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HELP: contact area of Cylinder inside a larger Cylinder?

  1. Sep 19, 2007 #1

    mhl

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    Laydies and Gents

    can anyone help me here? suppose there are well known formulas for this.

    That is, contact area of a known size cylinder lying inside a larger know size cylinder....

    hope problem is clear

    thank you

    best regards

    martin
     
  2. jcsd
  3. Sep 19, 2007 #2
    Contact area? is it involving volume or just area? or sth other than pure value of area?
    my guess is that, let CyLarge and CySmall,
    so if u re finding volume, calculate the CyLarge volume subtract CySmall volume.
    if it's area, CyLarge Area - CySmall Area.

    sorry if i misreading ur question. =)
     
  4. Sep 19, 2007 #3

    mhl

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    Hmm. To clearify:

    I am tryoing to find the contact area of a given cylinder that is lying inside another cylinder. That mean the outside area of the smallest cylinder touching the inner wall of a known larger cylinder.

    Ex: a 1 meter long cylinder with 5" diameter lyes inside a 1 meter long cylinder with 7" diameter. What is the contact area between the two cylinders....?

    hope this was better.
     
  5. Sep 19, 2007 #4

    HallsofIvy

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    No, it isn't. If the two cylinders have their axes vertical, under gravity, then the "contact" area is just the area of the two bases of the smaller cylinder:[itex]49 \pi m^2[/itex]. If the two cylinders have there axes horizontal, then there would be a very slight contact between the curved areas. Although, I suspect that in ideal cylinders, that would just be a single line of contacet, having 0 area: so we are back to [itex]49\pi m^2[/itex].
     
  6. Sep 19, 2007 #5

    mhl

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    mmm, yes hallsofivy, that was my though as well (the axis are horizontal, they are lying down i guess).

    Still, does that mean that a given cylinder, for example OD of 1m, lying on a straight plane has the same contact area to it's underlayer (tha plane) as the same cylinder lying inside a cylinder with ID of 1.001m??? (all things ideally and so on and so fourth)....

    thoughs...?
     
  7. Sep 19, 2007 #6
    Would it be a limit? like lim as deltaX approaches 0 of (Xo * Height)?

    (please excuse notation)
     
  8. Sep 19, 2007 #7

    AlephZero

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    Yes, if you assume both cylinders are perfectly rigid.

    For real cylinders the answer is no, because they are flexible. Google for "Hertz contact" for more about that.
     
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