Kor watering and outlet factor: If the optimum depth of kor watering for a crop is 15.12 cm, determine the outlet factor (hectares per cumec) for a four-week (28-day) kor period.

Introduction / Context:
Outlet factor expresses the area (in hectares) that can be adequately supplied by 1 cumec of discharge during the base (kor) period for a specified kor depth. It is frequently used in canal design and water distribution planning for seasonal irrigation demands.

Given Data / Assumptions:

• Kor depth Δ = 15.12 cm = 0.1512 m.
• Kor period B = 4 weeks = 28 days.
• Standard duty relationship: D (ha/cumec) = 8.64 * B / Δ, where B is in days and Δ in metres.

Concept / Approach:
Duty (or outlet factor for kor watering) relates discharge to irrigable area over a period and depth. The constant 8.64 converts cumec-days to hectare-metres because 1 cumec operating for 1 day supplies 86,400 m^3 and 1 ha-m equals 10,000 m^3. Therefore 86,400 / 10,000 = 8.64 ha-m per cumec-day.

Step-by-Step Solution:
1) Use D = 8.64 * B / Δ.2) Substitute B = 28 days, Δ = 0.1512 m.3) Compute D = 8.64 * 28 / 0.1512.4) D = 241.92 / 0.1512 = 1600 ha per cumec.

Verification / Alternative check:
Cross-check units: ha per cumec = (ha-m per cumec-day * days) / m depth → ha. Values are typical for kor periods of a few weeks and depths around 0.15 m, so 1600 is reasonable.

Why Other Options Are Wrong:

• 1000, 1200, 1400: all are below the computed duty based on the standard formula and given data.
• 2000: exceeds the computed value; would require a smaller kor depth or longer base period.

Common Pitfalls:

• Forgetting to convert centimetres to metres for Δ.
• Using weeks instead of days in the formula without multiplying by 7.

Final Answer:
1600 ha per cumec.