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Old 13th August 2019, 02:24 PM   #1
PhantomWolf
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Pressure Gradient in a Box?

Okay so I have a quandary.

We usually assume that if we have a container with a gas in it, then the gas pressure will be equalized inside the container, right?

However, what happens if I make that container 100 km high?

Gravity is still acting on the air inside the box, just as it does on the air outside of it, so why shouldn't it form a graduated pressure differential inside the box just as the atmosphere does?

If the box was open at the top there there is no question that it would have a graduated pressure inside, but why would this go away merely because the top was closed?

Am I missing something, or does the idea of a gas equalizing the pressure in a container start to break down when the container is tall enough that gravitation forces can start to play a part?
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Old 13th August 2019, 02:30 PM   #2
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Seems to me that there'd even be a pressure gradient in a 1 cubic meter box at sea level. It would probably be too small to measure, though.

Also, I'm not sure we do "usually assume" this in any meaningful way. We assume that's the default behavior of gases, absent any other significant forces. Thought experiments involving Maxwell's Demon and spherical cows come to mind.

I think mostly in practice we assume equalized pressure in scenarios where it is a reasonable and more than sufficient approximation. It's not like mechanically the gravity differential is going to play a noticeable part in a fuel injector or a jet engine.
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Old 13th August 2019, 02:33 PM   #3
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The air in the box will have a pressure gradient. So will the material the box is made of.
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Old 13th August 2019, 03:40 PM   #4
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Originally Posted by PhantomWolf View Post
Okay so I have a quandary.



We usually assume that if we have a container with a gas in it, then the gas pressure will be equalized inside the container, right?


It depends who "we" is. I don't assume that.

Any container of gas, whatever the size, in a gravitational field or undergoing acceleration will have a pressure gradient in it. Sometimes the gradient is small enough for it to be disregarded for most purposes.
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Old 13th August 2019, 04:03 PM   #5
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Originally Posted by PhantomWolf View Post
Okay so I have a quandary.

We usually assume that if we have a container with a gas in it, then the gas pressure will be equalized inside the container, right?
The way I learned it was that a gas exerts equal pressure on all sides of a container absent any other force to the contrary. Gravity is a force to the contrary, pulling the gas (and the container) toward the center of gravity.

Across small distances this is negligible for practical purposes. But in a gravitational field (or in any other accelerating frame) there will be a gradient inside the box even though in small containers it might be too small to measure.

Added after preview: Ninja'd by pretty much everyone else.
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Old 13th August 2019, 04:03 PM   #6
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I would suggest that most people don't usually assume that, because if we knew a sealed container had two types of gas in it, one heavier than the other, then we would assume that the heavier one would settle to the bottom, wouldn't we? So we usually assume there is a pressure gradient in a sealed container of gas.
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Old 13th August 2019, 04:08 PM   #7
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Originally Posted by Robin View Post
It depends who "we" is. I don't assume that.

Any container of gas, whatever the size, in a gravitational field or undergoing acceleration will have a pressure gradient in it. Sometimes the gradient is small enough for it to be disregarded for most purposes.

Don't count me among the we's either.

The pressure gradient in the box will depend on the gas, and depth also. Hydrogen being lighter will have a lesser gradient than say nitrogen, and the deeper the gas the higher the rate of change of pressure.
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Old 13th August 2019, 04:19 PM   #8
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Originally Posted by RecoveringYuppy View Post
The air in the box will have a pressure gradient. So will the material the box is made of.
This is pretty much what I had determined, I just wanted to make sure that my thinking wasn't in error.

The reason I brought it up was that often I see Flat Earth debunkers use the fact that we have a pressure gradient to "prove" that there is no container, because if the Flat Earthers were right then there'd be no pressure gradient. I was thinking about this, and I came to the conclusion that there would be a pressure gradient either way, so we can't use it as a proof of there being no container. Of course that it is caused by gravity, and so proves that we have gravity, which flat earthers deny, still means that it destroys their stupid flat model (if they ever come up with a consistent one) but it also means we need to be better in our arguments because the "gradient equals proof of no container" is not actually valid and as debunkers we should avoid using incorrect debunks.
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Old 13th August 2019, 05:08 PM   #9
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I'm pretty sure pressure differences can be readily measured between the ground and top floors inside tall buildings.


