GATE CE 2025 Set 2 — Question 33
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Water Resources Engineering → Pipe Flow → Darcy-Weisbach Equation
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Question
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, 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).
Correct answer
64 to 64
Solution
For steady flow in series, the discharge () is the same for both pipes.
Head loss due to friction () is given by the Darcy-Weisbach equation:
(using SI units where )Since and are constant for both pipes:
Ratio of head loss in Pipe-B to Pipe-A:
Given:
.
Head loss due to friction () is given by the Darcy-Weisbach equation:
(using SI units where )Since and are constant for both pipes:
Ratio of head loss in Pipe-B to Pipe-A:
Given:
.
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