Question

From a tap of inner radius $0.75cm$, water flows at the rate of $7m{s}^{-1}$. Find the volume in litres of water delivered by the pipe in one hour.

Answer 1

Step 1: Finding the volume of water delivered per second:

Let, $r$ be the radius of the pipe.

Given that, $r=0.75cm$, rate of flow of water through the pipe $=7m{s}^{-1}=700cm{s}^{-1}$

The cross-sectional area of pipe $={\mathrm{\pi r}}^2$

The volume of water flowing per second $=\frac{22}{7}\times {\left(0.75\right)}^2\times 700c{m}^3$ $(\mathrm{\pi }=\frac{22}{7})$

$$\begin{gathered} =22\times {\left(0.75\right)}^2\times 100c{m}^3 \\ =1237.5c{m}^3 \end{gathered}$$

Step 2: Finding the volume of water delivered per hour:

Volume of water flowing in 60 mins $=1237.5\times 60\times 60c{m}^3$

$=4455000c{m}^3$

So, the volume of water flowing through the pipe in an hour is $4455000c{m}^3$.

Step 3: Converting the volumetric units to litres:

We know, $1000c{m}^3=1litres$

So, the volume of water in litres is $=\frac{4455000}{1000}litres$

$=4455litres.$

Therefore, total volume of water delivered in an hour is $4455litres.$