Thin-walled sphere and fluid mechanics question

In summary, when a thin-walled sphere is fully submerged in a liquid and filled to the equator with a denser fluid, the lateral cross-sectional areas of the sphere will experience compressive stresses due to external hydrostatic pressure. The internal fluid does not hang on the shell wall and to achieve neutral buoyancy, the internal fluid must have twice the density of the external fluid. A diagram and specification of the internal gas pressure is necessary for accurate analysis.
  • #1
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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.
 
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  • #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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1. What is a thin-walled sphere?

A thin-walled sphere is a hollow, spherical object with a wall thickness that is significantly smaller than the sphere's diameter. It is commonly used in fluid mechanics as a simplified model for real-life objects such as bubbles, droplets, and balloons.

2. How is fluid mechanics related to thin-walled spheres?

Fluid mechanics is the study of how fluids (liquids and gases) behave under various conditions. Thin-walled spheres are often used in fluid mechanics experiments and calculations because they have a simple geometry and their behavior can be easily predicted and analyzed.

3. What is the significance of thin-walled spheres in fluid mechanics?

Thin-walled spheres are important in fluid mechanics because they allow for the study and understanding of fundamental concepts such as pressure, buoyancy, and fluid flow. They also serve as a basis for more complex models and real-life applications.

4. How do you calculate the pressure inside a thin-walled sphere?

The pressure inside a thin-walled sphere can be calculated using the equation P = 2T/R, where P is the pressure, T is the tension in the wall, and R is the radius of the sphere. This equation is derived from the Laplace's law, which states that the pressure inside a thin-walled sphere is directly proportional to its surface tension and inversely proportional to its radius.

5. What are some real-life applications of thin-walled spheres in fluid mechanics?

Thin-walled spheres are used in various industries, such as aerospace and automotive, for the design and testing of pressure vessels, fuel tanks, and other fluid-containing structures. They are also used in medical applications, such as in the study of blood cells and drug delivery systems. Additionally, thin-walled spheres are used in research and development of new materials and technologies in the field of fluid mechanics.

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