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GATE 2026 CE (CE1) – Question 16

Fluid Mechanics · Flow in pipes and pipe networks · 1 mark · Multiple choice

Two reservoirs having different water levels are connected by two long parallel pipelines of same length and same material but having diameters of 600 mm and 400 mm. Using Darcy-Weisbach equation, the ratio of flowrate of water in the bigger diameter pipe to that in the smaller diameter pipe is

  1. 0.54
  2. 1.22
  3. 1.84
  4. 2.76

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Show answer and explanation

Correct answer: (D) 2.76

Explanation

Both pipes carry the same head loss. From $h_f = \frac{fLQ^2}{12.1D^5}$, the flow rate is proportional to $D^{5/2}$ for the same friction factor. So the ratio is $\left(\frac{600}{400}\right)^{2.5} = 1.5^{2.5} = 2.76$.