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Using Bernoulli's Equation to find pressure in a wind tunnel

  1. Feb 10, 2015 #1
    1. The problem statement, all variables and given/known data
    A wind tunnel is designed to draw in air from the atmosphere and produce a velocity of 100m/s in the test section. THe fan is located downstream of the test section. What pressure is to be expected in the test section if the atmospheric temperature and pressure are -20C, 90kPa?

    2. Relevant equations
    Bernoulli's Equation: P1 + 1/2pv2 + pgh1 = P2 + 1/2pv2 + pgh2

    p = P/RT

    3. The attempt at a solution
    I cancelled out the heights as it doesn't state a height difference and says the fan is downstream, so assumed its a two dimensional problem. Leaving me with:

    P1 + 1/2pv2 = P2 + 1/2pv2

    Then I used p = P/RT to find the density of air, which came out to be 1.24kg/m3

    Then Isolated P2 = P1 - 1/2pv2, using atmospheric pressure for P1, I solved for the pressure afterwards but it came out to be -560kPa.

    Now i know taking the absolute value is acceptable with pressures but this number still seems wrong to me.
     
  2. jcsd
  3. Feb 10, 2015 #2
    err, I just tried it again and I must have punched something wrong in my calculator when I squared 100m/s.

    Got a value of P2 = 83.8kPa
     
  4. Feb 10, 2015 #3

    SteamKing

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    Atmospheric pressure is 101.325 kPa. A perfect vacuum is 0 kPa. A pressure of -560 kPa is meaningless.

    No, it's not. You also need to establish if your pressure readings are gage or absolute.
     
  5. Feb 10, 2015 #4
    Err, we have never discussed gage or absolute pressure in my fluid dynamics class thus far. It is asking what the pressure is as it blows in the wind back into the tunnel from the outside.
     
  6. Feb 10, 2015 #5

    SteamKing

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    A perfect vacuum is still 0 kPa absolute or -101.325 kPa gage. These are two bits of data which come in handy when working with fluid flow. :)
     
  7. Feb 10, 2015 #6
    The problem statement says that the atmospheric pressure is 90 kPa. That doesn't sound like gauge pressure.

    Chet
     
  8. Feb 10, 2015 #7

    SteamKing

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    Sigh, atmospheric pressure at sea level on earth is generally recognized to be 101.325 kPa at a temperature of 20°C.

    An atmospheric pressure of 90 kPa may be present in the problem's test section, which is also at a temperature of -20°C (Brrr! oo)), but this pressure is rather low to be an ambient condition, unless there is a hurricane or other cyclonic storm present... :rolleyes:
     
  9. Feb 10, 2015 #8
    Yes. That was also my impression. But, that's what they gave.
     
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