Rising Air Bubble in a River: Calculating Radius

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SUMMARY

The discussion focuses on calculating the radius of an air bubble as it rises from the bottom of a 3.3m deep river. Given an initial bubble radius of 2mm, atmospheric pressure of 10^5 Pa, and water density of 1000 kg/m³, the pressure at the bottom of the river (P1) is determined using the formula P1 = depth × density × gravitational acceleration. The volume of the bubble changes in proportion to the pressure ratio P1/P2, where P2 is the atmospheric pressure. The relationship between pressure and volume is clarified, emphasizing that pressure is inversely proportional to volume, not surface area.

PREREQUISITES
  • Understanding of basic physics concepts such as pressure, volume, and density.
  • Familiarity with the ideal gas law and its implications.
  • Knowledge of mathematical relationships involving pressure and volume.
  • Basic calculus for understanding changes in volume with respect to pressure.
NEXT STEPS
  • Study the ideal gas law and its applications in fluid dynamics.
  • Learn about hydrostatic pressure calculations in fluids.
  • Explore the relationship between pressure and volume in gases using real-world examples.
  • Investigate the effects of temperature on gas behavior and volume changes.
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Students in physics or engineering, educators teaching fluid dynamics, and anyone interested in understanding the principles of gas behavior under varying pressure conditions.

anand
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Homework Statement


An air bubble of radius 2mm if formed at the bottom of a 3.3m deep river.Calculate radius of bubble as it comes to the surface.
atmospheric pressure=10^5 pa and density of water=1000 kg/m^3
 
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Calculate the pressure at the bottom of the river(depth*density of liquid*graviational acceleration). Let it be P1 and the pressure above the surface of river (i.e equal to the atmosperic pressure) P2.
Then the volume enclosed by the buble change by the factor P1/P2 (pressure is inversely proportional to the volume).
Assuming the buble as a sphere you can easily work out the radius.
 
Why is the pressure inversely proportional to the volume and not the surface area?
 
anand said:
Why is the pressure inversely proportional to the volume and not the surface area?

At constant temperature, when pressure increases gas volume decreases(it is a general observation). Mathematically speaking, when pressure is doubled volume becomes halve of the original volume. So it is evident why volume and pressure are inversely related.

Pressure is independent of surface area. Because pressure is defined as force exerted perpendicularly on unit area(i.e P=F/A). So pressure must not be confused with force. :confused:
 
Thanks a lot!
 

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