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Homework Help: Volume Flow Rate in a Pipe for Viscous Fluid

  1. Jun 30, 2012 #1
    1. The problem statement, all variables and given/known data

    Hi, my first post here! I have a Thermodynamics resit over the summer and I'm trying to get my head around viscous flow, I'm stuck at a question and need help! Thanks :)

    Glycerine discharges to the atmosphere through a circular pipe 100mm in diameter. The gauge pressure 50m from the exit is 458 kPa. Data for glycerine: ρ=1260 kg/m^3, μ=0.9 kg/ms.

    Determine the volume flow rate Q for the following cases:
    (i) a horizontal pipe (verify the flow is laminar!) (Ans: 25 litres/s)
    (ii) a pipe inclined upwards by 20° (Ans: 13.5 litres/s)
    (iii) a pipe inclined downwards by 20° (Ans: 36.5 litres/s)

    2. Relevant equations

    I thought this equation was the right one to use but my answer is totally wrong when I plug the numbers in, it's not a units thing either...

    Q = (∏d^4 / 128μ) * (ΔPloss / length)

    3. The attempt at a solution

    I assumed the gauge pressure at the pipe exit is equal to atm pressure, so 100kPa - is this correct? The rest is just plugging numbers in. Am I missing something obvious here...?
  2. jcsd
  3. Jun 30, 2012 #2


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    Homework Helper

    Have you tried using Bernoulli's equation?
  4. Jun 30, 2012 #3
    Your formula works. I get 25 for part i. Are you mixing gauge pressure and absolute pressure?
  5. Jun 30, 2012 #4
    Hi LawrenceC, yes I think I am! Embarrassing moment, whoops...

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