Pressure Difference Between the Inside and Outside of a Balloon

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SUMMARY

The discussion focuses on calculating the material strength required for a balloon to withstand pressure differences, specifically 10 atm inside versus 1 atm outside, and the implications of using different materials like rubber and mylar. The relevant equation for biaxial tensile stress in a spherical balloon is provided: $$\sigma=\frac{(\Delta p) r_0}{2h_0}\left(\frac{r}{r_0}\right)^3$$. The conversation also touches on the applicability of this equation to various materials and its relevance to astronaut space suits. Understanding the yield stress of materials is essential for determining their suitability under these conditions.

PREREQUISITES
  • Understanding of basic physics concepts, particularly pressure and stress.
  • Familiarity with the equation for biaxial tensile stress in spherical structures.
  • Knowledge of material properties, including yield stress and tensile strength.
  • Insight into the behavior of different materials under pressure, such as rubber and mylar.
NEXT STEPS
  • Research the properties of mylar and its applications in pressure-resistant designs.
  • Study the mechanics of materials to understand yield stress and tensile strength calculations.
  • Explore the design considerations for astronaut space suits, focusing on material selection and pressure management.
  • Investigate the effects of pressure differentials on various materials, including rubber, plastics, and metals.
USEFUL FOR

Engineers, material scientists, and designers involved in creating pressure-resistant structures, particularly in aerospace applications, will benefit from this discussion.

Kyle Roode
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Hello all. I have a question about gasses and pressure: Is there a way to calculate how strong a material making up a balloon has to be to withstand a given pressure difference between the inside and outside?

In other words, if I have a balloon I need to fill to a pressure of 10atm inside vs 1atm outside the balloon, is there a way to calculate how strong the material needs to be to withstand this difference in pressure?

What if I took that same balloon and put it into a vacuum chamber (lowering from 1atm to say 0.1atm outside the balloon)?
 
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The biaxial tensile stress in the balloon rubber of a spherical balloon is given by $$\sigma=\frac{(\Delta p) r_0}{2h_0}\left(\frac{r}{r_0}\right)^3$$where ##r_0## and ##h_0## are the radius and material thickness when the internal pressure only slightly exceeds the external pressure and r is the balloon radius when the balloon is at full pressure. Is this what you were looking for? Or is this a mylar balloon?
 
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Thank you for the response. That equation is helpful for me.

What would change for the equation if it were mylar? I was really only using a balloon as an example. I am actually curious about using any material (be that rubber, mylar, steel, plastics, glass...). Does this equation work for any material?

It may be helpful to know my original thoughts before posting this were specifically in reference to an astronaught’s space suit. I thought maybe a balloon would just be a place to start.
 
Kyle Roode said:
Thank you for the response. That equation is helpful for me.

What would change for the equation if it were mylar? I was really only using a balloon as an example. I am actually curious about using any material (be that rubber, mylar, steel, plastics, glass...). Does this equation work for any material?

It may be helpful to know my original thoughts before posting this were specifically in reference to an astronaught’s space suit. I thought maybe a balloon would just be a place to start.
If the material comprising the balloon doesn't stretch significantly, then the term involving r/ro is unity.
 
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Thank you for taking the time to answer my question.

One last thing: what does the symbol on the left-side of the equation mean?
 
The symbol on the left stands for stress, the value of which can be compared against the yield stress of different materials
 

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