# Barometric pressure to find height of building

1. Nov 16, 2005

### MKM

A mercury barometer reads 740 mm on the roof of a building and 760.0 mm on the ground. Assuming a constant value of 1.29 kg/m3 for the density of air, determine the height of the building.
Okay I understand to find the h I use the formula h=patm/densityxg, and P2-Patm=pgh yet I am confused amd I supposed to convert the 740 and 760 to atm? When I do this calculation I get .02 differnce subtraction Patm from P2. Do I first have to find the density of the mercury and then compare it, or do I use it within the same formula that I use to find the height of the building. The order and addition of the steps confuse me although I thinkI have al the right formulas to find everything.

Last edited: Nov 16, 2005
2. Nov 16, 2005

### Tom Mattson

Staff Emeritus
It's not necessary to do that, and I think I understand why you are confused. The "$atm$" in the symbol $P_{atm}$ simply means "atmospheric pressure". That's what it means in any system of units, be it atmospheres, Pascals, mm Hg, etc.

The "$atm$" that appears after some pressure measurements (eg: "$P=1.2 atm$") means something different. It is a unit of measurement.

Now that that's out of the way, here's what I would do: Convert the pressures to Pascals. Then if you use the given density and $g=9.8m/s^2$, everything is in SI units and your value of $h$ will automatically be in meters.

3. Nov 16, 2005

### Kazza_765

This problem just reminded me of this. One of my lecturers read it once.
The following concerns a question in a physics degree exam at the University of Copenhagen:
"Describe how to determine the height of a skyscraper with a barometer."
One student replied:
"You tie a long piece of string to the neck of the barometer, then lower the barometer from the roof of the skyscraper to the ground. The length of the string plus the length of the barometer will equal the height of the building."
This highly original answer so incensed the examiner that the student was failed immediately. The student appealed on the grounds that his answer was indisputably correct, and the university appointed an independent arbiter to decide the case.
The arbiter judged that the answer was indeed correct, but did not display any noticeable knowledge of physics. To resolve the problem it was decided to call the student in and allow him six minutes in which to provide a verbal answer that showed at least a minimal familiarity with the basic principles of physics.
For five minutes the student sat in silence, forehead creased in thought. The arbiter reminded him that time was running out, to which the student replied that he had several extremely relevant answers, but couldn't make up his mind which to use. On being advised to hurry up the student replied as follows:
"Firstly, you could take the barometer up to the roof of the skyscraper, drop it over the edge, and measure the time it takes to reach the ground. The height of the building can then be worked out from the formula H = 0.5g x t squared. But bad luck on the barometer."
"Or if the sun is shining you could measure the height of the barometer, then set it on end and measure the length of its shadow. Then you measure the length of the skyscraper's shadow, and thereafter it is a simple matter of proportional arithmetic to work out the height of the skyscraper."
"But if you wanted to be highly scientific about it, you could tie a short piece of string to the barometer and swing it like a pendulum, first at ground level and then on the roof of the skyscraper. The height is worked out by the difference in the gravitational restoring force T =2 pi sqr root (l /g)."
"Or if the skyscraper has an outside emergency staircase, it would be easier to walk up it and mark off the height of the skyscraper in barometer lengths, then add them up."
"If you merely wanted to be boring and orthodox about it, of course, you could use the barometer to measure the air pressure on the roof of the skyscraper and on the ground, and convert the difference in millibars into feet to give the height of the building."
"But since we are constantly being exhorted to exercise independence of mind and apply scientific methods, undoubtedly the best way would be to knock on the janitor's door and say to him 'If you would like a nice new barometer, I will give you this one if you tell me the height of this skyscraper'."
The student was Niels Bohr, the only Dane to win the Nobel Prize for physics.

Completely irrelevant to your post, but funny.

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