Also: the pressure can be measured to increase at the rear of an accelerating, sealed car. The helium balloon experiment shows this: https://www.youtube.com/watch?v=2-UzBitLmf8

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Old 13th August 2019, 05:11 PM   #10
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Accelerations of less than a full G can produce noticeable (as well as measurable) changes within a closed container of gas as well.

One example you might have experienced is carrying helium party balloons in a car or other vehicle. When the vehicle accelerates, the balloons move forward (despite inertia), because the acceleration increases the air pressure toward the rear of the vehicle.
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Old 13th August 2019, 06:31 PM   #11
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Until the box is opened, there both is and is not a pressure gradient.
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Old 13th August 2019, 09:30 PM   #12
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Originally Posted by DevilsAdvocate View Post
Until the box is opened, there both is and is not a pressure gradient.
Schrödinger's Gas Law?
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Old 13th August 2019, 10:26 PM   #13
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I haven't read the thread and of course I should have.

Gravity is one of the forces acting on the gas molecules. So if the container is tall enough, of course there will be a density gradient.
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Old 14th August 2019, 12:22 AM   #14
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Originally Posted by PhantomWolf View Post
Am I missing something, or does the idea of a gas equalizing the pressure in a container start to break down when the container is tall enough that gravitation forces can start to play a part?
Unfortunately, below university level, it is often not made clear what (or even that!) simplifications are made.
Ignoring the effects of gravity is one, as has been pointed out.

Another simplification is that pressure travels instantly. Small disturbances in the pressure travel as waves, which we call sound. Changes in pressure travel at the speed of sound.
There's also the issue of density changes.
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Old 14th August 2019, 01:36 AM   #15
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Originally Posted by PhantomWolf View Post
The reason I brought it up was that often I see Flat Earth debunkers use the fact that we have a pressure gradient to "prove" that there is no container, because if the Flat Earthers were right then there'd be no pressure gradient. I was thinking about this, and I came to the conclusion that there would be a pressure gradient either way, so we can't use it as a proof of there being no container.
Yes, that's absolutely correct, so it's a bad argument. On the other hand, it's an equally bad argument when Flat Earthers argue (and I've seen it on these forums, not too long ago) that there must be a container at the top of the atmosphere, because (they claim) physics insists that the pressure of a gas in a container is everywhere equal, therefore without a container the atmosphere would escape into space. And, I must say, I've only encountered the latter argument, and not the former. What I have encountered is attempts to point out that the latter argument is invalid because, as you correctly note, any container of gas in a gravitational field, or in fact any other non-inertial frame of reference, must contain an internal pressure gradient; the normal response from the Flat Earther is, "But I read it in [insert name of first-year undergraduate textbook here] so if you're arguing with the laws of physics you must be the crank."

There are times when teaching by diminished deception feels like a seriously bad idea.

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Old 18th August 2019, 08:15 PM   #16
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Originally Posted by BillC View Post
I'm pretty sure pressure differences can be readily measured between the ground and top floors inside tall buildings.


Also: the pressure can be measured to increase at the rear of an accelerating, sealed car. The helium balloon experiment shows this: https://www.youtube.com/watch?v=2-UzBitLmf8
Absolutely. When I worked as a bike courier in Toronto, I had a watch with a built in altimeter function. It calculated it by measuring air pressure. You don't even need to go very high for a small device like that to measure the change. It would update every 2m change in my altitude.

Interestingly it also allowed me to clearly see what elevators were airtight as the altitude reading would not change while the elevator rose. But when the doors would open it would suddenly jump to the new reading.
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Old 19th August 2019, 03:01 AM   #17
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Originally Posted by theprestige View Post
Seems to me that there'd even be a pressure gradient in a 1 cubic meter box at sea level. It would probably be too small to measure, though.

Also, I'm not sure we do "usually assume" this in any meaningful way. We assume that's the default behavior of gases, absent any other significant forces. Thought experiments involving Maxwell's Demon and spherical cows come to mind.

