Gage Pressure, Absolute Pressure - Gage in Different Environment Problem

[lizzyb]

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

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

P    = 14.696 + 42 = 56.696 psia
 abs

2) P_chamber = 25 * 14.696 / 29.92 = 12.279 psi

and manipulating (1) a bit:

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:

 '
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)?

 

[nvn]

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.

 

[lizzyb]

Thank you for your help.

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

If the pressure is below that of the atmosphere, we call it a vacuum, and its gage value is the amount by which it is below that of the atmosphere.

So translating the statement to math:

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.

 

[nvn]

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).