# Water in a canal 6 m wide and 1.5 m deep is flowing with a speed of 10 km/h.

Question:

Water in a canal 6 m wide and 1.5 m deep is flowing with a speed of 10 km/h. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed?

Solution:

Depth of water in the canal = 1.5 m

Width of canal = 6 m

Volume of water flowing through the canal in 60 minutes $=(10 \times 1000) \times 6 \times 1.5 \mathrm{~cm}^{3}$

$(\because$ Speed $=10 \mathrm{~km} / \mathrm{hr}=10 \times 1000 \mathrm{~m}$ per $\mathrm{hr})$

Volume of water flowing through canal in 30 minutes

$=10000 \times 9 \times \frac{\mathbf{3 0}}{\mathbf{6 0}} \mathrm{m}^{3}=45000 \mathrm{~m}^{3}$

Let the required area be $x \mathrm{~m}^{2}$.

Then $x \times \frac{\boldsymbol{8}}{\mathbf{1 0 0}}=45000$

$\left(\because 8 \mathrm{~cm}\right.$ deep water $=\frac{\mathbf{8}}{\mathbf{1 0 0}} \mathrm{m}$ deep $)$

$\Rightarrow x=\frac{\mathbf{4 5 0 0 0 0 0}}{\mathbf{8}} \mathrm{m}^{2}=562500 \mathrm{~m}^{2}=\frac{\mathbf{5 6 2 5 0 0}}{\mathbf{1 0 0 0 0}}$ hectares $=56.25$ hectares