How much thickness for sphere to withstand atmospheric pressure?

  • #1
phys_hep_81
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TL;DR Summary
Hollow sphere withstanding the atmospheric pressure
Imagine a hollow sphere made of a material with high elasticity constant(e.g. steel). How much thickness should it have to prevent it from crushing when the air inside is pumped out?
Is it valid to use Lame solution to quantify the answer? What about Finite Element Analysis?
 
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  • #2
This would be a stability problem involving buckling.
 
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  • #3
Manufacturing such sphere would be a difficult task.
The material would have internal stresses and would be unevenly deformed; therefore, even shell thickness and welds and perfect sphere shape would be difficult to achieve.
If built, the calculations should allow a generous safety margin.

Please, see:
https://www.sciencedirect.com/science/article/pii/S0020768318302592#:~:text=The classical buckling pressure of,shell thickness and its radius.

:cool:
 

1. How do you calculate the required thickness for a sphere to withstand atmospheric pressure?

To calculate the required thickness for a sphere to withstand atmospheric pressure, you can use the formula: Thickness = (Pressure x Radius) / (2 x Allowable Stress). Where Pressure is the atmospheric pressure in Pascals, Radius is the radius of the sphere in meters, and Allowable Stress is the maximum stress the material can withstand in Pascals.

2. What factors affect the thickness required for a sphere to withstand atmospheric pressure?

The factors that affect the thickness required for a sphere to withstand atmospheric pressure include the material of the sphere, the radius of the sphere, the atmospheric pressure, and the allowable stress of the material.

3. Why is it important for a sphere to have the right thickness to withstand atmospheric pressure?

It is important for a sphere to have the right thickness to withstand atmospheric pressure to ensure the structural integrity of the sphere and prevent it from collapsing or failing under the pressure. Insufficient thickness can lead to deformation or rupture of the sphere.

4. What are some common materials used for spheres to withstand atmospheric pressure?

Some common materials used for spheres to withstand atmospheric pressure include steel, aluminum, and composite materials. These materials have high strength and can withstand the pressure exerted by the atmosphere.

5. Can the thickness of a sphere to withstand atmospheric pressure be reduced by using reinforcement or support structures?

Yes, the thickness of a sphere to withstand atmospheric pressure can be reduced by using reinforcement or support structures such as ribs, rings, or stiffeners. These structures help distribute the pressure more evenly across the sphere, allowing for a thinner wall thickness.

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