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Bernoulli Problem (Somewhat Complicated?)

  1. Nov 18, 2012 #1
    1. The problem statement, all variables and given/known data
    So I'm dealing with a flow as seen in this image. There are 2 tanks, filled with 2 gases of different known densities, gas A and gas B.

    Gas A flows from a tank with a static pressure sensor at point 1 through a line with diameter D1.

    Gas B flows from a tank with a static pressure sensor at point 3, through a pipe with diameter D2 before being expanded at point 5 to also D1.

    The two flows mix at point 6, and then travel further down the line. There is a pressure sensor at point 7, and the flow continues onwards after that (no information known beyond this point).

    Basically, all dimensions of the system are known (including the ones not pictured such as the pipe lengths) along with the static pressure sensors at points 1, 3, and 7, and the fluid densities, but the problem is to find out the mass flows. Considering all major and minor losses. Although the effect of different heights can be neglected!

    I'm not exactly sure how to deal with the 2 gases of different densities, and it's made even more confusing for me with the rightmost pipe having varying velocities and that impacting the losses. Any tips would be greatly appreciated! And I know how to account for the major/minor losses already (meaning the loss factors associated with the pipe roughness/bends/expansion/merge/etc) so I'm okay there. But not where the velocities come into play as part of those losses.


    2. Relevant equations
    Apply Bernoulli (many times!) to in and outlets:
    .5*ρ*V12 + P1 - ΔP= .5*ρ*V22 + P2

    where ΔP is .5*ρ*V2*(f*L/D+ƩK)

    with K being the minor loss coefficient.

    3. The attempt at a solution
    To be honest I'm not even sure where to start. Is the velocity in the two tanks zero, or can it be considered such?

    For left tank:
    P1 - ΔP (from the tank exit) = P2 + .5*ρA*V22

    For right tank:
    P3 - ΔP = P4 + .5*ρB*V42

    V4*D2 = V5*D1

    P4 + .5*ρB*V42 - ΔP (from expansion and friction) = P5 + .5*ρB*V52

    I'm not really too sure about any of this let alone what comes next! ... Thanks so much for any help!!!
     
  2. jcsd
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