GATE Papers >> Civil >> 2017 >> Question No 149

Question No. 149 Civil | GATE 2017

Water is pumped at a steady uniform flow rate of 0.01 m3/s through a horizontal smooth circular pipe of 100 mm diameter. Given that  the Reynolds number is 800 and g is 9.81 m/s2, the head loss (in meters, up to one decimal place) per km length due to friction would be ____________ 


Answer : 65.0 to 69.0


Solution of Question No 149 of GATE 2017 Civil Paper

Q = 0.01 m3/s

d = 100 mm

Re = 800

g = 9.81 m/s2

${\mathrm h}_\mathrm f=\frac{\mathrm f\mathcal l\mathrm V^2}{2\mathrm{gd}}$

Since Re is less than 2000 the flow will be laminar flow

Hence,$\begin{array}{l}\mathrm f=\frac{64}{{\mathrm R}_\mathrm e}\\\;\;=\frac{64}{800}=0.08\\{\mathrm h}_\mathrm f=\frac{\mathrm f\mathcal l\mathrm Q^2}{12.1\mathrm d^5}\\\;\;\;=\frac{0.08\times\mathcal l\times(0.01)^2}{12.1\times(0.01)^5}\\\;\;\;=0.0661\mathcal l\end{array}$

Hence head loss per km length = 0.0661 x 1000 = 66.1 m

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