A gardening pipe having an internal radius ' $R$ ' is connected to a water sprinkler having ' $n$ ' holes…
A gardening pipe having an internal radius ' $R$ ' is connected to a water sprinkler having ' $n$ ' holes each of radius ' $r$ '. The water in the pipe has a speed ' $v$ '. The speed of water leaving the sprinkler is
Using the equation of continuity, we have
$\mathrm{A}_1 \mathrm{v}=\mathrm{A}_2 \mathrm{v}^{\prime}$
where $v$ is speed of water in the pipe and $v^{\prime}$ is the speed of water leaving the pipe.
Area of the pipe $=\pi \mathrm{R}^2$
Area of each hole in the sprinkler $=\pi r^2$
$\therefore \quad$ Total area of the holes in the sprinkler $=n \pi r^2$
$\pi R^2 v=n \pi r^2 v^{\prime}$ ...from (i)
$\therefore \quad \mathrm{v}^{\prime}=\frac{\mathrm{R}^2 \mathrm{v}}{\mathrm{nr}^2}$