Understanding Stress in Pipe Walls: Impact of Internal Air Pressure

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Discussion Overview

The discussion centers on understanding the stress in pipe walls due to internal air pressure, examining how this stress relates to the material properties of the pipe and the effects of varying external conditions such as vacuum and hydrostatic pressure. The scope includes theoretical considerations and mathematical reasoning related to stress analysis in engineering contexts.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • Some participants propose that the through-thickness stress in the pipe is equivalent to the internal air pressure, suggesting that the pressure acts equally on both sides of the pipe wall.
  • Others argue that while the internal air pressure is low (101.325 kPa), it is often considered insignificant compared to material strength ratings, which are typically in MPa.
  • One participant notes that the wall thickness of the pipe will be greatest in a vacuum and will decrease under increasing hydrostatic pressures.
  • Another participant references a link indicating that stress through the thickness may vary with the radius when internal and external pressures are equal, leading to uncertainty about the implications of this relationship.
  • A later reply points out that entering zero internal and external pressure in a referenced calculator results in zero stress, raising questions about the conditions under which stress is calculated.
  • Further discussion includes a mathematical expression for radial stress, indicating that under zero pressure difference, the radial compression simplifies to the common pressure on both sides.

Areas of Agreement / Disagreement

Participants generally agree that internal air pressure affects stress in the pipe wall, but there are competing views regarding the significance of this pressure and the mathematical implications of stress variation with radius. The discussion remains unresolved regarding the exact relationship between pressure and stress in different conditions.

Contextual Notes

There are limitations in the discussion regarding assumptions about material behavior under varying pressures, the dependence on specific definitions of stress, and the implications of mathematical simplifications that have not been fully explored.

Ebi
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Consider a pipe. The pipe is not crushed by the air pressure because the same air pressure is acting from inside the pipe. But this means that the material of the pipe is being compressed on both sides by some air pressure. So is it correct to say that the through-thickness stress in the pipe would be the same as the air pressure?
 
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Yes, but its insignificant. Most material strengths are rated in MPa. The measly 101.325 kPa we've got as air pressure is hardly a challenge. Thats why it's just ignored...
 
The wall will be thickest when the open pipe is in a vacuum.

The wall will become progressively thinner as the open pipe is subjected to greater hydrostatic pressures.
 
Just like for every other material around us (with very few exceptions), yes.
 
Baluncore said:
The wall will be thickest when the open pipe is in a vacuum.

The wall will become progressively thinner as the open pipe is subjected to greater hydrostatic pressures.

Thanks for your response. What you said is intuitive but if you look at link below, for Pi=Po, it seems stress through the thickness varies with the radius r.
https://www.engineeringtoolbox.com/stress-thick-walled-tube-d_949.html

I am not sure if I am missing something.
 
If you go to the calculator at the bottom of the referenced page, and enter zero internal and external pressure, you get zero stress.
 
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Ebi said:
Thanks for your response. What you said is intuitive but if you look at link below, for Pi=Po, it seems stress through the thickness varies with the radius r.
The r, or r² term disappears for zero pressure difference.
σr = [(Pi·Ri² - Po·Ro²) / (Ro² - Ri²)] + [Ri²·Ro²· (Po - Pi) / ( r²· (Ro² - Ri²))]
 
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... and the first term simplifies to -Pi. Or -Po, same thing. Which means radial compression is simply the common pressure on both sides, as expected.
 
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