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I Internal pressure due to vessel collapse

  1. Jul 3, 2017 #1
    Hey All,
    I have a plastic vessel fully filled filled with an incompressible fluid (Water), at some time this vessel is impacted and crushed on one side (say 5% of the initial volume is lost).

    Only, I know the volume isn't lost, the fluid (being incompressible) will exert pressure on all surfaces of my vessel causing the vessel to expand (where it isn't being crushed) and the pressure of the fluid will increase.

    Is there a way of calculating this increase in pressure (maybe as a function of displaced fluid)?

    In my mind I picture this as a water balloon on a flat surface, as I push my hand down on the middle of the balloon the water moves to areas not being compressed, eventually the maximum stress of the material is reached and the balloon material fails. How would one predict the internal pressure of the fluid?

    Thanks for any help.
     
  2. jcsd
  3. Jul 3, 2017 #2

    anorlunda

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    :welcome:

    I would expect any such calculation to be dominated by the strength of the container walls.

    A SCUBA tank would permit much higher pressure before bursting than a water balloon.
     
  4. Jul 3, 2017 #3
    Suppose the loading were applied gradually, rather than as an impact. This would be one way of starting to analyze the problem. If you can't solve the problem for a gradually applied load, you certainly won't be able to do it for an impactful load. The deformation of the vessel would have to be analyzed, under the constraint that the fluid is only slightly compressible (and described by the bulk modulus of the liquid). The analysis would involve differential force balances on small parcels of the vessel wall, based on the stress equilibrium equation (equilibrium differential force balance). The hard part of this is that, to do the calculation, one would need to study and quantify the mechanical constitutive behavior (stress/strain/displacement) of the material comprising the vessel wall, including large deformations (beyond the elastic limit) and displacements. Calculations like this can and are done, typically using Finite Element stress analysis. In addition to all this, one would also need to quantify the failure behavior of the vessel material in terms of a properly formulated failure criterion. In short, it's doable, but it ain't easy.
     
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