts is "assume the boats are moving (on average) at constant speed".

9) I don't understand the concept of momentum "storage/depletion". Why isn't it taken account of in the net flux of momentum terms? (8 student). If this is you, welcome to the biggest category of misunderstanding from this lecture! This is a subtle point. We are going to do an example in class during the next lecture that I hope will clear it up for you. (The example is a rocket accelerating and we will do it for control volumes in both the inertial and vehicle coordinate frames just to show we get the same answer.) But for now, go back and read over the falling block example in the notes for the case where the control volume is fixed relative to an inertial coordinate frame. Here there is no flux across the boundaries of the control volume, but there is still a net change in momentum of the mass within the control volume (i.e. the block) due to an external force (gravity).

10) Flying back to Boston after Spring Break, I was seated in row 23 of a DC9 and thus was able to see both the control surfaces and look into the engines. I noticed a repeating pattern of small holes in the intake of the engine. Are these the holes through which air circulates to cool the engine? (1 student) No I don't think so. Only the internal parts of the engine are cooled. The others (like the inlet) operate well below the material limits. I am not sure however, what it is you were looking at (too many \$4 beers perhaps?). It may just have been a series of rivets used to fasten the skin to the structure. Since these are often raised they tend to collect more dirt around them and appear like dark rings---but that is just a guess.

11) No mud (23 students). Good!