# I Pressure Difference Between the Inside and Outside of a Balloon

#### Kyle Roode

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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#### Chestermiller

Mentor
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?

#### Kyle Roode

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.

#### Chestermiller

Mentor
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.

#### Kyle Roode

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?

#### Julian Phillips

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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