Thin-walled sphere and fluid mechanics question

  • #1
Suppose you had a thin-walled sphere fully submerged in a liquid. The sphere is filled to the equator with a liquid of sufficient density to reach buoyant equilibrium.

Will the lateral cross-sectional areas of the thin-walled sphere experience tensile stresses in the longitudinal axis? Why or why not?

Thank you for your consideration.
  • #2
I expect that all the stresses in the spherical shell will be compressive.
The top hemisphere is pressed against the lower hemisphere by external hydrostatic pressure. That assumes the pressure of gas above the liquid inside the sphere is the same or less than the external pressure at the top of the sphere.

The internal fluid does not hang on the shell wall. The fluid in the lower hemisphere presses normal to the shell surface, against an external higher pressure.

I think you need to draw a diagram, and specify the internal gas pressure above the fluid.
  • #3
To have neutral buoyancy, the density of the internal fluid must be twice that of the external fluid.

When the sphere is neutral with the top of the sphere level with the surface of the external fluid, the internal hydrostatic pressure at the equator will be zero. At the bottom of the sphere, the hydrostatic pressures will be the same inside and outside.

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