Final answer:
By calculating the volume of water that flows out of a 6 m wide and 1.5 m deep canal in 30 minutes, and dividing it by the required depth of standing water (8 cm), we find that 562950 m² of land can be irrigated.
Step-by-step explanation:
To calculate the area that will be irrigated in 30 minutes by water flowing in a canal, we need to use the given data. The canal is 6 m wide, 1.5 m deep, and the water is flowing with a speed of 10 km/h. Given that 8 cm of standing water is needed, we first need to find the volume of water that flows out of the canal in 30 minutes.
To find the flow rate of the water in m³/s, we convert the speed to m/s (10 km/h = 10000 m/3600 s ≈ 2.78 m/s) and then multiply by the cross-sectional area of the canal (6 m × 1.5 m = 9 m²).
Flow rate = speed × area = 2.78 m/s × 9 m² = 25.02 m³/s
Volume of water in 30 minutes (1800 seconds) = flow rate × time = 25.02 m³/s × 1800 s = 45036 m³
To find the irrigation area, we divide the volume by the depth of standing water required (0.08 m).
Irrigation area = volume / depth = 45036 m³ / 0.08 m = 562950 m²
Therefore, an area of 562950 m² will be irrigated.