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Air-Filled Membrane Curvature

  1. Jan 22, 2005 #1
    Suppose you have a tube made of nylon. It is filled with air. Obviously, the cross-section is a circle.

    Now, suppose that on the top and bottom of the tube, a length of rigid sheet metal is attached and does not permit curvature, so that the cross-section after inflation looks like this:


     ___
    (___)


    What is the nature of the nylon's curvature at the sides? I suspect that it is the arc of a circle (with a size that depends). However, could it be a more complex shape, like the arc on an ellipse?

    To summarize, I want to understand how membranes curve under inflation. I am doing volume calculations of such a tube as it inflates, and need to know the shape of the sides.

    Thank you.

    Edit: I just realized that it can't be simply the arc of a circle. It must be half an ellipse. If it was the arc of a circle, there is a sharp angular transition between the flat sheet-metal and the curving segment. The ends of each curve have to start parallel to the sheet metal (horizontal) and curve, becoming perpendicular to the horizontal axis midway, and then returning to being parallel to the sheet-metal. Can someone confirm this?
     
    Last edited: Jan 22, 2005
  2. jcsd
  3. Jan 23, 2005 #2

    Q_Goest

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    It should depend on how you attach the flexible membrane (tube) to the end, and how rigid each plate is. Assuming the metal plates at each end remain relativly flat, you still need to determine how the nylon is attached to them.

    Imagine having a flat plate (blind flange) and a circular, ring shaped flange that bolt together. And between these two you put the nylon tube. In this case you'll have what looks like a pipe with a flat end attached, and you'll have that sharp angular transition between the two that you mention.

    If on the other hand, you twisted the end of the nylon tube and tied it off, you would have a completely rounded transition.

    So if you had a flat plate that was attached to the nylon tube somewhere between the centerline of the tube and the diameter, it might take on a curve until the flat plate came into play.
     
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