## Effect of freefall on hydrostatic/atmospheric pressure

I was thinking about Walter Lewin's thinking question: "If an astronaut were to try to drink from a sphere of floating juice through a straw in a capsule pressurised at 1 atm, could he drink effectively?"
The answer to this is yes because of the atmospheric pressure. But it got me thinking about the hydrostatic pressure in this situation and also the atmospheric pressure of the air in the capsule.
If this satellite is in free fall (assuming it's orbit is circular, then everything is accelerating uniformly ie. the ball of juice, the air "above" it, the astronaut etc.). Now if we consider the ball of juice, would there be any hydrostatic pressure difference in the middle of the ball compared to the edges (atmospheric pressure)? I would argue not as the hydrostatic pressure of ro g h is due to the weight of the above bearing down on the considered point, but in this case, in freefall, it would seem the weight would not be "felt" as such by the fluid and so the hydrostatic pressure would not be applicable. This could be likened to dropping a 2 litre cola bottle with a few small holes and observing whether the water would stay inside when allowing to free fall, and, having tried it from my roof this afternoon it seems to be true. So this is all very well, if slightly strange, but the weirdest thought comes when considering the atmospheric pressure of the air inside the capsule, and this is where i would appreciate some thoughts to help out here. If the air is also accelerating in freefall, just as the juice which exhibits no hydrostatic pressure is, then how is it that this air can remain at 1 atm?? I feel as though i must be missing something here, but based on the previous reasoning, the atmospheric pressure should be 0, but that surely is wrong. Any thoughts at all from you folks on any of this would be appreciated- very interesting stuff in my opinion and even better if i can get the final puzzle piece in place.
Regards
Dom

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sorax: BRAVO>>>>>

 This could be likened to dropping a 2 litre cola bottle with a few small holes and observing whether the water would stay inside when allowing to free fall, and, having tried it from my roof this afternoon it seems to be true.
Great way to start!!

 If the air is also accelerating in freefall, just as the juice which exhibits no hydrostatic pressure is, then how is it that this air can remain at 1 atm??
What do you think would happen if you pressured the 2 litre cola bottle....say to two
atmospheres...would the freefall have any effect on it's leaking fluid??

 Quote by Naty1 sorax: BRAVO>>>>> Great way to start!! What do you think would happen if you pressured the 2 litre cola bottle....say to two atmospheres...would the freefall have any effect on it's leaking fluid??
Assuming that the hydrostatic pressure at the bottom of a new bottle is now two atmosheres, and we drop the bottle assuming no air resistance, the water above the bottom is still accelerating at the same rate as the bottom, so no net hydrostatic pressire is observed again. At least i think that's what would happen...

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## Effect of freefall on hydrostatic/atmospheric pressure

I would have thought the net pressure remained at the 'charge' of 1 atmosphere.

We are disregarding the slight effects of tidal gravity here....and the fact that gravity g
is not constant at the top and bottom of the bottle.....negligible effects here.

 Quote by Naty1 I would have thought the net pressure remained at the 'charge' of 1 atmosphere. We are disregarding the slight effects of tidal gravity here....and the fact that gravity g is not constant at the top and bottom of the bottle.....negligible effects here.
Hmmmmm.....
Assuming that water is incompressible, the only way you can pressurise a bottle to a higher pressure is to increase the size of the bottle. So in the first case, assuming that the 2l bottle is 30cm high, the density of water is 1000kg/m^3 and g= 10ms^-1, then the pressure is:
1000 x 10 x 0.3= 3000Pa=3kPa
This is the hydrostatic pressure at the bottom of the bottle, which is 3/100 ths of an atmosphere. Bear in mind that the absolute pressure is this + atmospheric pressure, but at an absolute pressure of 1 atmosphere in the bottle, nothing would happen so that's a fairly redundant concept.
So to get to two atmospheres i need a bottle of height:
200000/(10 x 1000)= 20m
In this case, if i were to drop this ridiculously big bottle there would still be no net force on the bottom and so no hydrostatic pressure and so no water out of the side.
The hypothetical situation in the spaceship is still baffling me though.
 Recognitions: Gold Member The space capsule is pressurized internally using high pressure gas cylinders. Because the effective gravity is zero in the capsule, there is no hydrostatic pressure of the air. But hydrostatic column is not the only way to create pressure. The air pressure outside the cabin is essentially zero. But, inside the cabin, there are gas cylinders at high pressure that release air to maintain the cabin pressure (which actually is somewhat less than 1 atmosphere). Any air that leaks out through the non-hermetically sealed shell is replaced by air from the cylinders. What do you think would happen with your free falling soda bottle if you covered the holes, shook it up, and then uncovered the holes?

 Quote by Chestermiller But hydrostatic column is not the only way to create pressure.