Question

Water in a canal, $5.4\mathrm{m}$ wide and $1.8\mathrm{m}$ deep, is flowing with a speed of $25\mathrm{km}/\mathrm{hour}$. How much area can it irrigate in $40\mathrm{minutes}$, if $10\mathrm{cm}$ of standing water is required for irrigation

Answer 1

Step 1:Finding the volume of canal

We have,

Breadth of the canal$=5.4\mathrm{m}$

Depth/height of the canal$=1.8\mathrm{m}$

Speed of water flowing in a canal$=25\mathrm{km}/\mathrm{h}$

Length of canal in $1\mathrm{hour}=25\mathrm{km}$

Length of canal in $40\mathrm{minutes}=\frac{40\times 25}{60}=\frac{50}{3}\mathrm{km}=\frac{5000}{3}\mathrm{m}$

$\begin{array}{rcl}\mathrm{Volume}\mathrm{of}\mathrm{canal}& =& \mathrm{l}\times \mathrm{b}\times \mathrm{h}\\ & =& 5.4\times 1.8\times \frac{5000}{3}{\mathrm{m}}^3\end{array}$

Step 2: Finding the area to be irrigated

Now,

$$\begin{gathered} \mathrm{Volume}\mathrm{of}\mathrm{water}\mathrm{in}\mathrm{canal}=\mathrm{Volume}\mathrm{of}\mathrm{area}\mathrm{to}\mathrm{be}\mathrm{irrigated} \\ \Rightarrow 5.4\times 1.8\times \frac{5000}{3}=\mathrm{Area}\mathrm{irrigated}\times \mathrm{height} \\ \Rightarrow 16200=\mathrm{Area}\mathrm{irrigated}\times \frac{10}{100}[\mathrm{Since}1\mathrm{m}=100\mathrm{cm}] \\ \Rightarrow \mathrm{Area}\mathrm{irrigated}=\frac{16200\times 100}{10} \\ \Rightarrow \mathrm{Area}\mathrm{irrigated}=1620000{\mathrm{m}}^2=162\mathrm{hectares}[\mathrm{Since}1\mathrm{hectare}=10000{\mathrm{m}}^2] \end{gathered}$$

Hence, it will irrigate $162\mathrm{hectares}\mathrm{or}1620000{\mathrm{m}}^2$ area in $40\mathrm{minutes}$.