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Effect of freefall on hydrostatic/atmospheric pressure

  1. Jan 3, 2013 #1
    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.
  2. jcsd
  3. Jan 3, 2013 #2
    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??
  4. Jan 3, 2013 #3
    Thanks for the reply :)
    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...
  5. Jan 3, 2013 #4
    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.
  6. Jan 3, 2013 #5
    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.
  7. Jan 3, 2013 #6
    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?
  8. Jan 3, 2013 #7
    Firstly thanks very much for your reply, it was very insightful.
    From the above quote, how else can pressure be provided in the spaceship: in other words what is the physics behind the high pressure gas from the tanks resulting in a high pressure in the spaceship? I would presume that it had something to do with PV=nRT from the ideal gas law, but does this apply in an accelerating frame of reference? Hmmm.
    Regarding your question, well if you were to shake the bottle with carbonated soda, the pressure inside would increase, forcing substance out of the side of the container more quickly, still reducing to 0 in freefall however, but then the question is: why does the pressure increase when i shake the bottle? Hmmmm. Once you start to think about something in physics you realise how many phenomena you truly take for granted...
    Last edited: Jan 3, 2013
  9. Jan 3, 2013 #8
    Yes. The pressure in the cylinders can be made as high as we want by stuffing more and more gas into the cylinders. The pressure in the cabin can be made as high as we want (within the mechanical limitations of the of the structural material) by stuffing more and more gas into the cabin. None of this has anything to do with gravity or acceleration. It all follows from the P-V-T behavior of the gas. The gas does not have to be an ideal gas.
  10. Jan 3, 2013 #9
    I see, so could we attribute the pressure of the gas to its PVT behaviour, so does that mean that the pressure ie. force per unit area exerted by the gas is due to the kinetic energy effect of the particles colliding with the surfaces of contact? If this is the case, then i think this could be explained by the centripetal acceleration having little effect on the individual particles as their speeds are so high. In other words, what's an acceleration of 5ms^-2 ( assuming this capsule is a fair distance to earth) to a particle travelling at thousands of m/s. Do you agree with this reasoning? By the way, does anyone have any explanation for the increase in pressure when the aforementioned cola can is shaken?
    Thanks for the suggestions :)
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