Answer to Question #179512 in Mechanical Engineering for Johan Nieuwoudt

Question

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

Answer 1

• 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

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

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