Water in a canal 40 decimetre wide and 16 decimetre deep is flowing with a velocity of 15 km/h. How much area (in m²) will it irrigate in 30 minutes if 12 cm of standing water is required for irrigation?

Given:

Width of canal = 40 dm

Depth of canal = 16 dm

Velocity of water flow = 15 km/h

Time for irrigation = 30 minutes

Required standing water = 12 cm

Formula Used:

Area irrigated = (Volume of water flowing in 30 minutes) / (Height of standing water)

Calculation:

Width and Depth in meters:

Width = 40 dm = 4 m

Depth = 16 dm = 1.6 m

Velocity in m/s:

Velocity = 15 km/h = 15,000 m/3600 s = 4.1667 m/s

Volume of water flowing in 30 minutes:

Time = 30 minutes = 30 × 60 s = 1800 s

Volume = Width × Depth × Velocity × Time

Volume = 4 m × 1.6 m × 4.1667 m/s × 1800 s

Volume = 4 × 1.6 × 4.1667 × 1800 = 48,000 m³

Height of standing water in meters:

Height = 12 cm = 0.12 m

Area irrigated:

Area = Volume / Height

Area = 48,000 m³ / 0.12 m

Area = 400,000 m²

The area irrigated is 400,000 m².