Pressurized Cylinder ?

A 10 mile long sealed cylinder is pressurised 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 very long cylinder is hoisted vertically into the air until point B is 10 miles in elevation.

We test the pressure at sea level, A, and at the same time, at B, 10 miles up.

Will the pressures be the same, or different ?

If the cylinder is slightly elastic, then it will expand a tiny amount as the air pressure on the outside goes down. That means the air pressure inside will decrease slightly.

But if the Cylinder is rigid, then nothing that happens outside will affect the pressure inside.

If the cylinder were a typical SCUBA type cylinder, they are compressed to 3000 psi. The 14.7 PSI outside air pressure dropping to rougly 2 or 3 PSI would be irrelevant in terms of stress on the cylinder.

Pressure at the bottom will be higher than at the top and the pressure at the top will be lower than when the cylinder was horizontal.

The gas in the cylinder is pulled by gravity towards the bottom just like in the atmosphere.

Oh, I misread the question. I agree with Billy. Gravity still works.

Thought experiment here:
Try constructing a 10 mile high cylinder. During construction the cylinder is open to the atmosphere, so pressure is high at the bottom and low at the top. When you finish construction and seal the cylinder, nothing will change. That final tiny bit of metal that you use to sealthe cylinder will not cause the gases inside the cylinder to go wildly wooshing around in search of some new equilibrium. The cylinder will still have high pressure on the bottom and low pressure on the top.
Now if you lower this cylinder to horizontal, the pressure will become uniform throughout, at some value X psi. This cylinder is thus equivalent to a cylinder that was built horizontally, on the ground.
Having lowered the cylinder to horizontal, now raise it back up and measure the pressure at the top and bottom. The pressure at the bottom must be higher than the pressure at the top. In fact, the pressures you measure this time must be identical to the pressures you measured when you first sealed the cylinder. -Any other result would imply that the gases in the cylinder could somehow remember the history of how you constructed and handled the cylinder. That is absurd, gases don’t remember things like that.

e.g. If you construct two identical vertical cylinders, and then lower and raise one of them, they had better both have the same pressure differential between top and bottom when they are both in the same orientation.

Since the cylinder you constructed vertically, initially had the same pressure gradient, top to bottom, as the atmosphere, any other cylinder in the same orientation with respect to the earths gravitational field must have a similar pressure gradient, no matter whether you construct it horizontally, vertically, or in orbit around Barnard’s star. :slight_smile:

So it is generally agreed that that gravity will have the same effect on the pressurised gas within the cylinder as it has on the atmosphere.

Although, in the pressurised cylinder, the molecules are moving much faster and are bouncing off the inside walls of the cylinder at great speeds. Would this not keep the pressure constant throughout the cylinder ?

I think you’re confusing “pressure” with “temperature” here. The fact that the cylinder is pressurized has nothing to do with the kinetic energy of the molecules inside. It means only that there are MORE molecules per volume on average inside, rather than outside the cylinder.

This is also why the pressure inside is greater than the pressure outside: each molecule “hits” with the same momentum on both inside and outside surfaces of the cylinder, but there are many more collisions INSIDE than outside, so the pressure inside is greater than the ambient pressure outside.

If the cylinder is at ambient temperature, the molecules inside and outside are moving about at the same rate (again, on average), and gravity still works, no matter how fast a body is moving. (Though of course if you move fast enough you’ll exceed escape velocity, or go far enough and its effects become nominal.)

Battry

One of the best First Posts I’ve seen to date. Welcome to the Boards, Battry.

And quite right. Pressurized and horizontal, pressure is equal at all points in the cylinder.

Pressurized and vertical, gravity is trying to pull the ten-mile-high column of air downward, so the pressure will be nominal-plus-X at the bottom, and nominal-minus-X at the top.

One gets the same effect with a column of water: Horizontal, the water pressure is equal at all points of the cylinder. Vertical, the pressure differential will be far greater than the air-filled cylinder.

In fact, at ten miles of head pressure, the base of the cylinder would have to be extremely thick- it would be seeing pressures greater than that at the bottom of the sea floor.

