Irrigation design – compute depth of water (Δ) from duty and base period Given duty D = 1428 hectares per cumec and base period B = 120 days for a crop, determine the required depth of water Δ in metres (use the standard relation with consistent units).

Introduction:
In canal irrigation, duty (D), base period (B), and delta (Δ) are interrelated. Designers often compute the seasonal depth of water required over the command area from the available discharge and cropping period. This problem tests the standard conversion using consistent units.

Given Data / Assumptions:

• Duty D = 1428 ha per cumec.
• Base period B = 120 days.
• Standard relation Δ (m) = 8.64 * B / D when B is in days and D in ha/cumec.

Concept / Approach:

The constant 8.64 comes from 1 cumec = 86400 m^3/day and 1 hectare = 10,000 m^2. Spreading 86400 m^3 over 1 ha for 1 day gives a depth of 8.64 m. Scaling by B days and dividing by D (ha per cumec) yields the seasonal depth Δ in metres.

Step-by-Step Solution:

Verification / Alternative check:

Order-of-magnitude: seasonal depths for many crops are below 1.5 m. The result 0.73 m is realistic and within typical ranges for moderate-duty crops.

Why Other Options Are Wrong:

102.8 and 1.38 arise from unit mistakes (missing the 10,000 m^2 per ha or misplacing decimals). 0.01 is two orders too small. 0.52 does not satisfy the formula with given D and B.

Common Pitfalls:

Forgetting to use B in days; misapplying duty units; rounding too early and losing accuracy.

Final Answer:

0.73