Answer to Question #179512 in Mechanical Engineering for Johan Nieuwoudt

Question #179512

Given that oil, with density p=700kg/m3 and kinematic viscosity v = 0.00001m2/s flow at 0.3 m3/s through 500 m of 250mm diameter cast iron pipe and the roughness of cast iron pipe e = 0.26mm


Determine


  • The Reynolds number
  • The friction factor f
  • The head loss due to friction
1
Expert's answer
2021-04-12T02:32:16-0400
  • The Reynolds number

"Re= \\frac{ud}{v}=\\frac{4 \\times0.3}{\\pi \\times0.25 \\times0.00001}=1527887.45"



  • The friction factor f

This a turbulent flow

"f=\\frac{1.325}{[\\ln(\\frac{e}{3.7D}+\\frac{5.74}{Re^{0.9}}]^2}=\\frac{1.325}{[\\ln(\\frac{0.00026}{3.7 \\times0.25}+\\frac{5.74}{1527887.45^{0.9}}]^2}=0.021714033"


  • The head loss due to friction

"u=\\frac{Q}{0.25 \\pi d^2}= \\frac{0.3}{0.25 \\pi \\times0.25^2}=6.1 m\/s"

"h_f=f \\frac{L}{d} \\frac{u^2}{2g}=0.021714033 \\times \\frac{500}{0.25} \\frac{6.1^2}{2 \\times 9.81}=82.4 m"


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