Question

Relationship between delta (d), Duty (D) and base period (B) is given as

• A. \(d = 8.6 \frac{B}{D}\)
• B. \(D = 8.6 \frac{B}{d}\)
• C. \(B = 8.6 \frac{d}{D}\)
• D. \(D = 8.6 \frac{d}{B}\)

Hint:

Direct formula: $\Delta = \frac{8.64 B}{D}$ (meters) or $\Delta = \frac{864 B}{D}$ (cm). Inverse: $D = \frac{8.64 B}{\Delta}$.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Duty (\(D\)), Delta (\(d\) or \(\Delta\)), and Base Period (\(B\)) are fundamental irrigation terms connecting crop water volume, command area, and time duration.
Key Formula or Approach:
\[ \Delta = \frac{8.64 \times B}{D} \text{ (meters)} \quad \text{or} \quad d = 8.6 \frac{B}{D} \]
where \(B\) is in days, \(D\) is in hectares/cumec, and \(d\) is in meters.

Step 2: Detailed Explanation:
Deriving the relationship from first principles:
1 cumec of water flowing continuously for \(B\) days delivers a total volume:
\[ V = 1\text{ m}^3\text{/s} \times (B \times 24 \times 3600\text{ s}) = 86,400 B \text{ m}^3 \]
This volume covers an area of \(D\) hectares (\(D \times 10^4\text{ m}^2\)) to a uniform depth \(d\) (meters):
\[ d = \frac{V}{\text{Area}} = \frac{86,400 B}{D \times 10^4} = 8.64 \frac{B}{D} \approx 8.6 \frac{B}{D} \]

Step 3: Final Answer:
Therefore, the relationship is \(d = 8.6 \frac{B}{D}\), matching option (A).