This is potentially a pretty stupid question - but are the differences in pressure roughly the same between a full, pressurised soda can and a cruising-altitude pressurised airline cabin?
I'm not sure why you'd think it's a stupid question (what is a stupid question?) -- but according to the Internetz[1,2], I think the answer is no.
The difference of pressure between an soda-can and air (at ground level) would appear to be between to and three atmospheres worth (or like sea-level and a depth of 20-30m/~60-90', if the rule-of-thumb I've learned is about correct; see also: Why is parachuting into water OK, while diving and then flying a bad idea?).
It would appear the interior and exterior and an air-plane typically differ at about half an atmosphere (5m/15' water).
I think the internet has just made me a little over-cautious, especially when being around so many smart people as there are on HN :)
So that pretty much answers what I was hesitant to suggest out loud - that even though the fuselage of an airplane is proportionately thinner, the soda can has to withstand a greater pressure difference. Thanks!
From a 2-minute google search, it looks like both are ~10 psi pressure difference (psig). The numbers I found were 7-10 psig for a plane and an estimate of 17 psig for the soda can. So they're quite similar and it's not a stupid question.
More important than pressure differences, is the circumferential stress on the fuselage/can, which is what the walls are actually withstanding. For a pressurized circular container, it is given by p*r/t, where p is the pressure, r the radius and t the wall thickness.
If we consider a 3 m wide airplane, with a 1.6 mm thick fuselage at cruise altitude (around 40k feet), you get around 56.5 kPa of pressure difference, and the above equation gives you approximately 52 MPa. (data from a real aircraft that I cannot mention).
For a coca-cola can, internets say 380 kPa of pressure, for a 6.6 cm diameter can, and 0.15 mm aluminum sheet. That results in approx. 85 MPa.
So as you can see, even though you have roughly 7x more pressure in the soda can, its much smaller diameter severely reduces the stress on the walls, resulting in about 1.5x the circumferential stress.
Hope that answers your question.
edit: several errors in my back-of-the-envelope calculations. sorry.
That's an odd model for me. So as the radius goes to infinity for a fixed thickness and differential the stress goes to infinity too? But take a pressurized cube with reinforced edges. You can say it's faces have infinite radius (or as small as you'd like) -- yet the stress should be finite? How do you reconcile this? Or does that work only for circles? (which would be odd since stress is a local concept to me)
I'm not sure of your background, but it is actually a pretty simple concept. To satisfy static equilibrium on a given transverse "dx" segment of a cylinder, the walls must balance the internal pressure (in this case taken as the pressure difference), so that:
Regarding your question, yes, as the radius goes to infinity, the stress goes to infinity. The area where the pressure is applied grows with r, but the cross-sectional area where the stress is applied is still (w * thickness * dx.) This equations work well for thin-walled cylindrical pressure vessels (r > 5t is general rule of thumb). For a cube, you would have to develop the equations, but keep in mind that you will have a singularity/discontinuity on the walls because of the right angle.
Ah makes more sense now, thanks for the explanation. I'm an undergrad in EE so mechanics is not my strong point.
So a planar face of a cube cannot satisfy the equilibrium equations? Interesting ... so then a cube will necessarily bulge so the radius is enough to satisfy the equations, right?
The difference of pressure between an soda-can and air (at ground level) would appear to be between to and three atmospheres worth (or like sea-level and a depth of 20-30m/~60-90', if the rule-of-thumb I've learned is about correct; see also: Why is parachuting into water OK, while diving and then flying a bad idea?).
It would appear the interior and exterior and an air-plane typically differ at about half an atmosphere (5m/15' water).
[1] http://hypertextbook.com/facts/2000/SeemaMeraj.shtml
[2] http://en.wikipedia.org/wiki/Cabin_pressurization