I think mostly in practice we assume equalized pressure in scenarios where it is a reasonable and more than sufficient approximation. It's not like mechanically the gravity differential is going to play a noticeable part in a fuel injector or a jet engine.
According to U.S. Standard Atmosphere 1976, atmospheric density varies from 1.225g/cm3 at 0m altitude to 1.112g/cm3 at 1000m, so I would expect the density at the top of the 1m cube box to be 1.225 - (1.225-1.112)/1000 = 1.224887 g/cm3, assuming it entrapped the same mass of air as an imaginary cube of the same size at sea level.
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Old 19th August 2019, 05:05 AM   #18
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Originally Posted by BillC View Post
According to U.S. Standard Atmosphere 1976, atmospheric density varies from 1.225g/cm3 at 0m altitude to 1.112g/cm3 at 1000m, so I would expect the density at the top of the 1m cube box to be 1.225 - (1.225-1.112)/1000 = 1.224887 g/cm3, assuming it entrapped the same mass of air as an imaginary cube of the same size at sea level.
Although I think the situation would be different with a sealed box. There would still be a pressure gradient, but much smaller.
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Old 19th August 2019, 06:29 AM   #19
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Originally Posted by Robin View Post
Although I think the situation would be different with a sealed box. There would still be a pressure gradient, but much smaller.
No, the pressure gradient will be the same in both sealed and unsealed box.
The gradient is caused basically by the air on top of the box pushing down on the air on the bottom of the box. The difference in pressure will always be height difference * density of air * 1g.
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Old 19th August 2019, 07:25 AM   #20
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Originally Posted by Dr.Sid View Post
No, the pressure gradient will be the same in both sealed and unsealed box.
The gradient is caused basically by the air on top of the box pushing down on the air on the bottom of the box. The difference in pressure will always be height difference * density of air * 1g.
Agreed. If you carefully slid a lid onto the top of the box, the air inside would not suddenly reorder itself into some not-so-affected-by-gravity arrangement.
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Old 19th August 2019, 07:29 AM   #21
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Originally Posted by Robin View Post
Although I think the situation would be different with a sealed box. There would still be a pressure gradient, but much smaller.
Perhaps it will be clearer if, instead of imagining pumping air into a sealed box, you picture it this way: Build a box around an existing mass of air. Let's go to the extreme and make it a cube 200 miles on a side. Floor first, no effect on air pressure. One side, the top now sticks up into space, sea level pressure at the bottom, no pressure at the top. Two more sides, still no effect. Last side, you have now cut off a block of air from contact with the rest of the atmosphere, still sea level at the bottom, vacuum on the top. Now put the top on. The top does not interact with the air in the box at all, since it is at the vacuum elevation and doesn't touch any air. Perfect pressure gradient from top to bottom.
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Old 19th August 2019, 07:42 AM   #22
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Originally Posted by Jack by the hedge View Post
Agreed. If you carefully slid a lid onto the top of the box,
I didn't say slide a lid onto it. I said a sealed box.

Quote:
the air inside would not suddenly reorder itself into some not-so-affected-by-gravity arrangement.
Still affected by gravity. Not so affected by all the air above it. Yes, it would reorder itself, having that weight above removed.

I didn't say there would be no pressure gradient. I said the situation would be different.

If you seal something then the top of the container is now taking the weight of all the atmosphere above.

The pressure gradient inside is now a function only of the weight of the air in the container.
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Old 19th August 2019, 07:48 AM   #23
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Originally Posted by Pope130 View Post
Perhaps it will be clearer if, instead of imagining pumping air into a sealed box, you picture it this way: Build a box around an existing mass of air. Let's go to the extreme and make it a cube 200 miles on a side. Floor first, no effect on air pressure. One side, the top now sticks up into space, sea level pressure at the bottom, no pressure at the top. Two more sides, still no effect. Last side, you have now cut off a block of air from contact with the rest of the atmosphere, still sea level at the bottom, vacuum on the top. Now put the top on. The top does not interact with the air in the box at all, since it is at the vacuum elevation and doesn't touch any air. Perfect pressure gradient from top to bottom.
Remember, this is a sealed box. It is air tight.

