GATE 2018 CE (CE2) – Question 58
A rough pipe has diameter 0.5 m, length 300 m and roughness height k = 0.25 mm. Water velocity is 3 m/s and kinematic viscosity $0.9\times10^{-6}$ m²/s. For laminar flow $f=64/\mathrm{Re}$; for turbulent flow $1/\sqrt f=2\log_{10}(r/k)+1.74$, where r is pipe radius. Take g = 9.81 m/s². Friction head loss, to three decimals, is ______ m.
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Correct answer: 4.50 to 4.70
Explanation
Reynolds number is $3(0.5)/(0.9\times10^{-6})=1.667\times10^6$, so use the turbulent relation. With $r/k=1000$, $f=[2\log_{10}(1000)+1.74]^{-2}=0.0166924$. Darcy–Weisbach gives $h_f=f(300/0.5)(3^2)/(2\times9.81)=4.594$ m.