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

  1. Dec 5, 2008 #1
    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) + [tex]\rho[/tex]gd
    [tex]\Sigma[/tex]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:

  2. jcsd
  3. Dec 5, 2008 #2

    Doc Al

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    Hint: What's the pressure of the compressed air in the tube?
     
  4. Dec 5, 2008 #3
    Isn't it equal to the atmospheric pressure?
     
  5. Dec 5, 2008 #4

    Doc Al

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    Not after being compressed. (How did its volume change?)
     
  6. Dec 5, 2008 #5
    By putting it in the water the volume was halved so the pressure is the atmospheric pressure divided by 2?
     
  7. Dec 5, 2008 #6

    Doc Al

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    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.
     
  8. Dec 5, 2008 #7
    But I don't know the volume or the number of moles either.
     
  9. Dec 5, 2008 #8

    Doc Al

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    You don't care about the actual volume, only that it went from V to V/2. The number of moles is constant.
     
  10. Dec 5, 2008 #9
    Ok so I solved for pressure now can I use this in the formula P = P(initial) + [tex]\rho[/tex]gd but I am not sure if that will work.
     
  11. Dec 5, 2008 #10

    Doc Al

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    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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