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Isothermal Expansion of Water/Moving Boundary

  1. Feb 13, 2013 #1
    Hello all,

    I've been wondering how water reacts in a closed, rigid system with one moving boundary. Assuming the system is perfectly filled with water, and one side of the boundary moves (increasing the volume), how does this affect the pressure in the system?

    Since water is incompressible, I would think that moving one boundary would dramatically increase the pressure on the other boundaries within the container (since the water attempts to maintain its original volume). However, I don't get how to modify the formulas for Bulk Modulus to prove this is true.

    I want to create a water-filled probe that rests on the skin and then move a boundary of that probe to raise the skin. In my mind, this should act much like a reverse hydraulic lift, forcing the skin to lift as the other boundary is drawn away. However, I don't know this with certainty and I don't get how to show this relation in exact, quantitative terms. I would appreciate any help that could be provided in modelling this system to be as realistic as possible.

    Thanks for your help!
  2. jcsd
  3. Feb 14, 2013 #2
    The system is subject to some external pressure, usually atmospheric. Initially, the internal pressure may be taken equal to the external. As the volume starts to expand,the internal pressure will start dropping off very rapidly, because water's volume does not change much under pressure, and at same stage a cavity will form there. The cavity will not be completely evacuated, it will contain water vapor. The pressure on all the boundaries will never exceed the external (atmospheric) pressure.

    If I understand your description correctly, what you are thinking about is basically a suction cup. It could be somewhat more efficient than a typical suction cup, but not in a major way.
  4. Feb 14, 2013 #3
    So then I do need to worry about cavitation? The maximum force I was hoping to exert on the skin is about 7N, or an internal pressure about 50kPa below atmospheric, so I had hoped that moving the boundary could accomplish this. Is there a way I could do this effectively with a linear servo as the drive and then have the skin directly acted on by the water pressure while avoiding cavitation?

    Since the cavitation pressure of water is lower than its equilibrium vapor pressure (~3kPa), I thought there wouldn't be cavitation unless the system featured significant cavitation nuclei?
  5. Feb 14, 2013 #4
    Water's bulk modulus is 2.2 GPa, which is quite high. That means you the pressure vessel must be quite large, so that even a low-precision servo could do it. Let's say the vessel contains one liter = 0.001 m^3 of water. Then the change in the volume is 2.3E-8 m^3. If your vessel has, say, a 10-mm long, 1-mm radius cylinder, then a piston would need to move 7.2 mm in that cylinder to create a 50 kPa pressure drop. I think this is quite achievable with modern servos.
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