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Speed of Efflux

A stream of w...

Question

A stream of water (density $ρ$ ) flowing horizontally with a speed v emerges from a tube of cross-sectional area A and hits on adjacent vertical wall. The force of impact on the wall when the water does not rebound is:

A

ρ A v^{2}

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B

ρ A v

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C

\frac{ρ A}{v}

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D

none of these

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Solution

The correct option is A $ρ A v^{2}$
The amount of water striking in time $d t$ will be

$d m = ρ A v d t$

Thus, change of momentum if water does not rebound will be

$d P = v (d m) = ρ A v^{2} d t$

Thus,

$F = \frac{d P}{d t} = ρ A v^{2}$

Answer is $ρ A v^{2}$

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