GATE CE 2020 Set 1 — Question 59
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Water Resources Engineering → Pipe Flow → Darcy-Weisbach Equation
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Question
Three reservoirs P, Q, and R are interconnected by pipes as shown in the figure (not drawn to the scale). Piezometric head at the junction S of the pipes is . Assume acceleration due to gravity as and density of water as . The length of the pipe from junction S to the inlet of reservoir R is .
Considering head loss only due to friction (with friction factor of for all the pipes), the height of water level in the lowermost reservoir R (in m, round off to one decimal place) with respect to the datum, is ___________.
Correct answer
97.2 to 97.8
Solution
1.Piezometric head at junction S, .
2.For pipe SR: Length , Diameter , Friction factor .
3.By continuity at junction S, the flow into the junction must equal the flow out: .
4.Flow from P to S: .
5.Flow from Q to S: .
6.Total flow to R: .
7.Velocity in pipe SR: .
8.Head loss in pipe SR due to friction: .
9.Piezometric head at reservoir R: .
10.Rounding to one decimal place, the height is .
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