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).

GATE Mechanical Engineering (ME) 2019 Shift 2 Solved Paper

Question : 42 of 65

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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

1.0 {m}

and that of pipe

B

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).

Your Answer:

Validate

Solution:

Frictional losses of pipe

h f ∝ f L \;{v^{2}}/{D} ∝ f L \;{({q}/{A})^{2}}/{D} ∝ f L \;{Q^{2}}/{D^{5}}

\;{h_{f B}}/{h f A}=\;{f_{B} L_{B} Q_{B}^{2}}/{f_{A} L_{A} Q_{A}^{2}} ;

Where

f=\;{64}/{R e}

\;{Q_{B}^{2}}/{Q_{A}^{2}}=\;{h_{f B} L_{A} f_{A}}/{h f_{A} L_{B} f_{B}}=\;{L_{A} f_{A}}/{L_{B} f_{B}}=\;{L_{A} Q_{B}}/{L_{B} Q_{A}}

\;{Q_{B}}/{Q_{A}}=\;{L_{A}}/{L_{B}}=0.5

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