To find out how much area the water can irrigate, we need to first calculate the volume of water flowing in the canal and then determine how much area that volume can cover with the desired standing water depth.
1. **Calculate the volume of water flowing per second:** The dimensions of the canal tell us the width is 15m, the depth is 6m, and the speed of the water is 10 km/h. We first convert the speed into meters per second:
10 km/h = (10 * 1000 m) / (3600 s) = 2.78 m/s
2. **Calculate the cross-sectional area of the canal:** The cross-sectional area (A) of the canal can be calculated by multiplying the width and depth:
A = width × depth = 15m × 6m = 90 m²
3. **Calculate the volume of water flowing through the canal per second:** The volume flow rate (Q) can be obtained by multiplying the cross-sectional area by the speed:
Q = A × speed = 90 m² × 2.78 m/s = 250.2 m³/s
4. **Calculate the total volume of water in 30 minutes:** We need to find out how much water flows in 30 minutes (which is 1800 seconds):
Total volume = Q × time = 250.2 m³/s × 1800 s = 450360 m³
5. **Determine the area that can be irrigated with the desired standing water:** To find the area (Area) that can be irrigated with a standing water depth of 8 cm (which is 0.08 m), we can use the formula:
Area = Total volume / desired water depth = 450360 m³ / 0.08 m = 5629500 m²
6. **Convert the area into hectares (if desired):** 1 hectare is 10,000 m², so:
Area in hectares = 5629500 m² / 10000 = 562.95 hectares
Thus, the water in the canal can irrigate approximately 562.95 hectares in 30 minutes with a standing water depth of 8 cm.