by Pepper White
The hint that Professors Gyftopoulos and Beretta gave me was as follows:
At the end of the process, two blocks will have the same temperature, and one block will have the highest available temperature. If the two blocks did not have the same temperature, the cyclic machinery could be used to raise the temperature of the third block further. The highest temperature of the third block will be obtained if all processes are reversible (there is no entropy increase).
The scene in which this problem was described is meant in no way to reflect negatively on Professor Gyftopoulos, but rather to present an example of a student's being overwhelmed by the pressure and standards of excellence at MIT. There are great teachers at MIT, and Professor Gyftopoulos is one of them. On numerous occasions during his lectures I had goose bumps from both the way he clearly presented the material, and from the nature of the material and how it coincided with my energy-conservation interests, and from his enthusiasm.
Plate Cooling Problem. Again refer to Rohsenow and Choi, Heat, Mass and Momentum Transfer, pp. 143-53. Presented there is the case of a flat plate with a uniform temperature distribution. The uniform heat flux case is presented in Handbook of Heat Transfer, by W. M. Rohsenow and James P. Harnett (New York: McGrawHill, 1973), pp. 159-160.
Also note, on p. 117 of Rohsenow and Choi, an example of when the solution of a theoretical problem, such as the infinite flat plate, can be applied to a real system, the wall of a rocket motor combustion chamber. The wall is a cylindrical shell, with a wall thickness that is small compared to the diameter, and is calculated as an infinite flat plate.
CHAPTER 4
Sport Death. The design on the Senior House T-shirt is from the cover of Fear and Loathing: On the Campaign Trail '72, by Dr. Hunter S. Thompson (San Francisco: Straight Arrow Books, 1973). The Sport Death design is identical to the cover design, by Thomas W. Benton, with the exception that the Sport Death skull doesn't have swastikas in the eyes, and the Benton design doesn't have anything legible written in the teeth. In Dr. Thompson's introduction, on page 17, "Sport Death" is written in pencil in the margin in the MIT library's copy of the book, next to this (here slightly abridged) paragraph:
People who claim to know jackrabbits will tell you they are primarily motivated by Fear, Stupidity, and Craziness. But I have spent enough time in jackrabbit country to know that most of them lead pretty dull lives; they are bored with their daily routines: eat ... sleep, hop around a bush now and then. ... No wonder some of them drift over the line into cheap thrills once in a while; there has to be a powerful adrenaline rush in crouching by the side of a road, waiting for the next set of headlights to come along, then streaking out of the bushes with split-second timing and making it across to the other side just inches in front of the speeding front wheels.
There will be more on Sport Death in the Chapter 11 notes.
Bernoulli Equation. See Potter and Foss, Fluid Mechanics, pp. 4955. The Bernoulli equation, stated by Daniel Bernoulli in his 1738 book Hydrodynamica, is a special case of the general equations of fluid mechanics, the Navier-Stokes equations. It applies to steady (no variation with time), inviscid (not viscous), irrotational (no whirlpools), incompressible flow. Besides the carburetor, it also applies to things like curveballs, perfume aspirators, and airplane wings. The actual equation is:
where P is fluid pressure, p is fluid density, g is gravitational acceleration constant, z is the height of the fluid, and v is the fluid velocity.
In Encyclopaedia Americana it is noted that Daniel Bernoulli was Swiss, born in Groningen, Netherlands. He was a professor of anatomy at the University of Basel, Switzerland. Since he was not Italian as his name suggests, but rather Swiss, it is unlikely that he either (a) had a cousin with a jewelry shop in Florence or (b) received funding from the Medici or Sforza foundations. We did not know this at our study session, however, so the image made sense.
The Carburetor. A discussion of a real carburetor is in The Internal Combustion Engine, by C. F. Taylor, Vol. 2, pp. 193ff. The difference between the real carburetors described in that book and what is described in here is that in real carburetors, the air is considered compressible, whereas we assumed the air was incompressible. For a simple description of a carburetor, see The Way Things Work, by David Macaulay (Boston: Houghton Mifflin, 1988), p. 148.