Is the air in that box going to be affected by the weight of all the air above it?
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Old 19th August 2019, 07:50 AM   #24
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Originally Posted by Dr.Sid View Post
No, the pressure gradient will be the same in both sealed and unsealed box.
The gradient is caused basically by the air on top of the box pushing down on the air on the bottom of the box. The difference in pressure will always be height difference * density of air * 1g.
OK.

So it would have the same gradient. It just wouldn't have sea level pressure.
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Old 19th August 2019, 08:04 AM   #25
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Originally Posted by Robin View Post
OK.

So it would have the same gradient. It just wouldn't have sea level pressure.
It would. Unless you change amount of gas inside, or change the volume, the pressure will be the same.
Imagine air in the box on the top plane, where the lid would be (but it's not at the moment). The air bellow the plane pushes against the air above the plane. Now you just push the lid between them. The pressure from both sides of the lid remains the same.

Pressure inside container really doesn't drop by simply sealing it:-)

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Old 19th August 2019, 08:12 AM   #26
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Originally Posted by Robin View Post
I didn't say slide a lid onto it. I said a sealed box...
If you slide an (airtight) lid onto a box, it becomes a sealed box. The air pressure is in equilibrium as the lid slides closed and nothing changes at the moment the lid seals shut. The air pressure immediately next to the lid is the same all over (assuming the lid is thin). The presence of the lid does not take pressure off the molecules in the top of the box.
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Old 19th August 2019, 08:14 AM   #27
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Originally Posted by Robin View Post
Remember, this is a sealed box. It is air tight.

Is the air in that box going to be affected by the weight of all the air above it?
There is no weight of air above it. There is no air above it.
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Old 19th August 2019, 08:17 AM   #28
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Originally Posted by Robin View Post
Remember, this is a sealed box. It is air tight.

Is the air in that box going to be affected by the weight of all the air above it?
While the lid is open, obviously yes; the weight of all that air above it presses a certain amount of air into the box, with a very small pressure gradient increasing the pressure deeper into the box. When the lid seals, that amount of air is now fixed. The pressure is stabilised and the gradient is stabilised. Changes in air pressure outside the box now have no effect on the pressure inside (presuming the box is rigid).
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Old 19th August 2019, 08:34 AM   #29
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To resolve the latest question of whether the lid changes anything you need to specify how rigid the box is. If it's rigid enough to resist the pressure difference (which is likely to be minor in the cases being discussed) then the air inside becomes independent of the weight of the air above the box.
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Old 19th August 2019, 08:38 AM   #30
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Originally Posted by RecoveringYuppy View Post
To resolve the latest question of whether the lid changes anything you need to specify how rigid the box is. If it's rigid enough to resist the pressure difference (which is likely to be minor in the cases being discussed) then the air inside becomes independent of the weight of the air above the box.
It will become independent, or in other words, isolated. But the pressure will not change just by closing the lid.
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Old 19th August 2019, 08:47 AM   #31
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Originally Posted by PhantomWolf View Post
This is pretty much what I had determined, I just wanted to make sure that my thinking wasn't in error.

The reason I brought it up was that often I see Flat Earth debunkers use the fact that we have a pressure gradient to "prove" that there is no container, because if the Flat Earthers were right then there'd be no pressure gradient. I was thinking about this, and I came to the conclusion that there would be a pressure gradient either way, so we can't use it as a proof of there being no container. Of course that it is caused by gravity, and so proves that we have gravity, which flat earthers deny, still means that it destroys their stupid flat model (if they ever come up with a consistent one) but it also means we need to be better in our arguments because the "gradient equals proof of no container" is not actually valid and as debunkers we should avoid using incorrect debunks.
I liked this thread better when it wasn't about a slapfight between flat-earth strawmen.
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Old 19th August 2019, 08:49 AM   #32
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If it were correct that pressure equalized inside a sealed container then you could use it as a pump. Put the lid on your hypothetical box, the pressure equalizes inside the box, the pressure at the top of box is higher inside than outside. You can now open a valve and air will blow out. Use the air flow to drive a generator. Free Energy!
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Old 19th August 2019, 09:24 AM   #33
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Originally Posted by Pope130 View Post
If it were correct that pressure equalized inside a sealed container then you could use it as a pump. Put the lid on your hypothetical box, the pressure equalizes inside the box, the pressure at the top of box is higher inside than outside. You can now open a valve and air will blow out. Use the air flow to drive a generator. Free Energy!
Opening and closing the valves costs energy. The real question is whether the box-pump (BP) produces more energy than is necessary to operate its own mechanisms. Running the BP at a lower altitude would tend to increase the pressure gradient and therefore the energy output. But it would also mean your valves would have to work harder against the pressure differentials involved. Same with a larger box, I think.

