GATE ME 2024 Set 1 — Question 37
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Fluid Mechanics → Viscous & Pipe Flow → Pipes in Series & Parallel
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Question
In the pipe network shown in the figure, all pipes have the same cross-section and can be assumed to have the same friction factor. The pipes connecting points , , and with point have an equal length . The pipe connecting points and has a length . The pressures at the ends , , and are equal. The flow rate in the pipe connecting and is . Assume that the fluid flow is steady, incompressible, and the pressure losses at the pipe entrance and junction are negligible. Consider the following statements:I : The flow rate in pipe connecting and is .II: The pressure difference between and is equal to the pressure difference between and .Which one of the following options is CORRECT?
Correct answer
(C) Both I and II are True
Solution
For pipe flow, the pressure drop is given by . Assuming laminar flow for a simple network where :
1.Let be the pressure at junction . Given .
2. where .
3..
4. where .
5.Since , then . Thus, Statement II is True.
6.From , we get .
7.From , we get .
8.By continuity at : .
9.Therefore, . Statement I is True.
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