Suppose you have a tube made of nylon. It is filled with air. Obviously, the cross-section is a circle.(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# Air-Filled Membrane Curvature

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