Question

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

• A. $2.25m{s}^{-1}$
• B. $4.5m{s}^{-1}$
• C. $9m{s}^{-1}$
• D. $18m{s}^{-1}$

Answer 1

The correct option is C $9m{s}^{-1}$

Rate of flow of volume will remain constant

i.e $A_1{V}_1=A_2{V}_2\left(2.4c{m}^2\right)\left(1.5m/s\right)=(20\times 2.0\times {10}^{-2})c{m}^2{V}_2\Rightarrow V_2=\left(\frac{2.4\times 1.5}{20\times 2.0\times {10}^{-2}}\right)m/s=9m/s$