GATE 2025 CE (CE2) – Question 33

Fluid Mechanics · Flow in pipes and pipe networks · 1 mark · Numerical answer

Consider steady flow of water in the series pipe system shown below, with specified discharge. The diameters of Pipes A and B are 2 m and 1 m, respectively. The lengths of pipes A and B are 100 m and 200 m, respectively. Assume the Darcy-Weisbach friction coefficient, $f$ as 0.01 for both the pipes.
The ratio of head loss in Pipe-B to the head loss in Pipe-A is ______ (round off to the nearest integer).

a reservoir feeding Pipe-A (diameter 2 m, length 100 m, f = 0.01) which is connected in series to Pipe-B (diameter 1 m, length 200 m, f = 0.01).

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Correct answer: 64

Explanation

The same discharge flows in both pipes, so $V_B/V_A = (D_A/D_B)^2 = 4$. The Darcy-Weisbach head loss is $h_f = \frac{fLV^2}{2gD}$. Then $\frac{h_{fB}}{h_{fA}} = \frac{L_B}{L_A}\cdot\frac{D_A}{D_B}\cdot\left(\frac{V_B}{V_A}\right)^2 = \frac{200}{100} \times \frac{2}{1} \times 16 = 64$.