Equal Pressure Canister Collapse

[Airman]

Say you had a very flimsy canister. Would it be possible for it to collapse or implode even if the pressure inside it and the pressure outside of it were equal, due to the fact that it has thickness and therefor a greater outside surface area than inside surface area? If so, are there real life examples of is this "effect", or is it negligible all the time?

 

[Robot B9]

No, not possible.

 

[Airman]

Okay why? What am I thinking wrong here:

I'll assume a cylinder has an inner radius of 1 and a thickness of 1. The inner surface area would be h(pi)(1)^2 or h*pi, and the outer surface area would be h(pi)(2)^2 or 4*pi. (I'm neglecting the ends, which are equal). So whatever the pressure is, it exerts 4 times the force on the cylinder from outside than inside. Wouldn't this put stress on the cylinder and crush it if the material was weak enough?

 

[Vreejack]

A surface has no thickness and has the same area on the inside and out. You are talking about two different surfaces.

 

[Curl]

The material can't be that weak or else it will not be a material at that pressure.

You can say the same thing about a piece of paper, it is getting crushed from both sides by the atmosphere.

This is an interesting question, one way to think about it is to draw a cutout (a "wedge") of the cylinder and pretend like it is glued on lightly on the cylinder. Then think about what type of forces the glue will experience.

I'll think about this later

 

[Robot B9]

This is actually a form of the old Pascals hydraulic paradox.

 

[Airman]

I know I must be talking about two different surfaces as I have two different surface areas.

Yes but the paper is experiencing the nearly the same force on both sides. For my object the force is much greater on one of the surfaces. If the internal structure isn't strong enough in my object wouldn't the inside and outside surfaces be pushed together? Is that what you mean by it not being a material? As it wouldn't retain it's integrity?

Doesn't Pascal's Hydraulics Paradox support this idea?

I'm sorry this is just bothering me and I still can't grasp the idea in my mind.

 

[cesiumfrog]

Say you had a very flimsy canister. Would it be possible for it to collapse or implode even if the pressure inside it and the pressure outside of it were equal, due to the fact that it has thickness and therefor a greater outside surface area than inside surface area? If so, are there real life examples of is this "effect", or is it negligible all the time?

In a way yes. For example, a marshmellow (or a piece of aerogel), which you can just think of as a cannister with zero internal surface area, is partially collapsed or crushed by the surrounding air pressure.

(Note especially the conclusion: if it is exposed to the air pressure suddenly, it might even implode or tear.)

Okay why? What am I thinking wrong here:

I'll assume a cylinder has an inner radius of 1 and a thickness of 1. The inner surface area would be h(pi)(1)^2 or h*pi, and the outer surface area would be h(pi)(2)^2 or 4*pi. (I'm neglecting the ends, which are equal). So whatever the pressure is, it exerts 4 times the force on the cylinder from outside than inside. Wouldn't this put stress on the cylinder and crush it if the material was weak enough?

Remember that force is a vector. If your cannister is closed, the total force on the outside is zero (because the normal force on the outer left balances the normal force on the outer right). Likewise, the total force integrated over all the inner surface is also zero.

If the cannister is open, then these two total forces may not be zero, but they will be opposite and always exactly equal in strength.

As an example (much as Curl is suggesting) draw a square, and inside that draw a diamond, and let this diagram be the cross section of your (prism shaped) cannister. Now consider just one quarter of the sidewall: the cross section is a right angle triangle where two outer sides have equal length and the inner hypotenuse is shorter than the total of the outer sides. So the inside has less area than the outside, but the force from the outside is still in balance with the force from the inside, because the force from the outside has two components that partially cancel each other out.

In actual fact (as is obvious if you imagine our container is sculpted from aerogel) these external forces will compress surfaces of the container, until the internal pressure in the material increases to about the same as the external pressure. At that point, the inward force on some particular atom located on the outer surface will be equal to the outward force directed on that same atom, and so on for every other atom that is located anywhere else in the material of the container, so the shape will have reached a stable equilibrium.

Doesn't Pascal's Hydraulics Paradox support this idea?

I'm sorry this is just bothering me and I still can't grasp the idea in my mind.

Make sure you've actually understood the paradox and its resolution; read:
http://scubageek.com/articles/wwwparad.html
Do you see how the apparatus will behave in real life, and why?

 

[Airman]

Thank you for the detailed response! Your examples and the link were very helpful. I understand it now, and I also found this page helpful: (This was linked to from your link about the hydrostatic paradox)

http://scubageek.com/articles/wwwhyd.html

Thanks again my mind is now at peace with the question.