Question

Water in a canal, 5.4 m wide and 1.8 m deep, is flowing with a speed of 25 km/hr. How much area can it irrigate in 40 minutes, if 10 cm of standing water is required for irrigation? [CBSE 2017]

Answer 1

Width of the canal = 5.4 m
Depth of the canal = 1.8 m
Height of the standing water needed for irrigation = 10 cm = 0.1 m
Speed of the flowing water = 25 km/h = $\frac{25000}{60}=\frac{1250}{3}$ m/min
Volume of water flowing out of the canal in 1 min
= Area of opening of canal × $\frac{1250}{3}$
= $5.4\times 1.8\times \frac{1250}{3}$
= 4050 m³
∴ Volume of water flowing out of the canal in 40 min = 40 × 4050 m³ = 162000 m³
Now,
$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{irrigation} \\ =\frac{\mathrm{Volume}\mathrm{of}\mathrm{water}\mathrm{flowing}\mathrm{out}\mathrm{from}\mathrm{canal}\mathrm{in}40\min }{\mathrm{Height}\mathrm{of}\mathrm{the}\mathrm{standing}\mathrm{water}\mathrm{needed}\mathrm{for}\mathrm{irrigation}} \\ =\frac{162000}{0.1} \\ =1620000{\mathrm{m}}^2 \\ =162\mathrm{hectare}\left(\because 1\mathrm{hectare}=10000{\mathrm{m}}^2\right) \end{gathered}$$
Thus, the area irrigated in 40 minutes is 162 hectare.