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 are $2.4c{m}^2$. 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 $9m{s}^{-1}$

Using the continuity equation $A_1{v}_1=A_2{v}_2$ we get:

$(2.4\times {10}^{-4})\times 1.5=20\times (2\times {10}^{-2})\times {10}^{-4}\times v$

$\Rightarrow v=\frac{2.4\times 1.5\times {10}^2}{40}m{s}^{-1}=\frac{24\times 15}{40}m{s}^{-1}=9m{s}^{-1}$