A fire hydrant delivers water of density ρ at a volume rate L. The water travels vertically upward through the hydrant and then does 90° turn to emerge horizontally at speed V. The pipe and nozzle have uniform cross-section throughout. The force exerted by the water on the corner of the hydrant is:-
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Question

A fire hydrant delivers water of density ρ at a volume rate L. The water travels vertically upward through the hydrant and then does 90° turn to emerge horizontally at speed V. The pipe and nozzle have uniform cross-section throughout. The force exerted by the water on the corner of the hydrant is:-

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G1 Physics · Accepted Answer

Step 1: The mass-flow rate is ṁ = ρL. The inlet velocity is vertical and the outlet velocity is horizontal, both with magnitude V. Step 2: The momentum-change vector has perpendicular components ρLV in the horizontal and vertical directions. Its magnitude is √[(ρLV)²+(ρLV)²] = √2ρVL. Correct answer: D.