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Homework Help: Venturi / Flow Rate

  1. Apr 10, 2007 #1
    1. The problem statement, all variables and given/known data
    • Known/Given
      • Water flows through a Venturi meter (mercury [density=13.6E3 kg/m^3] in the manometer).
      • Pipe size: 10.0cm diameter
      • Constriction size: 5.6cm diameter
      • Height difference of mercury: 2.3cm
    • Unknown - Flow Rate (L/s)

    2. Relevant equations
    • Bernoulli's - P1 + (1/2)*d*V1^2 = P2 + (1/2)*d*(V2)^2
    • Flow Rate - I = A1*V1 = A2 * V2
    • Pressure drop - the book has this exact example, and says that P1 - P2 = (D_fluid [water] - D_liquid [mercury])*g*H
    However, I don't understand why the pressure drop isn't just:

    3. The attempt at a solution
    Using the book's guided steps:
    • V2 = (A1/A2)*V1
    • P1 - P2 = (1/2)*D_water*((A1/A2)^2-1)*V1^2
    • (1/2)*D_water*((A1/A2)^2-1)*V1^2 = (D_water - D_mercury)*g*H
    • v1 = 0.7875m/s
    • v1 = 78.75cm/s
    • Flow = 78.75 * pi * (10cm/2)^2 = 6185 cm^3/s
    • 6185 cm^3/s * ([1 L/s] / [1000^3 cm^3/s]) = .03825 L/s

    This is off everyone's favorite online homework system, WebAssign, and I have used 5/6 submissions :bugeye: I'm terribly sorry for the awful formatting, but I don't have access to a good typesetting program as of yet (downloading TeX as we speak [well... as I type]).
    Last edited: Apr 10, 2007
  2. jcsd
  3. Apr 10, 2007 #2
    I agree that you should just use the delta P given in 23mm Hg. See what answer you come up with and we can look that over before No 6 submission.
  4. Apr 11, 2007 #3
    After confirming with a friend, I realized that I just had the conversion factor wrong. Their method worked, and apparently m^3/s * 1000 = L/s. Unfortunately, this leaves me no closer to understand why they used the two densities and not just the mercury density. With a lot of luck I might be able to extract a coherent [say: in English] answer from my TA, but probably not.
  5. Apr 11, 2007 #4
    anychance you can post a picture if given? I get 6.42L/s using just 23mmHg for delta P
  6. Apr 11, 2007 #5


    The correct answer turned out to be 12.7 L/s. I get everything except for the use of the change in densities.

    Thanks for all your help, by the way, I appreciate it! To think of my 40k / year tuition and I need to find help online from a helpful stranger.
  7. Apr 11, 2007 #6
    Thats too funny and sad at the same time. I went to school when many of the TA's still spoke english.

    anyhow, all i know is that the delta p and rho need to be in the same units as you cant mix and match say mm Hg with density of water in g/ml etc. Let me know if you get a good explanation.
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