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[Fluid Mechanics] Water Flow in a Hose

  1. Feb 10, 2013 #1
    1. The problem statement, all variables and given/known data

    Given:
    Water flows through a 15.24m long, 1.6cm diameter hose.

    pressure at the outdoor tap = 275.8kPa

    volumetric flowrate, Q = 7.5e-4 m^3/s (i.e. 7.5L for 10 seconds)

    viscosity of water, μ = 0.001 Pa*s
    density of water, ρ = 1000 kg/m^3

    Look for: the roughness of the hose

    2. Relevant equations

    Renolds number:
    23032e25451927df6094806dcd3ba4dd.png

    Darcy equation:
    d507bcd5f5091fb94dabf55d828f59a3.png

    Moody chart:
    800px-Moody_diagram.jpg

    3. The attempt at a solution

    I have calculated Renolds number = 7958 ==> turbulent flow

    I used Darcy equation and found out the friction factor, f, is great than 1.
    I am confused and stuck here.
    I must have used the wrong formula or missed some important steps.

    Please help me by providing some advice, double checking my work or giving some steps would be greatly appreciated!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 10, 2013 #2
    Show us your work.
     
  4. Feb 10, 2013 #3
    volumetric flowrate = Q = 7.5e-4 m^3/s
    D = diameter = 0.016m
    velocity = V =volumetric flow rate/cross sectional area = Q/(pi*D^2*0.25) = 0.497 m/s

    density = ρ = 1000kg/m^3
    viscosity = μ = 0.001 Pa*s
    Renolds number = Re = (density*velocity*diameter)/viscosity = 7958 > 2100 ==> turbulent flow

    L = length of the hose = 15.24m
    pressure at outdoor tap = ΔP = 275.8kPa
    friction factor = f = (2*ΔP*D) / (L*ρ*V^2) = 2.34 ==> doesn't make sense and I'm stuck here.
     
  5. Feb 10, 2013 #4
    Check your velocity calculation. I get 3.73 m/s.
     
  6. Feb 11, 2013 #5
    Thank you very much, Chestermiller!

    you are correct, V = 3.73 m/s,
    problem solved.
     
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