GATE 2019 CE (CE2) – Question 59
Two pipes of equal length, diameter and roughness withdraw water from a reservoir, discharging freely to atmosphere. They are connected in series in one case and parallel in another. Neglect minor losses and use the same friction factor. Find discharge ratio parallel/series, to two decimal places.
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Correct answer: 2.80 to 2.90
Explanation
For fixed diameter and friction factor, Darcy loss scales as $LQ^2$. Relative to a single pipe, series doubles length and gives $Q_s=Q_1/\sqrt2$. Parallel gives $Q_p=2Q_1$. Thus $Q_p/Q_s=2\sqrt2=$ **2.83**.