Atmospheric Pressure Problem - Need Help.

[kriegera]

Homework Statement

How does the pressure at a point in a fluid vary with the depth of the point below the surface of the fluid? A bottle, full of air at atmospheric pressure, whose volume is 500 cubic centimeters, is sunken mouth downwards below the surface of a pond. How far must it be sunk for 100 cubic centimeters of water to run up into the bottle?

Homework Equations

The Attempt at a Solution

I know that the deeper that point is placed in the fluid, the more pressure it experiences and the greater depth the bottle is lowered, the greater the compression. I know we're looking for the depth at which 100 cubic centimeters of air is replaced by 100 cubic centimeters of water but not sure how to proceed. Do I need to find the pressure of the bottle first? P=rgh but rearrange to find height/depth
H=P/rg ?

 

[ehild]

The pressure at the level of the bottle opening must be the same inside and outside.

Outside the bottle, the pressure is the sum of the atmospheric pressure Po and the hydrostatic pressure of water at depth h.
Inside the bottle, the pressure is the sum of the pressure of air, Pa, and the hydrostatic pressure of water column inside the bottle. You get the pressure or air in the bottle by using Boyle's law.

ehild

 

[kriegera]

The pressure at the level of the bottle opening must be the same inside and outside.

Outside the bottle, the pressure is the sum of the atmospheric pressure Po and the hydrostatic pressure of water at depth h.
Inside the bottle, the pressure is the sum of the pressure of air, Pa, and the hydrostatic pressure of water column inside the bottle. You get the pressure or air in the bottle by using Boyle's law.

ehild

Is there a hydrostatic equations for finding the pressure outside of the bottle?

we'll use Boyle's Law pV=k to solve for the inside but do we need to arrange: p=k/V?
Would we use the universal gas constant for this: 8.31432
So
p=500/8.31432 = 60.14 for inside pressure?