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Gage Pressure, Absolute Pressure - Gage in Different Environment Problem

  1. Sep 6, 2009 #1
    State the Problem

    A gage is connected to a tank in which the pressure of the fluid is 42 psi above atmospheric. If the absolute pressure of the fluid remains unchanged but the gage is in a chamber where the air pressure is reduced to a vacuum of 25 inHg, what reading in psi will then be observed.

    Related Equations, etc

    Code (Text):

    P    = P    +  P                 (1)
     abs    atm     gage
     
    Answer in back of book: 54.3 psi
    Standard atmosphere at sea level: 14.696 psia (29.92 inHg)

    Work Done So Far

    1) Determine the absolute pressure using P_atm = 14.696 and P_gage = 42 psi

    Code (Text):

    P    = 14.696 + 42 = 56.696 psia
     abs
     
    2) P_chamber = 25 * 14.696 / 29.92 = 12.279 psi

    and manipulating (1) a bit:

    Code (Text):

    P     = P    - P        = 56.696 - 12.279 = 44.417
     gage    abs    chamber
     
    Which isn't correct; how can I use equation (1) to determine P_gage correctly?

    I suppose my problem is not having the correct relationship between P_atm and P_chamber; should I use:

    Code (Text):

     '
    P    = P     - P        = 14.696 - 12.279 = 2.417   (2)
     atm    atm     chamber

     '               '
    P     = P     - P    = 56.696 - 2.417 = 54.279
     gage    abs     atm
     
    but how do I justify equation (2)?
     
  2. jcsd
  3. Sep 6, 2009 #2

    nvn

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    Science Advisor
    Homework Helper

    lizzyb: It currently appears to me your answer, 44.417 psi (gauge), is correct and the back of the book is wrong. I will be glad to hear from anyone if I am currently misinterpreting.
     
  4. Sep 7, 2009 #3
    Thank you for your help.

    Reading that section of the chapter again I noted the sentence:

    So translating the statement to math:
    Code (Text):


    P        = P    - P         => P         = P       - P
     chamber    atm    chamber      chamber     atm       chamber
     gage                                                 gage

                                          = 14.696  - 12.279
                                          = 2.417

     '
    P     = P    - P        = 56.696 - 2.417 = 54.279
     gage    abs    chamber
     
    I think the wording of the question could be improved.
     
    Last edited: Sep 7, 2009
  5. Sep 7, 2009 #4

    nvn

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    Science Advisor
    Homework Helper

    The cited Finnemore quotation doesn't preclude using absolute pressure. Vacuum is reported three ways; e.g., 85 kPa (absolute), 85 kPa (gauge), or -85 kPa (gauge). All three methods are clear if the pressure is followed by the string "(absolute)" or "(gauge)," per the SAE, ASTM, and IEEE requirements.

    The problem statement is ambiguous because the authors violated SAE TSB-003 and IEEE/ASTM SI10 requirements by not writing "25 inHg (absolute)" or "25 inHg (gauge)." But current evidence slightly points toward a chamber pressure of -25 inHg (gauge); i.e., 16.665 kPa (absolute).
     
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