Pressure in bottle - Finding depth

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SUMMARY

The discussion focuses on calculating the depth at which a bottle, submerged mouth downwards in a pond, allows 100 cubic centimeters of water to enter. The bottle has a volume of 500 cubic centimeters and is initially filled with air at atmospheric pressure. To solve the problem, participants emphasize the need to equate the pressures inside and outside the bottle using hydrostatic pressure formulas and Boyle's law. The key equations involve determining the external water pressure and the resulting air pressure inside the bottle as it is submerged.

PREREQUISITES
  • Understanding of hydrostatic pressure principles
  • Familiarity with Boyle's law
  • Basic knowledge of atmospheric pressure
  • Ability to manipulate algebraic equations
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  • Research hydrostatic pressure calculations in fluid mechanics
  • Study Boyle's law applications in real-world scenarios
  • Explore atmospheric pressure variations at different depths
  • Learn about buoyancy and its effects on submerged objects
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Students studying physics, particularly those focusing on fluid mechanics, as well as educators looking for practical examples of pressure calculations in submerged environments.

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Homework Statement



A bottle, full of air at atmospheric pressure, whose volume is 500 cubic centimeters, is sunken mouth downwards below the surface of a pond. How far must it be sunk for 100 cubic centimeters of water to run up into the bottle?

Homework Equations





The Attempt at a Solution


The only things i know are that the pressure at the level of the bottle opening must be the same inside and outside. But I'm not sure how to find the depth needed.
 
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I hope the attached picture helps. Determine the pressure outside and inside of the bottle at the level of opening. Apply the formula for hydrostatic pressure of water and Boyle's law to get the air pressure inside the bottle.

ehild
 
Last edited:

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