GATE 2022 CE (CE1) – Question 57
Two reservoirs are connected by two parallel pipes of equal length and of diameters 20 cm and 10 cm, as shown in the figure (not drawn to scale). When the difference in the water levels of the reservoirs is 5 m, the ratio of discharge in the larger diameter pipe to the discharge in the smaller diameter pipe is ____________. (round off to two decimal places) (Consider only loss due to friction and neglect all other losses. Assume the friction factor to be the same for both the pipes)
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Correct answer: 5.63 to 5.69
Explanation
Parallel pipes have the same head loss. Darcy–Weisbach with equal f and L gives $h_f\propto V^2/D$, so $V\propto\sqrt D$ and $Q\propto D^{5/2}$.
Therefore $Q_{20}/Q_{10}=(20/10)^{5/2}=5.656854$, rounded to **5.66**.