Rising Air Bubble in a River: Calculating Radius

[anand]

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

 

[Ahmed Abdullah]

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.

 

[anand]

Why is the pressure inversely proportional to the volume and not the surface area?

 

[Ahmed Abdullah]

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.

 

[anand]

Thanks a lot!