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Liquids involving continuity equation

  1. Jun 15, 2006 #1
    Any help would be appreciated -

    The water flowing through a 1.9 cm (inside diameter) pipe flows out through three 1.3 cm pipes. (a) If the flow rates in the three smaller pipes are 28, 15, and 10 L/min, what is the flow rate in the 1.9 cm pipe?

    The basic continuity idea is A1v1 = A2v2.
    The flow rate equation is R = Av.

    For each of the 3 pipes, the flow rate is given (R) and the area can be calculated (pi*r^2).

    To find the flow rate of the 1.9cm pipe, we need to know the speed of water flow (v, since R =Av).

    But I don't know how to put them all together and relate them. I tried things but I always got the wrong answer. Please give me a hint or help. Thanks.
  2. jcsd
  3. Jun 15, 2006 #2

    Doc Al

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    Staff: Mentor

    What does "flow rate" mean? Hint: All the water in the main pipe must end up in the smaller pipes.
  4. Jun 15, 2006 #3


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    Homework Helper

    The conservation of mass is the concept from which the continuity equation is derived. Therefore, if you have a Q from one main pipe and it divides into 3 other pipes, the Q on the main pipe must be the sum of the Qs on the 3 smaller pipers, so mass is conserved.
  5. Jun 15, 2006 #4

    I understand what both of you guys said, and you're thinking, "well...if she understands it then why can't she do the problem???" It is because I'm a dumbass.

    Anyhow, I understand the concept (at least, I think). I'm not asking for a completely solved problem, but can you help me a bit more with how to set up the problem? I promise I will try my hardest to solve it...I just need a starting point.

    I set the initial pipe as A1v1, and the 3 respective pipes as A2v2, A3v3 and A4v4. I did everything I know but still got it wrong.

    Thank you.
  6. Jun 15, 2006 #5
    Never mind! I got it: you just add all the flow rates of three pipes together. This makes sense, although I hate it when they put problems like this...it seems too easy.

    Thanks for your help.
  7. Jun 15, 2006 #6


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    Homework Helper

    I'd still advise you understand the underlying concept of the continuity equation. Good luck.
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