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Fluid Mechanics

Flow through Parallel Pipes

Three paralle...

Question

Three parallel pipes connected at the two ends have flow-rates $Q_{1}, Q_{2} a n d Q_{3}$ respectively and the corresponding frictional head losses are $h_{L 1}, h_{L 2}, a n d h_{L 3}$ respectively. The correct expressions for total flow rate (Q) and frictional head loss across the two ends $(h_{L})$ are

A

Q = Q_{1} + Q_{2} + Q_{3}; h_{L} = h_{L 1} + h_{L 2} + h_{L 3}

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B

Q = Q_{1} + Q_{2} + Q_{3}; h_{L} = h_{L 1} = h_{L 2} = h_{L 3}

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C

Q = Q_{1} = Q_{2} = Q_{3}; h_{L} = h_{L 1} + h_{L 2} + h_{L 3}

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D

Q = Q_{1} = Q_{2} = Q_{3}; h_{L} = h_{L 1} = h_{L 2} = h_{L 3}

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Solution

The correct option is B $Q = Q_{1} + Q_{2} + Q_{3}; h_{L} = h_{L 1} = h_{L 2} = h_{L 3}$
Total discharge

$Q = Q_{1} + Q_{2} + Q_{3}$

Head loss: $h_{L} = h_{L 1} = h_{L 2} = h_{L 3}$

For the pipe connected in series,
Total discharge,

$Q = Q_{1} = Q_{2} = Q_{3}$

Head loss; $h_{L} = h_{L 1} + h_{L 2} + h_{L 3}$

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Similar questions

Q. Water flows through two different pipes A and B of the same circular cross-section but at different flow rates. The length of pipe A is 1.0 m and that of pipe B is 2.0 m. The flow in both the pipes is laminar and fully developed. If the frictional head loss across the length of the pipes is same, the ratio of volume flow rates

Q_{B} / Q_{A}

is ________(round off to two decimal places).

Q. Consider the following statements:

P. Minor losses do not make significant effect in long pipes.

Q. The friction factor in fluid flowing through pipe depends upon Reynolds number only.

R. The head loss in fluid flowing through pipe due to friction is a minor loss and can be neglected in pipe network problems.

S. Head loss at the entrance of pipe is half the head loss at exit.

The correct option for above statements is :

Q. Two long pipes in parallel are used to carry water between two reservoirs. The diameter of one pipe is twice that of the other. Both the pipes have the same value of friction factor. Neglect minor losses. What is the ratio of flow rates through the two pipes?

Q. Two reservoir maintain a constant difference of water levels of 11.25 m and are connected by a 10 cm diameter pipeline of 294.3 m length. The total of all head losses, by friction valve losses, bend losses, inlet and exit losses, and velocity head can be taken as

98.1 v^{2} / 2 g

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