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Pressure in a Piston

  1. Nov 16, 2014 #1
    1. The problem statement, all variables and given/known data
    In a cylinder & piston system, where is the weakest point on the cylinder (the point that will break under increasing pressure)?
    You may assume the joint between edges are as strong as the material.
    This is homework for A-level students.
    2. Relevant equations
    P = F/A
    Surface Area of Flat Surface= πr2
    Surface Area of Curved Surface = 2πrl
    3. The attempt at a solution
    F = PA, if 2l > r, then curved surface will face more force and will break first?
     
  2. jcsd
  3. Nov 16, 2014 #2

    haruspex

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    I'm not sure that the idea is to compare flat with curved. Maybe you are just supposed to consider different regions and/or different failure modes of the curved surface.
    The failure mode of the flat surface is complicated. It depends on how the piston flexes.
    Anyway, it isn't total normal force on the component that matters. Start with something simpler, like a sphere, and consider how it will fail.
     
  4. Nov 16, 2014 #3
    Does the cylinder wall have a thickness, or is it infinitely thick? Is the stress in the cylinder wall higher if the wall is thin or if it is thick? What course is this from? Is it Strength of Materials? Do you know how to calculate the stress in the cylinder wall? If so, what are the principal stresses on the inside and the outside of the wall?

    Chet
     
  5. Nov 17, 2014 #4
    It is a homework that is supposed to be challenging and makes us think, AS level physics knowledge should be adequate. material for flat and curved surface is the same, with uniform thickness, and the joint is as strong as the material itself.
     
  6. Nov 17, 2014 #5
    Have you learned about the concept of principal stresses?

    Chet
     
  7. Nov 17, 2014 #6
    nope. only basic pressure, and young modulus.
     
  8. Nov 17, 2014 #7
    It seems like you don't have enough knowledge yet to solve this problem properly. There is going to be a hoop stress in the cylinder wall, and there is going to be an axial stress. These need to be taken into account in evaluating the failure of the cylinder wall. You would also need a failure criterion expressed in terms of the principal stresses.

    Chet
     
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