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Fluid Statics/depth in a cylinder

  1. Apr 19, 2017 #1
    1. The problem statement, all variables and given/known data
    Mercury is added to a cylindrical container to a depth d and then the rest of the cylinder is filled with water. If the cylinder is 0.8 m tall and the pressure at the bottom is 1.3 atmospheres, determine the depth of the mercury. (Assume the density of mercury to be 1.36 multiply.gif 104 kg/m3.)

    2. Relevant equations
    Ptotal=Patmosphere+Pwater+Pmercury
    P=density x g x height
    1 atmosphere=1.013e5 Pa
    density of water=1 x 103 kg/m3
    pressure of atmosphere=1 atm
    3. The attempt at a solution
    I first subtracted out the pressure of the atmosphere, so
    .3 atm=Pwater + Pmercury
    .8m=Hwater + Hmercury
    Pmercury=1.36 x 104 x 9.8 x Hmercury
    Pwater=1 x 103 x 9.8 x Hwater

    I am having difficulty putting all 4 of these equations together. I feel like there is substitution needed, but which equations should I use?
     
  2. jcsd
  3. Apr 19, 2017 #2

    kuruman

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    Perhaps you should be more systematic, Starting with your equation
    Ptotal=Patmosphere+Pwater+Pmercury
    substitute
    Pwaterwaterg hwater
    Pmercurymercuryg hmercury
    and solve for hmercury.
     
  4. Apr 19, 2017 #3
    You have 4 linear algebraic equations in 4 unknowns. Are you familiar with Gaussian elimination?
     
  5. Apr 19, 2017 #4
    Ok, if I do that
    .3atm=(1000 x 9.8 x Hwater) + (1.36 x 104 x 9.8 x Hmercury)
    I still need to find the height of water, right? Where would that come from?
     
  6. Apr 19, 2017 #5
    No, never heard of that. What is Gaussian elimination?
     
  7. Apr 19, 2017 #6

    kuruman

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    Since the cylinder is filled to the top,
    Height of water = height of cylinder - height of mercury
     
  8. Apr 19, 2017 #7
    thank you! Got it!
     
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