Final answer:
The irrigated area can be calculated by finding the volume of water flowing through the canal in 30 minutes and dividing it by the required depth of standing water. At a flow speed of 10 km/hr, a canal 6 m wide and 1.5 m deep will irrigate 56.295 hectares in 30 minutes with 8 cm of water.
Step-by-step explanation:
The question asks about the area that can be irrigated by water flowing through a canal that is 6 meters wide and 1.5 meters deep, with a flow speed of 10 km/hour, assuming 8 cm of standing water is needed. To calculate the irrigated area, we need to determine the volume of water flowing through the canal over 30 minutes and divide that by the depth of water required for irrigation.
Firstly, we convert the flow speed to meters per second: 10 km/hour is approximately 2.78 m/s. The volume of water flowing per second is then the speed multiplied by the cross-sectional area of the canal (6 m × 1.5 m), which gives us 25.02 m³/s. Over 30 minutes, or 1800 seconds, this amounts to 45,036 m³ of water.
To find the irrigated area, we divide this volume by the depth needed, which is 0.08 meters (or 8 cm). The irrigated area is therefore 562,950 m², or 56.295 hectares since 1 hectare equals 10,000 m².