Water running in a cylindrical pipe of inner diameter 7 cm, is collected in a container at the rate of 192.5 litres per minute.
Question:

Water running in a cylindrical pipe of inner diameter 7 cm, 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.

Solution:

We have,

Radius of cylindrical pipe, $r=\frac{7}{2} \mathrm{~cm}$ and

The rate of flow of water $=192.5 \mathrm{~L} / \mathrm{min}$

$=\frac{192.5 \mathrm{~L}}{1 \mathrm{~min}}$

$=\frac{192.5 \times 1000 \mathrm{~cm}^{3}}{1 \mathrm{~min}} \quad\left(\right.$ As, $\left.1 \mathrm{~L}=1000 \mathrm{~cm}^{3}\right)$

$=192500 \mathrm{~cm}^{3} / \mathrm{min}$

$\Rightarrow$ The volume of water flowing out from the cylindrical pipe in $1 \mathrm{~min}=192500 \mathrm{~cm}^{3}$

Now, the rate of flow of water in the pipe $=\frac{\text { The volume of water flowing out from the cylindrical pipe in } 1 \text { min }}{\pi r^{2}}$

$=\frac{192500}{\left(\frac{22}{7} \times \frac{7}{2} \times \frac{7}{2}\right)}$

$=\frac{192500 \times 2}{77}$

$=5000 \mathrm{~cm} / \mathrm{min}$

$=\frac{5000 \times 60}{1 \times 100000} \mathrm{~km} / \mathrm{hr}$

$=3 \mathrm{~km} / \mathrm{hr}$

So, the rate of flow of water in the pipe is 3 km/hr.