Topic: Try This Thought Experiment

[flamethrower]

The thought experiment is this:

A very long sealed cylinder is pressurized to X psi with air. At horizontal, the pressure is tested at each end of the cylinder at test point A, which stays at sea level, and point B, which is to be elevated. The pressures, as expected, are identical, X psi. The pressures are measured non-intrusively and magically and accurately, as X psi, + or - say .0001psi.

By miraculous means, (remember it's a thought experiment), the very long cylinder is hoisted into the air until its top is level with say Mt Everest, around 28,000 ft. The atmosphere is of constant temperature, and insulation is not a consideration.

We test the pressure at the low end, A, and at the same time, at B, the high end. Will the pressures be the same, or different?

The essential concept to be explored is whether a sealed, pressurized cylinder, when turned (magically), through a 90 degree angle, from horizontal to vertical, will have the same internal pressure at the top as at the bottom.

Reply with your reasoning. Good Luck.

[clifdweller]

Well,without really thinking about it,I would say that the pressure stays the same at both ends. Outside pressure won't have an effect on a pressurized container. Then again,gravity has a greater effect on the air molecules closer to the ground.

[archiebald]

I would ask this question first;

"Why is sea level pressure higher than the pressure at 9,000 meters.  Is it gravity??  If so then the answer for the sealed tube would be similar to that of the external atmosphere.

As far as I know (not far) air does have a mass and it is that mass combined with gravity that creates the varying vertical pressure.  (many other minor factors notwithstanding)

Do the same thought experiment with water...

[spacefan1]

I would say that the psi within the canister would stay constant at both ends; however, the external pressure on the cansiter would be much greater at the higher altitude. If the canister was to fail, it would occur at the higher altitude.

Can't a similar analogy be applied to the space shuttle? At its launch pad, it is xxx psi. And when it's launched into space the internal cabin pressure remains the same. Sure, they have to decompress a little before entering the ISS, but that's another story altogether.

[archiebald]

Spacefan,
What you are saying is comparing apples and pears.  From the original question, the long cylinder is extremely long - at least 9,000 meters.  You cannot compare this with a small cabin as in the space shuttle.

You need to consider a huge volume of air in a very long cylinder.

[broomstar]

I agree with Archie, and it's because of gravity's effect that the two ends have different pressures.
I'm curious that if flamethrower have ever read of Feynman's book, in the chapter of statistic dynamics, he discussed a similar problem.

[spacefan1]

Hi Crab!
I haven't heard from you in a while!

[broomstar]

Hi! I haven't saw your posts on this forum for quite a while either...
Now I am totally FREE for the vacation!!!

[flamethrower]

clifdweller - you say the same at both ends but you are unsure due to gravity. Would you think that gravity would have an effect on the 28,000 foot cylinder of air? Or not? Why?

archiebald - It appears you're going with different pressures at each end due to gravity. Correct?

spacefan1 - You say the pressure is the same at both ends. Why?

broomstar - Same as archiebald, different pressure due to gravity. I don't think the answer is in statistical dynamics, but you're close.

I was hoping for alternate views and I see there are a few. Good! Keep em coming!

Anyone else wish to throw their hat into the ring??

[archiebald]

Flamey,

Just to clarify...

Assuming that the external temperature effects on the long cylinder are equal at all altitudes (lets say for example that the cylinder is very well insulated), then the pressure at the base of the cylinder will be higher for the reasoins outlined below.

And, if we take into account the external temperature gradient (cooler at the top), then this will add further to the pressure differential.

I am not suggesting that the gravity is higher at the bottom, (although it will in fact be slightly higher).  I am saying that the mass of the air itself with gravity acting upon it causes the air to "pile up" at the botom of the cylinder causing an increase in the pressure at the bottom.

If you compare it with the analogy of water in a pipe, then all you have done is created a head of pressure, which is exactly why you see water towers in flat countryside.

Another analogy - at the circus a team of 3 acrobats are standing on each other's shoulders.  Who has the most pressure exerted on their shoulders, the top (no people on his shoulders), middle (one person on his shoulders) or bottom person (two people on his shoulders).  Or does anyone think they will have equal pressure exerted?

Or to put it more simply, everything that has mass tries to flow downhill in a gravity field and if you resist that flow you end up with pressure.

[clifdweller]

Well, I'm going to go out on a limb here with a totaly weird answer. Yes air pressure is a result of gravity. And due to the inverse square law, the molecules at the bottom not only weigh more than those at the top, but they have the force of the air above them acting on them. There's where my thinking goes astray.

We have a cylinder of unknown diameter,granted. But let's say the the cylider is 1" in diameter. There isn't enough air above to over come centrifugal forces of the earths spin. The top of the cylinder is spinning faster,and the air molecules are forced upwards.  The top of the cylinder has greater air pressure.

Hey, it made sense when I started to type it. :rollin :rollin

[flamethrower]

archie,

Don't worry about temperatures outside of the cylinder, not an issue. But you're on the right track in describing the problem as a 'pile of air.' You are therefore sticking to the answer that the pressures will be different at the top and the bottom. How much different?

clifdweller,

You are now saying the pressure will be greater at the top of the cylinder due to Earths spin. Interesting.

Anybody else?

I was hoping to hear from yale.

[clifdweller]

Interesting? All I get is an "interesting" ?!?

From what I remember from my skoolin in the three "R"s ,the pressure would remain the same at both ends. However, no-one ever asked if half of the container was EXTREMELY higher than the other half. If I had to put money on it, I would say that the pressure is the same at both ends. But I would never bet on my limited knowledge of the behavior of gasses.

[yales]

Lord Archiebald is correct.

Cliffies idea may be a real effect, but I think it is small. I will do some calcs and see.

Yale, back from the Outer Limits.

[clifdweller]

That CAN'T be the answer. It's way too easy to figure out. It's a trap! You MUST over think this to get the correct answer. Over thought answers, combined with lots of bullsh!t ALWAYS work. Which is, in fact , the first law of student /teacher dynamics.