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Fluid pressure problem and units confusion

  1. Oct 17, 2011 #1
    1. The problem statement, all variables and given/known data

    Exercise Find the pressure at a depth of 10 m below the
    surface of a lake if the pressure at the surface is 1 atm.
    (Answer: With P0 = 1atm = 101kPa, ρ=103kg/m[itex]^{3}[/itex], and g= 9.81 N/kg, we have P = P0 + ρgh = 1.97 atm. The pressure at a depth of 10 m is nearly twice that at the surface.)


    2. Relevant equations

    P = P0 + ρgh

    1 atm = 101.325 kPa = 101325 Pa

    ρ = 10[itex]^{3}[/itex] kg/m[itex]^{3}[/itex]

    3. The attempt at a solution

    Doing what they did:

    P = 101 kPa + 10[itex]^{3}[/itex]*9.81 N/kg*10 m = 98,201 kPa = 972 atm.

    Hmm... Trying it with atm:

    P = 1 atm + 10[itex]^{3}[/itex]*9.81 N/kg*10 m = 98,101 atm.

    Trying it with Pa:

    P = 101,325 Pa + 10[itex]^{3}[/itex]*9.81 N/kg*10 m = 199,425 Pa = 1.97 atm.

    So I was only able to get the answer they did when using Pa. I think they neglected to mention that pivotal part when solving the problem. I have questions two:

    1). Why does the equation have a strong preference for Pa?
    2). How would I have to restructure the equation to use kPa, atm, or mmHg?
     
  2. jcsd
  3. Oct 17, 2011 #2

    SammyS

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    1 Pa = 1 N/m.

    1kPa = 103 N/m2

    103*9.81 N/kg*10 m = 9.81×104 Pa = 98.1 kPa
     
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