Question

Total depth of irrigation applied for a wheat crop of 90 days base period is 70 cm, what will be the duty of water.

• A. 1111 ha/ cumec
• B. 672 ha/cumec
• C. 630 ha/cumec
• D. 1344 ha/cumec

Hint:

Ensure \(\Delta\) is converted from centimeters to meters before using the equation:
\[ \Delta = 70\text{ cm} = 0.70\text{ m} \] Failure to convert units is the most common error in this calculation.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Duty, Delta, and Base Period are key variables in irrigation planning:
- Base Period (B): The time in days from the first watering of a crop to its last watering before harvest.
- Delta (\(\Delta\)): The total depth of water required by a crop during its base period (in meters).
- Duty (D): The area of land in hectares that can be irrigated by a continuous flow of 1 cumec of water throughout the base period.

Step 2: Key Formula or Approach:
The relationship between Duty (D), Delta (\(\Delta\)), and Base period (B) is given by: \[ D = \frac{8.64 \times B}{\Delta} \] where:
\(D\) is in ha/cumec
\(B\) is in days
\(\Delta\) is in meters

Step 3: Detailed Explanation:
Given:
Base period, \(B = 90 \text{ days}\)
Delta, \(\Delta = 70 \text{ cm} = 0.70 \text{ m}\)
Substitute the values into the formula: \[ D = \frac{8.64 \times 90}{0.70} \] \[ D = \frac{777.6}{0.70} \approx 1110.86 \text{ ha/cumec} \] Rounding to the nearest whole number gives 1111 ha/cumec.

Step 4: Final Answer:
The duty of water is 1111 ha/cumec, matching option (A).