How Does Mathematics Explain the Mechanism of a Cartesian Diver?

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SUMMARY

The Cartesian diver operates based on the principles of pressure and volume as described by the equation P1*V1=P2*V2. In a closed system, applying pressure to the water bottle compresses the air inside the diver, leading to a decrease in air volume. This increase in water density causes the diver to sink when the density surpasses that of the surrounding water. Understanding these mathematical relationships is crucial for grasping the mechanics of the Cartesian diver.

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  • Understanding of the Ideal Gas Law
  • Basic knowledge of fluid dynamics
  • Familiarity with closed systems in physics
  • Concept of density and buoyancy
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Students of physics, educators teaching fluid mechanics, and hobbyists interested in experimental science will benefit from this discussion on the mathematical principles behind the Cartesian diver.

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i would like to know how a cartesian diver works using mathematics. I have found how the diver works using words and explanation but not using equations and math. Please HELP!
 
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P1*V1=P2*V2 Since you basically have a closed system (the diver plus the water bottle) by applying pressure on the bottle, you are effectively transferring this pressure to the cartesian diver. This is because water is pretty much uncompressible. So, because the pressure is increased, the volume of air must decrease. Because we have a closed system, the water goes into the void created by the compressed air, the density increases until it is greater than that of water and it sinks.
 
Hey I am new here and i also need help on the Cartesian Diver. I was just wondering if The air pressure is the same, less than, much less than, greater or much greater than the air pressure outside of the bottle or container before pressure is applied to the container.
 

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