2

Let's say I have a Sphere made out of Acrylic, with a diameter d meters.

And I want to submerge it down in the ocean. The depth is such that it reaches up to p PSI.

How thick does the Sphere have to be, in order to withstand pressure of up to p PSI?

(I used the variables d and p so I can be given a formula that I can learn/understand instead of a raw answer.)

Coto
  • 63
  • 2
  • 6
  • You need the strength of the material to start with and there are questions similar to this on this site... – Solar Mike Sep 08 '17 at 21:07

3 Answers3

3

take note if you are talking about dropping to the deepest parts of the ocean the pressure can be as high as 15,000 psi. the Yield strength of acrylic is maybe 10,000 psi.

Your wall will be very thick! You can not use most of the thin shell based formulae you might look up.

You can take an extreme view and imagine a large block of material with a tiny void. The wall hoop stress at the void wall is approximately 3/2*pressure, or over 20,000 psi. Which is to say your cavity is liable to collapse no matter how thick you make it.

agentp
  • 949
  • 6
  • 11
1

The basic formula used in analyzing thin-walled spherical pressure vessel is:

stress = PD / 4t

where P is the pressure inside or outside, D is the inner diameter, and t is the wall thickness.

therefore:

t = PD / [(allowable stress of the material) * 4]

Note that this formula is only applicable if D/t >= 10

Note also that allowable stress in acrylic is 10,000 psi @ room temperature. This changes when you submerge this in water, so might want to consider this too.

Edit: The unit of measurement in the formula is:

For English system: stresses should be in pounds per sq.inch (psi) while dimensions should be in inches (in.)

For SI system: stresses should be in megaPascal (MPa), and dimensions should be in millimeters (mm)

Jem Eripol
  • 850
  • 5
  • 16
0

I need 2 answers, Ill post in this thread before I start a new one.

How to withstand say at 6000 ft ocean depth, of a 6", 1/4 thick bronze sphere. How would I calculate this to see if its possible? Note: the air space will be filled with minimal porous material, so only around 10% air volume).

"Bronze" shear strength is roughly - at the low end, 35,000 psi (?) depending on alloys used.

Depth pressure at 6000ft is roughly 3000 psi, so this should be, no problem?

https://bluerobotics.com/learn/pressure-depth-calculator/

Jimm
  • 1
  • 1