GATE Civil Engineering (CE) 2019 Shift 2 Solved Paper

Question : 56 of 65

Marks: +1, -0

Two identical pipes (i.e. having the same length, same diameter, and same roughness) are used to withdraw water from a reservoir. In the first case, they are attached in series and also discharge freely into the atmosphere. In the second case, they are attached in parallel and friction factor is same in both the cases, the ratio of the discharge in the parallel arrangement to that in the series arrangement (round off to 2 decimal places) is _____

Your Answer:

Validate

Solution:

Case (1): Series connection,

∆ {h}=\;{ {f} ×(2 ℓ) {Q}_{\;\text "series "\;}^{2}}/{12.1 {d}^{2}}

Case (ii) : parallel connection

then,

∆ {h}=\;{f × ℓ ×( {Q}_{\;\text "parallel"\;} {/} 2)^{2}}/{12.1 {d}^{5}}

....(ii)
then from equation (i) and (ii)

\;{f(2 ℓ) × Q_{\;\text "series "\;}^{2}}/{12.1 d^{5}}=\;{f× ℓ ×(Q_{\;\text "parallel "\;} \/ 2)^{2}}/{12.1 d^{5}}

⇒ \;\; 2 Q_{\;\text "series "\;}^{2}=\;{Q_{\;\text "parallel "\;}^{2}}/{4}

⇒ \;\; \;{Q_{\;\text "parallel "\;}}/{Q_{\;\text "series "\;}}=(8)^{1 {/} 2}=2 √{2}

\;{ {Q}_{\;\text "parallel"\;}}/{ {Q}_{\;\text "series "\;}}=2.828

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