Why Does Surface Tension Allow Bubbles to Form Despite External Pressure?

[tellmesomething]

Homework Statement

A small hollow sphere which has a small hole in it is immersed in water to a depth of 40cm before any water penetrates into it. If the surface tension of water is 7.3×10^-2N/m., find radius of the hole. The density of water Is 10^3 ka/m^3 and g=9.8N/m²

Relevant Equations

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The solution manual says that before water enters the hollow So here an air bubble of radius R will escape from the sphere. The excess of pressure inside the bubble is 2T/R. The excess of pressure prevents the penetration of water into the sphere. Water begins to penetrate when the excess of pressure is balanced by the excess of pressure of water at a depth h.






I do not understand why this would happen, maybe someone can make a relevant FBD and show everything at play. According to me if the pressure inside is equal to the pressure outside no water should come inside and it should stay in equilibrium, but im definitely missing a force. Please let me know. thankyou! !!

 

[haruspex]

So here an air bubble of radius R will escape from the sphere

I don’t see why. The pressure will be greater outside than inside.
The problem is saying that at 40cm, the outside pressure is not enough, but any deeper it will be.
I would take 40cm as being the depth of the hole, wherever the hole is in relation to the depth of the sphere’s centre.

 

[tellmesomething]

I don’t see why. The pressure will be greater outside than inside.
The problem is saying that at 40cm, the outside pressure is not enough, but any deeper it will be.
I would take 40cm as being the depth of the hole, wherever the hole is in relation to the depth of the sphere’s centre.

Can you expand on this? how is the pressure outside greater? from inside the sphere we only have the atm pressure and the surface tension pressure. From outside we would have atm pressure and hydrostatic pressure. Right? so anytime above 40 cm, say 30 cm the pressure outside is smaller than the pressure inside, therefore wouldnt the bubble escape then ?

 

[haruspex]

the surface tension pressure

Sorry for the delay… flaky internet here.

Surface tension is not, in itself, a pressure. It is what it says, a tension in which the surface is trying to contract.
Inside the sphere you have atm, outside, that plus hydrostatic, so the water starts to push into the sphere. But as the surface bulges inwards, the surface tension over that cap gives rise to a net force opposing the water.
You can think of it as a bubble of water with air outside it.