GATE CE 2022 Set 1 — Question 57
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Water Resources Engineering → Pipe Flow → Darcy-Weisbach Equation
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Question
Two reservoirs are connected by two parallel pipes of equal length and of diameters and , as shown in the figure (not drawn to scale). When the difference in the water levels of the reservoirs is , the ratio of discharge in the larger diameter pipe to the discharge in the smaller diameter pipe is ____________. (round off to two decimal places)(Consider only loss due to friction and neglect all other losses. Assume the friction factor to be the same for both the pipes)

Correct answer
5.6 to 5.7
Solution
For flow through pipes, the head loss due to friction is given by the Darcy-Weisbach equation:For pipes in parallel, the head loss is the same for both pipes:Given that the length , friction factor , and head loss are the same for both pipes:Where:
- (larger diameter)
- (smaller diameter)
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