Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Simple Bernoulli's exercise to find air flow rate

  1. Dec 29, 2011 #1
    I'm having problems with what seems like a simple Bernoulli exercise where I can plug in all known variables but not get an answer (using Excel).

    If I reduce my system down, it would be exactly like a venturi/pipe flow problem except that flow is in the direction of small pipe to large pipe. P1 and A1 are for small pipe, P2 and A2 are for larger pipe.
    A1=.002in^2 (very small orifice)
    density (rho) air at 90F/60psi=.367lb/ft^3
    Bernoulli's eqn at continuity gives flow rate Q = A2*[((2*deltaP)/rho)/(1-(A2/A1)^2)]^0.5

    When I plug in the numbers as shown, I get a number error in Excel because the 1-(A2/A1)^2 in the denominator ends up negative.

    Any ideas where I might have gone wrong? Thanks very much.
  2. jcsd
  3. Dec 29, 2011 #2


    User Avatar
    Science Advisor
    Gold Member

    Why not just start from the actual Bernoulli equation? You can derive the equation you just cited and determine that your denominator is flipped. It should be
    [tex]\left(\frac{A_2}{A_1}\right)^2 - 1[/tex]
  4. Dec 30, 2011 #3
    Thanks, boneh3ad. I actually did derive the above equation from the original where
    P1+0.5*rho*v1^2 = P2+0.5*rho*v2^2. Since A1v1 = A2v2, I solved for v2 and substituted back into the original.
    I think my error was... as I was ignoring the sign of my deltaP, I was subtracting from the wrong side of the equation, i.e., I should have been subtracting system 1 variables from system 2 variables. Anyway, I came up with an answer for v2 (instead of finding Q). V is what I want anyway.
    What confuses me is... where do the time units come into the equation? How do rho, area, and pressure give me a distance/time unit?
  5. Dec 31, 2011 #4


    User Avatar
    Science Advisor
    Gold Member

    The SI unit of pressure, the pascal has units
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Simple Bernoulli's exercise to find air flow rate
  1. Air flow (Replies: 4)