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U-tube filled with water and inmiscible liquid

  1. Mar 31, 2012 #1
    1. The problem statement, all variables and given/known data

    A U-shaped tube is partly filled with water and partly filled with a liquid that does not mix with water. Both sides of the tube are open to the atmosphere. If h1 = 0.52 m and h2 = 0.16 m, what is the density of the liquid?


    2. Relevant equations

    ρ[itex]_{u}[/itex]=h[itex]_{1}[/itex]/h[itex]_{2}[/itex] * ρ[itex]_{k}[/itex]

    as in: unknown density = ratio of heights times known density

    ρ[itex]_{k}[/itex]= density of water = 1 cm[itex]^{3}[/itex]/mL


    3. The attempt at a solution

    so I just plugged the info in, seems relatively simple...
    ended up with

    ρ[itex]_{u}[/itex]= 52 cm/16 cm * 1 cm[itex]^{3}[/itex]/mL = 3.25 cm[itex]^{3}[/itex]/mL

    but for some reason this is wrong.

    just for kicks I also tried
    ρ[itex]_{u}[/itex]= 16 cm/52 cm * 1 cm[itex]^{3}[/itex]/mL = .31 cm[itex]^{3}[/itex]/mL

    but this is also wrong.

    any ideas?
     
  2. jcsd
  3. Mar 31, 2012 #2

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    Hi xannaxiero, welcome to PF! :smile:

    Your unit for density is wrong.
    It's not cm3/mL.

    Btw, your formula assumes that the separation of the fluids is at the bottom of the U-tube.
    I guess you have to make that assumption, because otherwise you do not have enough data.
     
  4. Apr 1, 2012 #3
    Oops you're right, I'm sleepy >.< Its g/mL. My bad. That doesn't make any difference in the equation though does it? And yes, I'm assuming separation is in the bottom...this is supposed to be a pretty simple, standard u-tube problem, no tricks...
     
  5. Apr 1, 2012 #4

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    Beyond that, your answers are right.
    Why do you think they are wrong?
     
  6. Apr 1, 2012 #5
    Online homework...they're being graded as incorrect :'(
     
  7. Apr 1, 2012 #6

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    Oh those!
    That usually means you did not follow the format that they expected.

    Try rounding to 2 digits (since your input data is 2 digits each).
    And try the unit kg/L or perhaps kg/m3 (adjusting of course the result to match).
     
  8. Apr 3, 2012 #7
    The answer ended up being .563 g/mL. Any idea why this is? There's no explanation with the homework :(
     
  9. Apr 3, 2012 #8

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    Nope. No idea.

    I can only guess that there is a typo in the problem statement, or that there is more information that is not given.
     
  10. Apr 3, 2012 #9
    Do you think it could be because the tube is open to the atmosphere? Would that impact my formula at all?
     
  11. Apr 3, 2012 #10

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    No, the atmosphere gives the same pressure of 1 atmosphere on both tubes.
    It cancels out.

    It would matter if the tubes had different diameters, or if the separation is not at the bottom.
     
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