Question

Water in a canal $1.5\mathrm{m}$ wide and $6\mathrm{m}$ deep is flowing with a speed of $10\mathrm{km}/\mathrm{hr}$. How much area will it irrigate in $30\mathrm{minutes}$ if $8\mathrm{cm}$ of standing water is desired?

Answer 1

Step 1: Finding the volume of canal

We have,

Breadth of the canal$=1.5\mathrm{m}$

Depth/height of the canal$=6\mathrm{m}$

Speed of water flowing in a canal$=10\mathrm{km}/\mathrm{h}$

Length of canal in $1\mathrm{hour}=10\mathrm{km}$

Length of canal in $30\mathrm{minutes}=\frac{30\times 10}{60}=5\mathrm{km}=5000\mathrm{m}$

Therefore,

$\begin{array}{rcl}\mathrm{Volume}\mathrm{of}\mathrm{canal}& =& \mathrm{l}\times \mathrm{b}\times \mathrm{h}\\ & =& 5000\times 1.5\times 6{\mathrm{m}}^3\end{array}$

Step 2: Finding the area to be irrigated

Now,

$$\begin{gathered} \mathrm{Volume}\mathrm{of}\mathrm{water}\mathrm{in}\mathrm{canal}=\mathrm{Volume}\mathrm{of}\mathrm{area}\mathrm{to}\mathrm{be}\mathrm{irrigated} \\ \Rightarrow 5000\times 6\times 1.5=\mathrm{Area}\mathrm{irrigated}\times \mathrm{height} \\ \Rightarrow 45000=\mathrm{Area}\mathrm{irrigated}\times \frac{8}{100}[\mathrm{Since}1\mathrm{m}=100\mathrm{cm}] \\ \Rightarrow \mathrm{Area}\mathrm{irrigated}=\frac{45000\times 100}{8} \\ \Rightarrow \mathrm{Area}\mathrm{irrigated}=562500{\mathrm{m}}^2=56.25\mathrm{hectares}[\mathrm{Since}1\mathrm{hectare}=10000{\mathrm{m}}^2] \end{gathered}$$

Hence, it will irrigate $56.25\mathrm{hectares}\mathrm{or}562500{\mathrm{m}}^2$ area in $30\mathrm{minutes}$.