Equal Pressure Canister Collapse

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Discussion Overview

The discussion revolves around the possibility of a flimsy canister collapsing or imploding when the internal and external pressures are equal, particularly considering the effects of surface area and material strength. Participants explore theoretical scenarios, mathematical reasoning, and real-life examples related to this concept.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions whether a canister could collapse if it has a greater external surface area than internal surface area, despite equal pressures inside and outside.
  • Another participant asserts that it is not possible for the canister to collapse under these conditions.
  • A participant provides a mathematical example involving a cylinder to illustrate that the external pressure exerts more force due to the larger surface area, raising concerns about material stress.
  • Some participants clarify that a surface has no thickness and that the forces acting on the canister are balanced if it is closed.
  • One participant draws a parallel to a piece of paper, suggesting that it experiences equal atmospheric pressure on both sides, which may not apply to the canister scenario.
  • Another participant introduces Pascal's hydraulic paradox as a relevant concept, suggesting it may support the idea of pressure effects on the canister.
  • A later reply discusses the balance of forces in a closed canister and how external forces compress the material until internal pressure stabilizes.
  • One participant expresses confusion about the concepts and seeks further clarification on the implications of material integrity under pressure.
  • A participant provides examples of materials like marshmallows and aerogels to illustrate how they can be affected by external pressure, even with equal internal pressure.

Areas of Agreement / Disagreement

Participants express differing views on whether a canister can collapse under equal pressures, with some asserting it cannot while others present arguments suggesting that material properties and surface area considerations could lead to collapse in specific scenarios. The discussion remains unresolved with multiple competing views.

Contextual Notes

Participants discuss the implications of material strength and surface area without reaching a consensus on the conditions under which a canister might collapse. The mathematical reasoning presented includes assumptions about the canister's geometry and material properties that are not fully resolved.

Who May Find This Useful

This discussion may be of interest to those exploring concepts in fluid mechanics, material science, and pressure-related phenomena in engineering contexts.

Airman
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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?
 
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No, not possible.
 
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?
 
A surface has no thickness and has the same area on the inside and out. You are talking about two different surfaces.
 
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
 
This is actually a form of the old Pascals hydraulic paradox.
 
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.
 
Airman said:
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.)

Airman said:
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.

Airman said:
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?
 
Last edited by a moderator:
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.
 

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