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I read a story in which an it was asked in an exam to show how it is possible to determine the height of a tall building with the aid of a barometer.

This story is quite famous I guess, and the student gave several non-conventional answers (which were all correct) because he was fed up of instructors trying to teach him how to think. Here is a link to the story. In the end the student says that he knew the conventional answer to the question.

I was trying to figure out what should have been the conventional answer or the answer instructor wanted from students?

Qmechanic
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Bhaskar Vashishth
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  • Consider what it is that a barometer measures and ask yourself how that quantity is related to height. Note that it is going to have to be both a very nice barometer and a fairly tall building for the conventional answer to yield any kind of precision. – dmckee --- ex-moderator kitten Feb 10 '16 at 04:31
  • For extra credit, let's see if someone can come up with a all-NEW! IMPROVED! solution. – Carl Witthoft Feb 10 '16 at 13:50
  • Come to think of it, I have an old-fashioned mercury-column barometer in my office right now. I think I can reliably judge to better than one torr on it. I wonder how tall a building I can find within reasonable distance? I could make a video or something. – dmckee --- ex-moderator kitten Feb 10 '16 at 14:36
  • @dmckee Make sure the building you choose has an onsite superintendent who likes barometers :-) – Carl Witthoft Feb 10 '16 at 16:12

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I like throwing it of the roof and count the seconds the most, but what the instructors wanted to hear is most likely to apply the barometric formula, which reads $p(h)=p_0 \exp (\frac{-mgh}{k_BT})$, assuming the same temperature hat level $p_0$ and $p(h)$

rtime
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With a tall building there will be a difference in air pressure between the top and the bottom. Near ground level, the pressure drops about 10% per 1000m (it levels off gradually). See Wikipedia's entry on Atmospheric pressure for more details.

So, if you measure the pressure at the top and the bottom, you can use the difference to compute the height. If the building is 200m high, you'll see the barometer drop 2%.

hdhondt
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  • But only if you know the current atmospheric conditions, and you can get up and back down before they change. The altitude-pressure curve depends on what air masses are in the area. – Carl Witthoft Feb 10 '16 at 13:51
  • @CarlWitthoft You can, of course, read the ground pressure twice—once immediately before climbing and immediately upon descending—to get a measurement of the speed of the local change and to allow you to subtract it off to first order. These are the kind of things a experimenter learns to take for granted. – dmckee --- ex-moderator kitten Feb 10 '16 at 14:53
  • @dmckee Yes, I'm painfully aware of that methodology -- but other than jumping, I don't see a way to get back down quickly. And the atmosphere changes on relatively short time scales. – Carl Witthoft Feb 10 '16 at 16:11
  • Er ... you don't want to get down faster than you go up. Ideally you'd like to have the assent and descent take the same time because you are trying to measure the rate of change of the baseline over the course of the experiment in such a way as to optimize you estimate of the pressure at the ground at the time you take the pressure at the top. So take the elevator both ways. – dmckee --- ex-moderator kitten Feb 10 '16 at 19:49
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Determine the height of a tall building with the aid of a barometer.

  1. Look at the building's facade and windows and determine how many floors the building has. Consider whether the ground floor actually counts as two floors (etc.) high. Example: 52 floors. Note that in the case of many extremely tall buildings, the architect may use a trick where what looks like one floor is actually two, to make the building appear more inviting and less menacing (common in Las Vegas Strip Hotel Casinos).

  2. If the barometer is mounted to a board or plaque, estimate the height of the barometer itself, 10" for example, then use it to measure a portion of the side of the building. If the first floor is actually about the height of two floors, then measure 1/4 way up the first floor knowing this is half of a floor, or equivalent.

  3. Perform basic math to come up with a statement: "One floor is 120" high.

  4. Multiply that times the number of floors you came up with earlier. 52 floors at 120" high each = 6,240, / 12 inches = 520' tall. That's your answer. It's gotta be just as accurate as using the barometer at the top of the building vs. the ground level. And, well, you used the barometer.

Farrara
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