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Homework Help: Calcualte water discharge of a pipeline at different heights

  1. Jan 8, 2012 #1
    A pipeline is 8 km long and is required to convey water from a reservoir, at 500 m
    above datum, to the intake of a water treatment works at 425 m above datum. If
    the pipe has a diameter of 225 mm, what is the discharge of water through the
    pipe? The density of water is 1000 kg/m3.

    relevant equations:

    bernoullis Energy Conservation:

    P1/ρg + u1^2/2g + z1 = p2/ρg + u2^2/2g + z2

    mass conservation equation:

    U1A1 = U2A2

    Q1 = Q2

    3. The attempt at a solution

    U1 = 0 Since the resovoir is stationary,

    p1 = ρgh p2 = ρgh

    putting values in to bernoullis:

    4905000/9810 + 500 = 4169250/9810 + u2^2/19.62 + 425

    150 = u2^2/19.62

    u2^2 = 2943
    √2943 = 54.24 m/s

    at this point the answer should be: 38.36 m/s

    and the final answer should be: Q = 1.525m^3/s

    i am completely lost, any help would be massively appreciated!
  2. jcsd
  3. Jan 9, 2012 #2


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    Homework Helper

    escobar147: What is the reservoir depth at the pipe inlet? And what is the reservoir depth (if any) at the pipe outlet? It currently appears you made a mistake in computing either pressure p1 or p2, or on both p1 and p2. Show how you computed p1 and p2, and why?
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