Gravity and Atmospheric Pressure: A Thought Experiment

[Saketh]

Consider the following situation.

We have an evacuated straw, one meter in diameter, closed at both ends (but the ends can be easily opened). One end is here at ground level on Earth, and the other is at ground level on the moon. Assume that the straw is strong enough to resist breaking.

We simultaneously open both ends of the straw. What happens? If you put into the straw a sealed cylinder of the same diameter, would the cylinder be sucked up onto the moon? Would air be sucked from Earth onto the Moon until there is a pressure equilibrium, or gravity balances out the pressure difference force?

I appreciate any help in performing this thought experiment.

 

[disregardthat]

Assuming the inside of the straw is vaccum, the straw would be filled with air in the density that the air outside the straw is. Think if it as a pipe of air close at both ends, you put half of it in water, and open the ends. The pipe will be filled up with water up to the surface of the water sorrounding the pipe.

 

[Saketh]

Assuming the inside of the straw is vaccum, the straw would be filled with air in the density that the air outside the straw is. Think if it as a pipe of air close at both ends, you put half of it in water, and open the ends. The pipe will be filled up with water up to the surface of the water sorrounding the pipe.

But what if the water is in a vacuum, and you put in the evacuated, closed straw? When you open the ends, there will be no pressure keeping the water down, so wouldn't the water come out of the top of the straw?

 

[russ_watters]

If the pipe and water are both in a vacuum, the pipe fills up to the level of the water in the container the water is in.

Pressure works both ways: there needs to be pressure pushing the water up.

Also, a vacuum isn't a really like how people think about a vacuum cleaner - there is no eternal, insatiable sucking. What it really is is the absence of pressure. So what happens in an evacuated container or straw is determined by what is outside the container pushing into it.

 

[disregardthat]

Nature hates a vacuum ;)

 

[billiards]

I guess by diffusion some air might one day reach the moon, but it'd probably take over a million years.

 

[DaveC426913]

Nature hates a vacuum ;)

No, nature hates order. Cats hate a vacuum!

 

[DaveC426913]

But what if the water is in a vacuum, and you put in the evacuated, closed straw? When you open the ends, there will be no pressure keeping the water down, so wouldn't the water come out of the top of the straw?

The only thing pushing anything up the straw is air pressure. The total amount of force exerted on anything inside the straw is 14.7psi (the weight of the air above us). It can only push a theoretically weightless object up about 100 miles (i.e. the height of the atmosphere.)

 

[Saketh]

The only thing pushing anything up the straw is air pressure. The total amount of force exerted on anything inside the straw is 14.7psi (the weight of the air above us). It can only push a theoretically weightless object up about 100 miles (i.e. the height of the atmosphere.)

Ah, that makes sense. Thanks for the explanation!

 

[Werg22]

My hypothesis: The cylinder will suck air into it up to the Earth's atmosphere surface. The air there would have some kinetic energy and some will escape until it is beaten by the Earth's gravitational field. It wouldn't reach the moon.

 

[DaveC426913]

My hypothesis: The cylinder will suck air into it up to the Earth's atmosphere surface. The air there would have some kinetic energy and some will escape until it is beaten by the Earth's gravitational field. It wouldn't reach the moon.

How will it escape? The straw goes all the way to the Moon.

[ EDIT ] Oh, you mean escape the height of Earth's atmo, you don't mean escape from the top end of the straw.

You're talking about imparting the air with momentum. It is very hard to impart a gas with momentum. It will rise to the height of the atmo.

 

[disregardthat]

The air being pressured up inside the straw might go a bit further than the Earth's atmosphere, but only because of it's speed when it is stabilizing itself. In time, it will be totally parallell with the atmosphere outside.

 

[Werg22]

How will it escape? The straw goes all the way to the Moon.

[ EDIT ] Oh, you mean escape the height of Earth's atmo, you don't mean escape from the top end of the straw.

You're talking about imparting the air with momentum. It is very hard to impart a gas with momentum. It will rise to the height of the atmo.

Really? I'm not an expert in fluid mechanics, but a drag from the surface of the Earth to the surface of the atmophere wouldn't impart some considerable momentum? Won't some gas be able to go a little further before it is brought back by the Earth's gravitational field?

 

[DaveC426913]

Really? I'm not an expert in fluid mechanics, but a drag from the surface of the Earth to the surface of the atmophere wouldn't impart some considerable momentum? Won't some gas be able to go a little further before it is brought back by the Earth's gravitational field?

Sure, a little further maybe.

You could try the experiment in your kitchen. Put some water in a bowl and hold a straw vertically in the bowl. Stir the water. See how high the water inside the straw rises above the average surface of the water in the bowl. I'm saying it would be insignificant.



In Gr 11 physics we were given a vector problem to solve where the smoke from a locomotive would end up after a few minutes depending on the speed of the train and a cross-wind. It was a trick question. The speed of the train is a red herring. The train does not impart any significant momentum on the air or smoke. Its momentum drops to zero virtually instantly and you only calculate external forces.

 

[hustleberry]

first of what causes atmospheric pressure, it is the gravitational attraction of the Earth that gives the air it weight that why the pressure at sea level is greater than that of 10,000 ft because at sea level we have more air exerting a force above downwards , the moon has no atmosphere hence no atmospheric pressure. when the straw is opened up the force that the atmosphere exerts downards per unit area will have an equal reaction upwards forcing the air into the straw the air woul fill up the straw until the limits of the atmosphere or the limits of gravity air would not be evacuated to the moon because the gravitational force would hold the air to a certain level (i.e. the atmospheres limit).