Percentage change in interior volume

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SUMMARY

The discussion focuses on calculating the percentage change in the interior volume of a hollow iron spherical shell, or submarine, when submerged at a depth of 2000 meters, where the pressure is approximately 200 times atmospheric pressure (200 atm). The formula used is delta V/Vo, which represents the change in volume over the original volume, calculated using the change in pressure divided by the bulk modulus of iron. The initial calculation yielded a percentage change of 0.02%, which was deemed incorrect, prompting further analysis of the calculations and the sign of the percentage change.

PREREQUISITES
  • Understanding of pressure concepts, specifically atmospheric pressure and its conversion.
  • Knowledge of bulk modulus and its application in volume change calculations.
  • Familiarity with the formula for percentage change in volume (delta V/Vo).
  • Basic principles of fluid mechanics and the behavior of materials under pressure.
NEXT STEPS
  • Review the calculation of percentage change in volume using the formula delta V/Vo.
  • Study the properties of bulk modulus for different materials, focusing on iron.
  • Explore the effects of pressure on the volume of gases and liquids in fluid mechanics.
  • Investigate real-world applications of submarines and their structural integrity under high-pressure conditions.
USEFUL FOR

Students studying physics or engineering, particularly those focusing on fluid mechanics and material science, as well as professionals involved in submarine design and underwater exploration.

tige99
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Homework Statement



Deep sea fish experience a tremendous amount of atmospheric pressure.

When you are at a depth of 2000 m in the sea, the pressure that you will experience is about 200 times atmospheric pressure (1atm=1.0×105N/m2)which you will experience on land.

If you are lowering a hollow iron spherical shell, imagine a spherical submarine, then by how much does the volume of the interior of this shell change at this depth? Express the ratio in terms of percentange change in interior volume.

Express your answer to two significant figures and include the appropriate units

delta V/Vo

Homework Equations



The Attempt at a Solution


I know DeltaV/Vo is equal to change in pressure over bulk mod, and change in pressure is 200 atm/Biron. I get 0.02% but that doesn't work.[/B]
 
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Show you calculations. Is the percentage change in volume positive or negative?
 

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