Pressure inside a soap bubble just under surface

[takando12]

Homework Statement

What should be the pressure inside a small air bubble of 0.1,, radius,situated just below the surface? st of water=7.2 *10^-2 and atmospheric pressure=1.013*10⁵.

Homework Equations

The Attempt at a Solution

I am of the understanding that the pressure inside the bubble is the sum of the surrounding pressure and the excess pressure( 4s/r). But what I don't understand is the surrounding pressure. Should I take the atmospheric pressure? But since it's just below the surface,the top of the bubble would be exposed to atmospheric pressure and the rest of the bubble to whatever pressure the water exerts( I don't think I'm right, I need help). So which pressure is it that I take for external?

 

[haruspex]

The Attempt at a Solution

I am of the understanding that the pressure inside the bubble is the sum of the surrounding pressure and the excess pressure( 4s/r). But what I don't understand is the surrounding pressure. Should I take the atmospheric pressure? But since it's just below the surface,the top of the bubble would be exposed to atmospheric pressure and the rest of the bubble to whatever pressure the water exerts( I don't think I'm right, I need help). So which pressure is it that I take for external?

Have you calculated how much difference that makes?
There is another difference between a bubble above the surface and one under the surface which might have rather more significance.

 

[takando12]

Have you calculated how much difference that makes?
There is another difference between a bubble above the surface and one under the surface which might have rather more significance.

if a bubble was under the surface, the pressure inside the bubble would be 4s/r + the hydrostatic pressure at that height( P_a+hρg).
I am unable to understand what exactly you mean by difference. Since the bubble is just below the surface,will the second term reduce to just P_a?

 

[haruspex]

I asked if you had calculated how much difference it makes taking into account that little extra hydrostatic pressure. I mean the numbers, not the algebraic expression. I suspect it is negligible.

I am unable to understand what exactly you mean by difference.

There is rather an important difference in the forces. Do you know how the $4\sigma/r$ formula is derived? If you follow that through you should see why it is different.