The main point of the Bernoulli equation in this case is that when the fluid speeds up, its static pressure (the pressure you would read if you put a barometer on the wall of the tube) goes down. Since the flow speeds up in the contraction, the static pressure does go down, below atmospheric pressure, and the liquid, at atmospheric pressure, is sucked in by the vacuum created by the sped up air.
Just looking at the air side, the equations are:
Continuity:
Bernoulli:
The Tea Leaf Problem. For more on this, refer to Illustrated Experiments in Fluid Mechanics, p. 97. The film, entitled Secondary Flow, was produced by Professor Edward Taylor of MIT.
The Firehouse Problem. The question was: "How many firemen will it take to hold on to a fire hose shooting out 800 gallons per minute at 100 feet per second, if each is capable of providing a horizontal force of 125 pounds?"
The force required to restrain the hose will be equal to the mass flow rate times the velocity going out of the hose. First, convert everything to metric units:
CHAPTER 5
The Tube in the River Problem. You could extract power from a flowing river without building a dam by constructing an underwater turbine resembling a windmill. This would be able to extract 16/27, or 59 percent of the energy flowing through the circular area swept by the turbine blades. For a discussion of this limit for regular windmills, see Wind Power and Other Energy Options, by David Rittenhouse Inglis, (Ann Arbor: University of Michigan Press, 1978), p. 248. The maximum power that could be derived from an underwater turbine would be:
CHAPTER 6
Radiation Heat Transfer. Refer to Rohsenow and Choi, Heat, Mass and Momentum Transfer, Ch. 13. Also refer to Thermal Radiation Heat Transfer, 2nd ed., by Siegel and Howell (New York: Hemisphere Publishing, 1981).
CHAPTER 7
Here are a couple of afterthoughts that didn't really fit in the flow of the book. First, I derived a lot of support and hands-on education from various technicians and machinists at MIT. Nick is a composite of all of these people.
Second, when I was putting the experiment together, friendly salesmen's voices on the other end of the line would help me work my way through some of the design problems. And so it seems to be in the consulting engineering world I work in now. I, the engineer, am educated by the vendors, who may or may not be engineers, but who have been thoroughly briefed on how their products fit within larger systems.
Finally, I became a lot less scared of the word design when I translated it to, in the context of my experiment, "figuring out where to put things," and/or "figuring out how big things should be."
Some definitions pertaining to my experiment:
Test Matrix. The set of experiments used to enhance one's knowledge about a process. For example, if you think two variables, such as initial air temperature in the cylinder and amount of air motion, affect a third result, such as the time it takes the diesel fuel to ignite, you could construct something that looks like a tic-tac-toe board as shown below:
The delay times are the outputs of the experimentally varied inputs, air motion, and temperature.
Turbulence Level. Also known as turbulence intensity, this is defined in Internal Combustion Engine Fundamentals, by J. B. Heywood (New York: McGraw-Hill, 1988), p. 331, as "the root mean square value of the fluctuating component of the instantaneous fluid velocity in a turbulent flow." Turbulence intensity is a measure of how chaotic a flow is; rapids in a river have higher turbulence intensity than smooth, straight stretches.
Swirl Rates. The rate at which air spins within the engine's cylinder.
Parametric Influences. Referring to the test matrix above, the parameters a
re temperature and air motion. These parameters are varied on the input of the experiment, to see the influence on the output of the experiment, in this case the ignition delay time.
Ignition Delay. The time between the start of fuel injection and the start of combustion of the fuel in a diesel engine.
Engines. For more discussion of how engines work, consult The Way Things Work, by David Macaulay, pp. 164-65. Or for more technical discussion, consult The Internal Combustion Engine in Theory and Practice by C. F. Taylor (Cambridge, Mass.: MIT Press, 1960 and 1966 [Vol. 1], 1968 [Vol. 2]), or Internal Combustion Engine Fundamentals, by J. B. Heywood. Also, Internal Fire, by Lyle Cummins (as in Cummins Engine Company), is available from the Society of Automotive Engineers (mail $34 to Department 2414; SAE; 400 Commonwealth Drive; Warrendale, PA 15096).
