Three reservoirs A, B and C are interconnected by pipes as shown in the given figure. Water surface elevations in the reservoirs and the piezometric level at the junction D are also indicated in the figure.

$Flow Q_{1}, Q_{2} and Q_{3} are related as$

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

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

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Q_{2} - Q_{1} = Q_{3}

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Q_{1} + Q_{2} + Q_{3} = 0

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Solution

The correct option is A $Q_{1} + Q_{2} = Q_{3}$
The direction of flow can be determined from head difference as the flow occurs from high head to low head.

$Piezometric head at A> Piezometric level at D so flow Q_{1} is from A toward D.$

$Piezometric head at B> Piezometric level at D so flow Q_{2} is from B towards D.$

$Piezometric head at C< Piezometric level at D so flow Q_{3} is from D towards C.$

$∴ Q_{1} + Q_{2} = Q_{3}$

:: Q₁ + Q₂ = Q3

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