Delta–Duty–Base period relation (consistent units) For irrigation planning with Delta Δ in cm, Duty D in hectare per cumec, and Base period B in days, select the correct relationship connecting these parameters.

Introduction:
The Delta–Duty–Base period relation converts continuous discharge availability into seasonal depth over an area. Getting the unit conversions right is essential in irrigation scheduling and canal capacity design.

Given Data / Assumptions:

• Δ in centimeters.
• D in hectare per cumec (ha per m^3/s).
• B in days.

Concept / Approach:

One cumec supplies 86,400 m^3 in a day. Spread over 1 hectare (10,000 m^2), this gives a depth of 8.64 m per day. Converting meters to centimeters multiplies by 100, giving 864 cm per day. Therefore, for B days and duty D (ha per cumec), the seasonal depth is Δ = (864 * B) / D.

Step-by-Step Solution:

Verification / Alternative check:

If Δ is required in meters, the relation becomes Δ(m) = 8.64 * B / D, consistent with standard texts.

Why Other Options Are Wrong:

Option D uses the meter-based constant 8.64 with Δ in cm—unit mismatch. Other options rearrange incorrectly or multiply instead of divide by D.

Common Pitfalls:

Mixing hectare with square meter, forgetting to multiply by 100 when converting m to cm, or inverting duty inadvertently.

Final Answer:

Δ = 864 * B / D