Fluid Mechanics: Determine volumetric flowrate

  1. 1. The problem statement, all variables and given/known data


    *See attachment for diagram*

    With steady-state operation, an energy balance between point 1 and point 2 along the A side dictates:

    *See attachment for equation 1*

    And an energy balance between points 1 and 2 along the B side dictates:

    *see attachment for equation 2*

    Comparing the two balances, the following can be determined:

    *See attachment for equation 3*

    Which states that frictional losses over parallel segments are equal. With this in mind, develop a model for the system and fill in the missing entries in the table below.

    Qtot LA DA LB DB QA QB
    gpm ft in ft in gpm gpm

    150 85 4 100 4 ? ?
    80 100 4 400 3 ? ?
    300 120 2 120 3 ? ?
    300 120 6 50 4 ? ?
    180 80 ? 80 4 60 ?
    300 ? 3 70 3 140 ?
    ? 300 6 100 4 100 ?

    2. Relevant equations
    Use chen equation for friction factor:

    1/(f)^1/2 = -2.0log((e/D)/3.7065 – 5.0452A/Re)
    A = log((e/D)^1.1098/2.8257 + (5.8506/Re^0.8981))

    3. The attempt at a solution

    We are allowed to use Excel goal seek (I think we HAVE to). However, i cannot seem to get a system of equations that will solve for Va and Vb. I believe that if I had those terms, I could easily calculate Qa and Qb. If that's not the direction I need to be going, then I am completely lost.

    For the first row, we were given the answers so that we could check our model. Qa=83.1 gpm and Qb=66.9 gpm.

    Thanks for any help!
     

    Attached Files:

  2. jcsd
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