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How do you calculate pressure using english units?

  1. Feb 11, 2013 #1
    1. The problem statement, all variables and given/known data
    The reading on a mercury manometer at 25 degrees Celsius (open to the atmosphere at one end) is 25.62 inches. The local acceleration of gravity is 32.243(ft)(s^2) Atmospheric pressure is 29.86 (in Hg). What is the absolute pressure in psia being measured? The density of mercury at 70 degrees Fahrenheit is 13.543 (g/cm^3).


    2. Relevant equations
    Hydrostatic Pressure = pgh
    psia = atm pressure + pgh
    3. The attempt at a solution

    I know how to do this question in metric units but, im having a hard time figuring out the answer in english units.

    So far I have converted all units for hydrostatic pressure to english units.
    p = 844.65 (lb/ft^3)
    h = 2.135 (ft)
    g = 32.243 (ft/s^2)

    I get 57706.508 psi (Is that the correct units?...)

    The answer is suppose to be 27.22 psia. I didn't bother adding (inHg) because i already know its too much...


    I'm really confused on how to the english system works.
    How do you properly convert/interpret problem?...
     
  2. jcsd
  3. Feb 11, 2013 #2

    SteamKing

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    Staff Emeritus
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    Homework Helper

    The first thing to remember is that a pound is a unit of force, not mass.

    To find abs pressure, you must add atmospheric pressure to the reading from the manometer.

    The density of mercury (13.543 g/cc) is also numerically the same as the specific gravity. Fresh water has a specific gravity of 1.0 (by definition), and the weight density of fresh water (without looking at a table) is approx. 62.4 lbs / cu. ft.

    The weight density of mercury is the specific gravity of mercury times the weight density of water. (the gravitational acceleration is already included, since we are dealing with weight rather than mass)

    Once you know the absolute pressure in inches of mercury, you can finish the problem in two ways.

    1. Convert inches of mercury to feet, and use the weight density of mercury in lbs / cu. ft.
    2. Convert the weight density of mercury from lbs/cu. ft. to lbs / cu. in. 1 foot = 12 inches

    3. If you use method 1, remember to check your units. The answer comes out in lbs / sq. ft. In order to convert to psia, you must divide pounds per square foot by 144 sq. in./ sq. ft.
     
  4. Feb 11, 2013 #3

    Borek

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    Staff: Mentor

    Not enough information to say what you did wrong, at first sight everything you wrote so far looks OK.

    English units work the same way SI units do. You deal with length, mass and time, regardless of what symbols and units are, the idea behind is identical.
     
  5. Feb 11, 2013 #4

    Borek

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    I thought it can be both, depending on the context (lbm and lbf).
     
  6. Feb 11, 2013 #5

    mfb

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    2016 Award

    Staff: Mentor

    If it does not work with imperial units, you can convert everything to metric units, calculate, and convert back for the answer. Not a very handy way, but it is possible.

    Did you consider the ft<->inch conversion?
     
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