Pulleys. Again, see The Way Things Work, pp. 58-65.
CHAPTER 8
Steam Engine. See again The Way Things Work, pp. 166-67. Basically, a heat source, either a coal, gas, or oil fire, a nuclear fission, or focused sunlight, boils water as in a teakettle. The steam pressure increases as it's heated, and the high-pressure steam pushes on steam turbine blades. As the steam pushes on the turbine blades it cools and drops in pressure and is sucked into the condenser, where it is cooled by water from the nearby lake or ocean or cooling tower. The water then is pumped back into the boiler, where it again becomes steam. This was all developed in the late 1700s. At first, they didn't have separate condensers, and then in 1765 Watt figured out they'd save a lot of fuel if they added those. And then about 1800 Trevithick added the innovation of high-pressure steam, so more power could be packed into a smaller engine.
"Pong " video game invention. According to the goalie on my soccer team, who took 6.111, the digital electronics lab, in 1974, this game was invented as a class project when he took the class. He has no more data on what happened to the invention after the class.
Balloon Problem. The balloon problem presented in the main text is simplified to a case with incompressible flow and with no energy losses associated with the flow through the orifice. The equations for this simplified example are presented below:
CHAPTER 9
The example of the bicycle race breakaway as it relates to a system with better information flow and hence lower entropy and higher efficiency alludes to the application of information theory to thermodynamics. For further reading on this subject, refer to Thermostatics and Thermodynamics: An introduction to Energy, Information, and States of Matter, with Engineering Applications, by Myron Tribus, (Princeton, N.J.: Van Nostrand, 1961).
CHAPTER 10
First Amusing Anecdote. Norbert Weiner, MIT genius from earlier in the century, was teaching a calculus class when one of the students asked him to do one of the homework problems on the board. Professor Weiner looked at the problem in the textbook, did it in his head, and wrote the answer on the board. The intrepid student then asked, "Could you do that another way?" Professor Weiner again looked at the problem statement in the book, did it in his head another way, and wrote the same answer on the board.
CHAPTER 11
More on Sport Death. This took a little digging. The term Sport Death was imported to Senior House and MIT by a geology student from Arizona, who had picked it up from rock climbers and parachutists at Yosemite and other rock-climbing sites out West. The T-shirt appeared in the academic year '76-'77, when several students on Runkle 4th and 5th had the idea. They were in fact reading the Hunter Thompson book at the time (Fear and Loathing on the Campaign Trail '72) and the reference to Sport Death penciled in the margin of the library copy of the book was in fact the connection that brought the two images together on the shirt. The painting on the fourth floor of Runkle was painted some time after the T-shirt appeared.
Some of the Senior House alums of ten or so years ago who I talked to had interesting things to say about MIT as well, and some of their comments follow:
The real story is over at Baker House. That's where they die of loneliness. And then beyond that the real story is that these dweebs who were pathetic as students stay pathetic as maladjusted adults. The men marry the first women they can, and since they never learned any social or human skills, they find themselves stuck in low-level management jobs. Harvard's just as bad, but you have to remember what these people were doing while they were going through puberty. The kids at Harvard got in there by being editor of the school newspaper and being on the student council and stuff like that, while most of the people at MIT were just studying their science and math all the time, so their grades and SAT's would be good enough to get them into MIT.
