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Pressure Question using 'mm-Hg'

  1. Apr 7, 2013 #1
    1. The problem statement, all variables and given/known data

    Intravenous infusions are often made under gravity. Assuming the fluid has a density of 1.00g/cm^3, at what height h should the bottle be placed so the liquid pressure is 55mm-Hg?

    2. Relevant equations

    Atmospheric pressure, Po, = 101kPa = 101000Pa
    density of fluid, ρ, = 1g/cm^3 = 1000kg/m^3
    density of Hg, ρ, = 13.6x10^3

    P=ρgh
    P=Po + pgh

    3. The attempt at a solution

    Pressure of Hg, P= ρgh
    = (13.6x10^3) x 9.8 x (5.5x10^-3)
    = 733.04 Pa

    P=Po + pgh

    h= [itex]\frac{P - Po}{ρg}[/itex]
    h= [itex]\frac{733.04 - 101000}{1000 x 9.8}[/itex]
    h= -10.23

    Therefore, the bag must be 10.23m below whatever the reference point is. Which is obviously wrong!


    The answer gives nearly what I've got but I don't understand one aspect of it.
    It says...

    h= [itex]\frac{ΔP}{ρg}[/itex]
    h= [itex]\frac{(55mm-Hg)(\frac{133Pa}{1mm-Hg})}{1000 x 9.8}[/itex]
    h= 0.75m

    I don't understand where the 133Pa came from and why they are doing this calculation.
    Can someone please explain?
     
  2. jcsd
  3. Apr 7, 2013 #2

    SteamKing

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    Staff Emeritus
    Science Advisor
    Homework Helper

    5.5*10^-3 m is 5.5 mm, not 55 mm.
     
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