Find the depth of a tube submerged in water that is half filled with air

1. The problem statement, all variables and given/known data

A tube of length L = 25 m that is open at one end contains air at atmospheric pressure. This is done in Denver so atmospheric pressure P = .667 X (1.10 X 105 Pa). The tube is thrust vertically into a freshwater lake until water rises halfway up in the pipe. Find the depth of the tube in the water. Note: air can be treated as an ideal gas.

In the attachment there is a picture on problem #5. The picture will really help clarify the problem.

2. Relevant equations
P = P(initial) + $$\rho$$gd
$$\Sigma$$F = ma
P=F/A

3. The attempt at a solution
I know the pressure of the air inside the tube and I also know that the forces exerted by the air and the water are the same but I am just not sure how to tie all of these things together to find the depth.
Attached Files
 Ch15Homework.doc (34.0 KB, 5 views)
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 Mentor Blog Entries: 1 Hint: What's the pressure of the compressed air in the tube?
 Isn't it equal to the atmospheric pressure?

Mentor
Blog Entries: 1

Find the depth of a tube submerged in water that is half filled with air

 Quote by KEØM Isn't it equal to the atmospheric pressure?
Not after being compressed. (How did its volume change?)
 By putting it in the water the volume was halved so the pressure is the atmospheric pressure divided by 2?

Mentor
Blog Entries: 1
 Quote by KEØM By putting it in the water the volume was halved so the pressure is the atmospheric pressure divided by 2?
No. Use the hint that the air can be treated as an ideal gas. (What's the ideal gas law?) You can assume the temperature is constant.
 But I don't know the volume or the number of moles either.

Mentor
Blog Entries: 1
 Quote by KEØM But I don't know the volume or the number of moles either.
You don't care about the actual volume, only that it went from V to V/2. The number of moles is constant.
 Ok so I solved for pressure now can I use this in the formula P = P(initial) + $$\rho$$gd but I am not sure if that will work.
 Mentor Blog Entries: 1 Make use of the fact that the pressure must be the same at the same height in a fluid. What must the water pressure be right at the air/water interface in the tube?

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