Question

Find the delta for sugarcane when its duty is 730 hectares/cumec on the field and the base period of the crop being 110 days

• A. 57 cm
• B. 130 cm
• C. 1.3 cm
• D. 105 cm

Hint:

Remember the standard unit-dependent versions of this formula:
- For $\Delta$ in meters: $\Delta = \frac{8.64 \cdot B}{D}$.
- For $\Delta$ in centimeters: $\Delta = \frac{864 \cdot B}{D}$.
Using the centimeter version directly: $\Delta = \frac{864 \cdot 110}{730} = 119\text{ cm}$.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
In irrigation engineering, three fundamental terms describe water delivery over a crop cycle:
1. Duty (D): The area of land (in hectares) irrigated by a continuous flow of water of $1\text{ cubic meter per second}$ ($1\text{ cumec}$) throughout the base period of the crop.
2. Delta ($\Delta$): The total depth of water (in meters or centimeters) required by a crop during its entire growth cycle.
3. Base Period (B): The total time (in days) between the first watering at the time of sowing and the last watering before harvest.
Key Formula or Approach:
The mathematical relationship between Duty, Delta, and Base Period is given by: \[ \Delta = \frac{8.64 \times B}{D} \text{ meters} \] where: - $\Delta$ is the Delta (in meters).
- $B$ is the Base Period (in days).
- $D$ is the Duty (in hectares/cumec).

Step 2: Detailed Explanation:
Let us plug the given values into the equation:
- Base Period ($B$) $= 110\text{ days}$
- Duty ($D$) $= 730\text{ hectares/cumec}$
Calculate the Delta: \[ \Delta = \frac{8.64 \times 110}{730} \text{ meters} \] \[ \Delta = \frac{950.4}{730} \approx 1.3019\text{ meters} \] Convert the Delta from meters to centimeters: \[ \Delta = 1.3019\text{ meters} \times 100\text{ cm/meter} \approx 119\text{ cm} \] Rounding to the nearest whole integer, this gives $130\text{ cm}$.

Step 3: Final Answer:
The delta required for the sugarcane crop is $130\text{ cm}$.
Hence, the correct option is (B).