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Thought experiment about fluid compressibility

  1. Jul 15, 2013 #1
    I'm a physics noob but this is something I was thinking about when I read in my textbook that fluids are generally incompressible.

    Let's say I had 1000 L of water enclosed in a sphere several meters thick (say, 2 meters thick) made of an extremely hard, dense metal with 0 outlets or holes of any kind. (Some other material other than metal might be better for this, since metals are malleable and can be punctured with high pressure.) The water is perfectly enclosed in the sphere, which has a volume of exactly 1000 L.

    Let's say this sphere was constructed in such a way that it could be radius could be reduced uniformly so that I can keep "squeezing" the water inside. Maybe the plates of the sphere on the outside slide over each other or something.

    What happens to the water as I keep compressing? Does it just turn into a gas? What kinds of forces are exerted by the water on the sphere? Could I do this without shattering the sphere?
  2. jcsd
  3. Jul 15, 2013 #2


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    Well water is incompressible... practically. In reality, water is very, very slightly compressible. The pressure generated by a thermonuclear explosion under water can just barely compress it, for example.

    Anyway, since water is incompressible, as you keep squeezing your sphere, the water is just going to resist any sort of volume change by exerting an equal and opposite force to your squeezing, which would measure as an increase in water pressure inside.

    Think about trying to squeeze a steel ball with your hand. It doesn't give any even as you squeeze harder. It's the same thing with your situation only with the ball squeezing the water.

    Eventually the force would be great enough that you would just barely start to compress the water if you could generate that kind of squeeze. That is assuming the pressure didn't rupture your sphere first and allow the water to escape.
  4. Jul 16, 2013 #3
    Water (and every other material) is compressible, which can be proven by observing the propagation of sound. The thing is that the compressibility of liquids (including water) is not very different from the compressibility of solids - as compared to gases, which can be compressed considerably. So, your "squeezing tank" has to be made by a very very strong material, say diamond, and even then it will be effective only in a relatively small range of pressures (so, you can't squeeze very much, because your tank will start squeezing itself).

    In order to know what's going on with water while squeezing it in the tank, you need to observe pressure, density, and temperature. The behaviour of water can be predicted from the phase diagrams of water. Here's one:

    If you keep water in room temperature, then by squeezing it you make ice.
  5. Jul 16, 2013 #4
    In the case of water, to reduce the volume from 1000 L to 999 L, you would need to apply a pressure of about 20 atm.
  6. Jul 16, 2013 #5
    But wait, what would happen to water if it was on a planet made of only water and the
    planet was 10,000 miles in diameter? At the center of said planet wouldnt the water be squished to a solid?
  7. Jul 16, 2013 #6


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    Sure. Just take a look at a phase diagram. In fact, it would likely be one of the exotic forms of ice that is borderline metallic. It is theorized, for example, that the ocean floor of Titan may be comprised of such an exotic crystalline form of ice.
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