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How does a doughnut-shaped object expand?
A tube from a car tire is free (no tire on it, no wheel within it) and it's inflated to a regular torroidal shape.
Say the diameter across the inside (the wheel diameter) is 50cm. If we inflate it further, will this distance increase, decrease, or remain the same?
The tube itself will become "fatter" but will this be compensated by its becoming longer?
1 Answer
- Born YesterdayLv 77 years agoFavorite Answer
A torus has two radii, and as these become closer
to equal more "fattening" will result from inflation.
As the radii diverge, more lengthening will result
due to the distribution of stress over the surface
compared with the volume.
Maximizing volume to surface results in greatest
fattening. Minimizing volume to surface favors
rapid increase in major radius.
For the proportions of an automobile inner tube
I suspect both radii will increase, but the major radius
will increase faster.