---

That's what makes fossil fuels so amazing. They've been packed with energy by ridiculously expensive processes, that cannot be profitably synthesized.

Same with radioactive minerals as fuels. They have a huge energy density, but it takes a rapidly-expanding matter-dense universe with a *lot* of supernovae, to produce them in industrial quantities.
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Old 19th August 2019, 09:30 AM   #34
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Originally Posted by BillC View Post
I'm pretty sure pressure differences can be readily measured between the ground and top floors inside tall buildings.


Also: the pressure can be measured to increase at the rear of an accelerating, sealed car. The helium balloon experiment shows this: https://www.youtube.com/watch?v=2-UzBitLmf8
A bit off topic, but that reminds me of the old story where a physics exam has a question asking how to determine the height of a building using a baramoter.

A student answers the question that this would be done by dropping the barometer from the roof of the building, timing the fall, and using the formula: d = 1/2 at*2.
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Old 19th August 2019, 09:59 AM   #35
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Originally Posted by CORed View Post
A bit off topic, but that reminds me of the old story where a physics exam has a question asking how to determine the height of a building using a baramoter.

A student answers the question that this would be done by dropping the barometer from the roof of the building, timing the fall, and using the formula: d = 1/2 at*2.
Without knowing the drag on the barometer, that method is going to have a margin of error. On a very tall building, you'll end up ordering the wrong number of stair-steps, and the wrong length of elevator cable. On a very tall building, you might even end up ordering the wrong number of fixtures for each floor, due to miscalculating the number of floors from the height of the building.
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Old 19th August 2019, 10:01 AM   #36
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Moving the barometer from the bottom to the top of the building can take time and that can introduce errors in to that method too.
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Old 19th August 2019, 10:20 AM   #37
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Guys please, if you make a joke, use smiley face. It should be norm at least on forums like these where ignorance, wisdom, and severe sarcasm meet on daily basis.
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Old 19th August 2019, 10:35 AM   #38
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Originally Posted by theprestige View Post
Without knowing the drag on the barometer, that method is going to have a margin of error...
A typical barometer measures to the nearest millibar, so unless the building is extraordinarily tall the answer is going to be that it's height is zero +/- 250m.

On balance I think I'll throw the thing off and count seconds.
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Old 19th August 2019, 01:17 PM   #39
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Oh well, I was wrong on the second count too then.
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Old 19th August 2019, 01:23 PM   #40
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Originally Posted by CORed View Post
A bit off topic, but that reminds me of the old story where a physics exam has a question asking how to determine the height of a building using a baramoter.

A student answers the question that this would be done by dropping the barometer from the roof of the building, timing the fall, and using the formula: d = 1/2 at*2.
I heard it on the radio from a guy who claimed to be the person setting the exam.

The first answer the student gives is that he would tie a string to the barometer, lower it to the ground and then measure the length of the string.

When he gets this marked wrong he goes and complains saying 'why don't you think my method would work?'.

The lecturer then gives him a second chance to do the question. This time he provides two methods, the first was the formula given above and the second was that he would offer it as a gift to the building manager in exchange for the information about the height of the building.

So the lecturer says "Do you know the answer I was expecting?" and the student says "Yes" and he gives him the marks.

I doubt it is actually true, so more of a tall tale than a gag.

I forget the point the guy on the radio was making.
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