Rising Air Bubble in a River: Calculating Radius

In summary, the conversation discusses the calculation of the radius of an air bubble as it rises to the surface of a river. It is determined by calculating the pressure at the bottom of the river and comparing it to the atmospheric pressure. The volume of the bubble is inversely proportional to the pressure, and this is why the pressure is not dependent on the surface area.
  • #1
anand
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0

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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  • #2
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.
 
  • #3
Why is the pressure inversely proportional to the volume and not the surface area?
 
  • #4
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:
 
  • #5
Thanks a lot!
 

FAQ: Rising Air Bubble in a River: Calculating Radius

1. What is a rising air bubble in a river?

A rising air bubble in a river is a pocket of air that is released or trapped in a river. It is caused by various factors such as the movement of the water, changes in temperature, and the release of gases from decaying organic matter.

2. How do you calculate the radius of a rising air bubble in a river?

The radius of a rising air bubble in a river can be calculated using the formula r = (2ST)/P, where r is the radius, S is the surface tension of water, T is the time it takes for the bubble to rise, and P is the pressure of the surrounding water.

3. What factors affect the size of a rising air bubble in a river?

The size of a rising air bubble in a river is affected by several factors such as the surface tension of water, the pressure of the surrounding water, and the temperature of the water. Other factors like the size of the source of the air bubble and the rate of gas production also play a role.

4. Is there a relationship between the size of a rising air bubble and the speed of the river?

Yes, there is a relationship between the size of a rising air bubble and the speed of the river. As the speed of the river increases, the size of the air bubble also increases. This is because faster-moving water has a lower pressure, which allows for larger air bubbles to form and rise.

5. Why is it important to calculate the radius of a rising air bubble in a river?

Calculating the radius of a rising air bubble in a river is important for understanding the dynamics of the river and its ecosystem. It can also provide valuable information for activities like fishing, where the presence of air bubbles can attract fish. Additionally, studying air bubbles can give insight into the health of the river and its surrounding environment.

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