Material thickness to withstand Pressure

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.)

• You need the strength of the material to start with and there are questions similar to this on this site... – Solar Mike Sep 8 '17 at 21:07

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.

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)

• Why does temperature have to be involved in this when it's not involved in the Formula ^? On datasheets of materials (found online), when they mention how much pressure (PSI) the material can hold, at what conditions do they mean it? What temperature, thickness, shape etc.? Also, what is the unit measurement for each variable in the formula ^? – Coto Sep 9 '17 at 0:33
• Material tend to loose strength when they are heated or cooled. Imagine a steel bar being heated, it will lose its elasticity. Same goes when you are going to submerge in deep ocean, where temperature starts to vary @ very large depths. I am only saying this because room temperature is absolutely different from sea temperature. Thus, he needs to consider the case in determining the allowable stress of material. :) – Jem Eripol Sep 9 '17 at 0:38
• Where can I find how much a material gets affected under x Degrees? – Coto Sep 9 '17 at 0:41
• @JemEripol why will thin wall expressions be suitable in this case? – Solar Mike Sep 9 '17 at 21:00
• @JemEripol so in short, you have provided a "solution" that will not give correct results in the situation described. Why do you think the different formulae for thin and thick pressure vessels were developed ? Boilers exploded due to this... – Solar Mike Sep 11 '17 at 6:07