Question

Water running in a cylindrical pipe of inner diameter $7cm$, is collected in a container at the rate of $192.5$ litres per minute. Find the rate of flow of water in the pipe in $km/hr$.

Answer 1

Diameter of the pipe = $7cm$

radius, r = $\frac{7}{2}=3.5$

Quantity of water flowing in 1 minute =$192.5$ litres

Volume of water flowing in 1 hour = $192.5\times 60\times 1000c{m}^3----\left(1\right)$

Also, Volume of water flowing in 1 hour = $\pi r^2\times rate\left(R\right)cm/h-----\left(2\right)$

From (1) and (2), we get,

$\pi r^2\times rate\left(R\right)=192.5\times 60\times 1000c{m}^3\frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\times R=192.5\times 60\times 1000R=\frac{192.5\times 60\times 1000\times 2}{77}=300000cm/h=3000m=3km/h$

Hence, the rate of flow of water is $3km/h$.