FInding distance from top of diving bell to lake surface

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SUMMARY

The discussion centers on calculating the distance from the top of a cylindrical diving bell to the lake surface when the water rises 8.0m inside the bell. The solution involves applying principles of fluid mechanics, specifically using the relationship between pressure, volume, and density. The final calculation reveals that the distance from the top of the bell to the lake surface is 16.6m, derived from the pressure of water and air volume changes. Key equations include the use of Pascal's principle and Boyle's law, emphasizing the importance of understanding pressure dynamics in fluids.

PREREQUISITES
  • Understanding of fluid mechanics principles, particularly Pascal's principle and Boyle's law.
  • Familiarity with pressure calculations in fluids, including the equation P = pgh.
  • Knowledge of atmospheric pressure and its role in fluid systems.
  • Basic algebra for solving equations related to volume and pressure.
NEXT STEPS
  • Study the application of Pascal's principle in various fluid systems.
  • Learn about the implications of Boyle's law in real-world scenarios involving gases.
  • Explore advanced fluid dynamics concepts, such as hydrostatic pressure and buoyancy.
  • Investigate the effects of atmospheric pressure on submerged objects in fluids.
USEFUL FOR

Students in physics or engineering, educators teaching fluid mechanics, and professionals involved in underwater engineering or diving operations will benefit from this discussion.

  • #31
Also I was focusing too much on the inside of the tube and missed that that interface sat at a certain height in the lake overall.

I solved it before with no idea about this. I guessed and missed all this thanks for the help!

One last thing. Is it corret to say that the pressures at that interface are the same?
 
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  • #32
Moose100 said:
Is it corret to say that the pressures at that interface are the same?
Yes. Action and reaction, equal and opposite.
 
  • #33
Ok. So the air portion in the tube has a uniform pressure correct? While the fluid portion varies with depth?

This is why there is a partition. The Gas exerts the same pressure on the liquid as it does on the gas.
 
  • #34
Moose100 said:
Ok. So the air portion in the tube has a uniform pressure correct? While the fluid portion varies with depth?

This is why there is a partition. The Gas exerts the same pressure on the liquid as it does on the gas.
Yes. Strictly speaking, the pressure also varies with depth in the air, but the density of air is so low that you can ignore that over a height of a few metres.
 
  • #35
RIght because gravity does affect it but so much that it's negligible so. You can use pascual on gases so to speak but the affect or calulation would be super small..

I guess another way to look at it is that the gas has to be equal because it stops the water from moving(equal and opposite).