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Finding Average Velocity

A lawn sprink...

Question

A lawn sprinkler has $20$ holes, each of cross-sectional area $2.0 \times 10^{- 2} {c m}^{- 2}$ , and is connected to a hose pipe of cross sectional area $2.4 c m^{2}$ . If the speed of water in the hose pipe is $1.5 m s^{- 1}$ , the speed of water as it emerges from the holes is

2.25 m s^{- 1}

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4.5 m s^{- 1}

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9 m s^{- 1}

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18 m s^{- 1}

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Solution

The correct option is C $9 m s^{- 1}$
Rate of flow of volume will remain constant
i.e $A_{1} V_{1} = A_{2} V_{2} (2.4 c m^{2}) (1.5 m / s) = (20 \times 2.0 \times 10^{- 2}) c m^{2} V_{2} \Rightarrow V_{2} = (\frac{2.4 \times 1.5}{20 \times 2.0 \times 10^{- 2}}) m / s = 9 m / s$

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