GATE CE 2019 Set 2 — Question 59
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Water Resources Engineering → Pipe Flow → Pipes in Parallel
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Question
Two identical pipes (i.e., having the same length, same diameter, and same roughness) are used to withdraw water from a reservoir. In the first case, they are attached in series and discharge freely into the atmosphere. In the second case, they are attached in parallel and also discharge freely into the atmosphere. Neglecting all minor losses, and assuming that the friction factor is same in both the cases, the ratio of the discharge in the parallel arrangement to that in the series arrangement (round off to 2 decimal places) is ________.
Correct answer
2.8 to 2.9
Solution
Let be the head of the reservoir and be the head loss in each pipe, where is a constant for identical pipes.Case 1: Pipes in series
The total head loss is the sum of head losses in each pipe:
Case 2: Pipes in parallel
The total head loss is the same for both pipes, and the total discharge is split equally between them ( each pipe):
Ratio of discharges:
Rounding off to 2 decimal places, the ratio is 2.83.
The total head loss is the sum of head losses in each pipe:
Case 2: Pipes in parallel
The total head loss is the same for both pipes, and the total discharge is split equally between them ( each pipe):
Ratio of discharges:
Rounding off to 2 decimal places, the ratio is 2.83.
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