Question

Water in a canal, 30 dm wide and 12 dm deep, is flowing with a velocity of 20 km per hour. How much area will it irrigate, if 9 cm of standing water is densired?

Answer 1

Width of the canal = 30 dm = 3 m (1 m = 10 dm)

Depth of the canal = 12 dm = 1.2 m

Speed of the water flow = 20 km/h = 20000 m/h

∴ Volume of water flowing out of the canal in 1 h = 3 × 1.2 × 20000 = 72000 m³

Height of standing water on field = 9 cm = 0.09 m (1 m = 100 cm)

Assume that water flows out of the canal for 1 h. Then,

Area of the field irrigated

$$\begin{gathered} =\frac{\mathrm{Volume}\mathrm{of}\mathrm{water}\mathrm{flowing}\mathrm{out}\mathrm{of}\mathrm{the}\mathrm{canal}}{\mathrm{Height}\mathrm{of}\mathrm{standing}\mathrm{water}\mathrm{on}\mathrm{the}\mathrm{field}} \\ =\frac{72000}{0.09} \\ =800000{\mathrm{m}}^2 \end{gathered}$$
$$\begin{gathered} =\frac{800000}{10000}\left(1\mathrm{hectare}=10000{\mathrm{m}}^2\right) \\ =80\mathrm{hectare} \end{gathered}$$

Thus, the area of the field irrigated is 80 hectares.

Disclaimer: In this question time is not given, so the question is solved assuming that the water flows out of the canal for 1 hour.