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Question

A fire hydrant delivers water of density ρ at a volume rate L. The water travels vertically upwards 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



A
ρvL
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B
Zero
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C
2ρvL
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D
2ρvL
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Solution

The correct option is D 2ρvL

Given volume rate is L
Mass of the water crossing in time t m=ρLt

From the diagram above,
Change in momentum in vertical direction =mv=ρLtv
Change in momentum in horizontal direction =mv=ρLtv
Total change in momentum =(mv)2+(mv)2=2mv=2ρLtv

Force exerted by the water on the corner = change in momentum per unit time=2ρvL

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