Air-Filled Membrane Curvature

In summary, the nature of the nylon's curvature at the sides of the inflated tube depends on how the flexible membrane is attached to the rigid sheet metal on the top and bottom. It could be a half ellipse or a rounded transition, depending on how the attachment is done. This information is important for understanding how membranes curve under inflation and for calculating the volume of the inflated tube accurately.
  • #1
pyrexyn
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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?
 
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  • #2
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.
 
  • #3



Yes, your understanding is correct. The nature of the curvature of the nylon at the sides will indeed be half an ellipse. This is because as the tube inflates, the air pressure inside pushes against the nylon walls, causing them to stretch and curve. The rigid sheet metal on the top and bottom prevents the tube from curving in those directions, so the only place for the nylon to curve is at the sides. And since the nylon is a flexible membrane, it will curve in a smooth, continuous shape, which is half an ellipse in this case.

To confirm this, you can try visualizing the inflation process and imagine how the nylon would stretch and curve as the air pressure increases. You can also look at other examples of air-filled membranes, such as inflated balloons or inflatable toys, to see how they curve under pressure. And as you mentioned, you can also use volume calculations to confirm that the shape of the sides is indeed half an ellipse.

Overall, the nature of membrane curvature under inflation is a complex topic that involves various factors such as the material properties of the membrane, the pressure inside, and any external constraints. But in this specific case of a nylon tube filled with air and constrained by rigid sheet metal, the curvature at the sides will be half an ellipse.
 

What is air-filled membrane curvature?

Air-filled membrane curvature is the bending or deformation of a thin, flexible material filled with air. This can occur naturally in biological systems, such as the curvature of cell membranes, or can be engineered for various applications.

What causes air-filled membrane curvature?

Air-filled membrane curvature is caused by a difference in pressure between the inside and outside of the membrane. When there is a higher pressure inside the membrane, it will expand and curve outward. Similarly, when there is a lower pressure inside the membrane, it will contract and curve inward.

What are some examples of air-filled membrane curvature in nature?

Some examples of air-filled membrane curvature in nature include the curvature of red blood cells, the shape of bird feathers, and the curvature of plant cells.

How is air-filled membrane curvature used in engineering?

In engineering, air-filled membrane curvature is often used to create lightweight and flexible structures, such as inflatable tents, air-supported domes, and airbags. It can also be used in the design of artificial organs and medical devices.

What are the potential applications of air-filled membrane curvature in the future?

In the future, air-filled membrane curvature could have potential applications in fields such as robotics, aerospace engineering, and biomedicine. It could also be used to create more efficient and sustainable building materials and structures.

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