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Calculating required pump pressure to maintain flowrate in a uniform horizontal pipe

  1. May 25, 2010 #1
    1. The problem statement, all variables and given/known data
    I am having trouble with calculating the required pump pressure in a horizontal water pipe, 3Km long. i know that the flowrate is 600Kg/s, average velocity 5.6m/s, cross-sectional area of pipe is 0.107143m^2 and losses due to friction average 0.002 per meter

    2. Relevant equations
    bernoulli's equation

    3. The attempt at a solution
    pressure = (flowrate x G)/cross-sectional area
    = (600 x 9.81) / 0.107143 = 54935.92 Pa

    i think that this is the pressure at the end of the pipe however i am unsure how to caculate the pump pressure given the frictional loss coefficient. i have had very little teaching in fluid mechanics but have researched Bernoulli's equation however i cannot see how it, is applicable to this problem is there any other equations i could use given the known elements
    Last edited: May 25, 2010
  2. jcsd
  3. Jun 5, 2010 #2
    Re: Calculating required pump pressure to maintain flowrate in a uniform horizontal p

    Reynolds number is about

    [tex] \frac{U D}{\nu} = 1.7 \times 10^6 [/tex]

    This is clearly turbulent and not potential. Bernoulli's equation is not applicable here.

    The solution is based on the exact statement, that for a steady flow in pipes mean pressure gradient is balanced by the shear at the wall. IF you work it out in spherical coordinates and by "friction" you mean Darcy friction factor, then

    \Delta P = f \rho U^2 L / D /8 = 0.002 * 5.6^2 * 3000 / 0.3 / 8 \approx 80 \, Pa
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