10 miles is a significant distance and more so on a cloudy day. For the pressure to be equal the cylinder would need to be an arc with center at the center of the earth but a straight horizontal cylinder would be closer to the center of the earth at the center and the pressure would be higher there. A straight cylinder 10 miles long, tangent to the surface of the earth would have the ends separated from the surface of the earth by a distance of 16.68 feet.

The pressure that a gas exerts on the walls of its container is determined by the momentum of the atoms and molecules of the gas, which in turn is determined by the temperature. As the temperature increases the atoms and molecules move faster, and so exert a greater pressure on the walls. If the walls are rigid, such that the volume of the container is held constant, then the relationship between pressure P and temperature T is given by Charles’ Law: P=constant x T

Raising the temperature increases the speed of the molecules increases. If the pressure were greater at the bottom, so would the temperature. If the temperature were greater at the bottom than the top, the molecules would be moving at high speed at the bottom but not the top. How is it the molecules can move at high speeds at the bottom and not travel up the length of the cylinder towards the top, thus equalizing the pressure in the cylinder.

Not necessarily true. When you’re talking about holding the volume constant, you’re implicitly assuming “volume of some uniform system”, which this cylinder is not. In other words, for PV = Nk[sub]B[/sub]T , you’re talking about the pressure of the entire cylinder, which is not well-defined. If you instead talk about “the bottommost portion of the cylinder”, say, then you don’t have a fixed volume. It’s perfectly possible for this column of gas to be at a uniform temperature, in which case the pressure will be higher at the bottom.

Molecules will move from the bottom to the top, which is why the atmosphere doesn’t all fall into a thin layer on the ground with vacuum directly above it. But diffusion is only one effect here, and gravity still works, so you get a pressure gradient.

In terms of kinetic theory, the pressure of a gas is due to the rate of change of momentum of molecules when they strike the boundaries of the system (walls of the container). If the system is liquid, pressure is defined similar, except that the effect of gravity, at a point in the liquid, must often included. The inclusion of this effect depends upon its relative magnitude; for example the pressure in a large vertically mounted air cylinder may be so nearly the same at the top and bottom that differentiation need not be made, but if the cylinder were filled with liquid water or a more dense liquid, a decision to include the difference would depend upon the context of the application.

http://www.indiana.edu/~geog109/topics/pressure/GasPressWeb/PressGasLaws.html

This paper talks about the cylinder being of near uniform pressure at the top and the bottom. Is it crank ?

Qeue, I don’t see that quote in the link you provided. Did you get the link correct?

From what you quoted, it sounds like their idea of a “large cylinder” is at most tens of meters. Fill up a 10-meter deep tank with water, and the pressure at the bottom is twice the pressure near the surface (one atmosphere). Fill it with air, and you need an very good barometer to measure any difference.

scr4

Sorry, You’re right. Here is the correct link:

http://www.me.mtu.edu/~sshaikah/pressure.pdf

Why aren’t we allowed to edit our posts ?

Yeah but …

If you erect a vertical cylinder open to the air and then seal it it will have the same pressure distribution along its length as the atmosphere. In particular, the pressure on the base of the cylinder will be 14.7 lb/in[sup]2[/sup] (assuming the base at sea level on a standard day). This means that an elementary column of air within the cylinder and having a cross sectional area of 1 in[sup]2[/sup] will weigh 14.7 lb.

But if you start with the cylinder horizontal and open to the air and then seal it up as the OP said, you get a different result. An elementary tube of air with an area of 1 in[sup]2[/sup] in this cylinder weighs 27.5 lb. Such an elementary tube has a volume of 367 ft[sup]3[/sup] for a cylinder 10 miles long and air weighs 0.075 lb/ft[sup]3[/sup] at sea level and about 70 [sup]o[/sup]F.

This means that when you stand the cylinder on end, all the weight of the air presses down on the bottom and the pressure will be 27.5 lb/in[sup]2[/sup]. And at the top of the cylinder there is no air above a plane through the top so the pressure would be zero.

So the cylinder should have 27.5 lb/in[sup]2[/sup] pressure at the bottom and zero at the top and vary approximately exponentially from the high to the low pressure.

All this is after the transient changes from raising and lowering pressures within the cylinder have died out and steady state has been obtained. And it is assumed that no heat leaks into or out of the cylinder from the atmosphere.