Question

A garden hose having an internal diameter $2.0\text{cm}$ is conducted to a low sprinkles that consists of an enclosure with $24\text{holes}$, each $0.125\text{cm}$ in diameter. If water in the hose has a speed of $90\text{cm/s},$ the speed of water leaving the sprinkle holes is

• A. $480\text{cm/s}$
• B. $960\text{cm/s}$
• C. $48\text{cm/s}$
• D. $96\text{cm/s}$

Answer 1

The correct option is B $960\text{cm/s}$

Let
$D=$ diameter of hose $=2.0\text{cm}$
$v=$ speed of water in hose $=90\text{cm/s}$
$d=$ diameter of each hole $=0.125\text{cm}$
and number of holes, $n=24$
If $v^{\prime }$ is the velocity of water flowing out of each holes then,
volume of water entering the hose per second is equal to the volume of the water leaving out per second through the holes:
$\Rightarrow \frac{\pi D^2}{4}\times v=\frac{n\pi d^2}{4}\times v^{\prime }$
$\Rightarrow v^{\prime }=\frac{D^{2}v}{n{d}^2}=\frac{2^2\times 90}{24\times (0.125{)}^2}$
$\Rightarrow v^{\prime }=960\text{cm/s}$