And from the alumna who told me the Sport Death story:
Two of my friends there killed themselves. That's one of the reasons some of us started Nightline, the phone service that you could call to have someone to talk to in times of desperation. I think it happens for a couple of reasons, beyond the loneliness and the intense work atmosphere. A lot of students are pushing that fine line between genius and insanity, and some go back and forth across that line: In the case of Senior House, maybe the drugs exacerbated the problem in some cases. The key is that when many of these people were in high school they weren't that well adjusted, and when they come to the abnormal environment of MIT there's no great opportunity to become well adjusted, and then when they leave they're still maladjusted. When I was there there was also the added issue that there were eight men for every woman, so when a woman student left MIT, she'd have to cope with not as much attention as she had at MIT. Plus you come here and you're used to being the best in high school and you're just average, or below. I was the only piano player in my high school, and I came here and everyone plays.... I like your title. I think that sums it up well. I used to call it "Metal Guru," after the song by T. Rex. I think it has that same cold metallic sense.
And from the primary Sport Death T-shirt source: "Everybody at MIT has something going on. If they're into something they're way into it ... they're so wired up. Nobody's lethargic; they're really involved in what they're doing."
Graduate Student Horror Stories. This is as good a place as any for this. I bumped into a friend at MIT on February 9, 1991. His name will be Alfred Weil. He has been working on his Ph.D. for seven years, beyond his master's degree.
"Put the picture of the boxes in. I want you to put the picture of the boxes in."
"What's the big deal about the boxes?" I asked while I looked at the wooden crates in the photo.
"I built them. Every nail in them was hammered in by my hands. Is this the work of a Ph.D.? Let me show you my stack of drawings. Seven years I built every piece of equipment in this laboratory. It was an empty room when I started, and the professor says, 'We would like to study the effect of such and such on such and such.' That was it. Finally the thing is built, after seven years of work, and I complain that I've not done enough real science, and the guy, knowing he has a good slave here in his dungeon says, 'You can stay as long as you want.' Three years ago I complained all I was doing was technician work and they said, 'You can quit.' They put you in a position where the only rational thing to do is to quit. If you complain that you're doing meaningless drudgery, slave labor, they tell you you're not good enough. It wasn't that it was hard, it's that it wasn't appropriate to a Ph.D. effort. Another guy I know complained, and his adviser said to him, 'You're the pacing item.' Like you're a machine.
"See, the public perception of MIT is like a peak detector. They only see the Nobel prizes, the discoveries coming out of this place, the books, the products. But those are the spikes, here, high above zero. Where most of the people at this place are here wasting their lives below zero.
"It's very non-homogeneous, the graduate education here. It all depends on who your adviser is. Some people I know, after they passed the qualifiers, it was smooth sailing from then on. But others ...
"There was one guy, he spent three years on his master's, then he passed the qualifiers, but in his department they have generals at t
he end, and after six years of being a slave he fails his generals. Then he goes away for a year, comes back, and takes them again, after he petitioned the dean. They let him pass, and then they say, You need to prove your ability to do research on another project.' So the six years he spent building the experiment is shot. It's like they passed him but they didn't pass him.
"And another graduate student got electrocuted, and this technician I know told me that the guy's adviser told him, 'You have to sacrifice a student to science now and then.' This, of course, was taken out of context, and was probably the professor's way of dealing with any feelings of guilt he might have had, but it was said.
"I'd sum it up like this," Alfred continued. "They lure talented but gullible people in here with MIT's reputation, and they use them."
Alfred's case may not be representative, but it does exist.
Poisson Distribution. A Poisson Distribution is defined as follows: If the average arrival rate is v, the probability of having m arrivals in time t is:
It was 6:55 when Howard made his calculation, so 15 minutes is the total time, 9 is the total number of arrivals, and v, the average rate of arrival, is 9/15, or 0.6. The probability of a total of 3 (m) people arriving in 10 (t) minutes is:
CHAPTER 12
An historical note on 2.70: It was started in the early seventies by Woodie Flowers, professor in the design group of the mechanical engineering department.
CHAPTER 13
For more about the Schwarzschild radius and black holes, consult A Brief History of Time by Steven Hawking (New York: Bantam, 1988). For more about the twin paradox in relativity, consult The Special Theory of Relativity, by H. Muirhead, (New York: John Wiley & Sons, 1973), p. 39, or Relativity, by Ray Skinner, (Waltham, Mass.: Blaisdell Publishing, 1969), p. 94.