In an irrigated field, the crop requires 60 cm of water in 15 days, while the effective rainfall during that period is recorded as 15 cm. Find the duty at the head of field. Assume no losses.
- A288 ha/cumecCorrect
- B268 ha/cumec
- C278 ha/cumec
- D298 ha/cumec
Solution
Concept
Duty is found from the net water depth (δ) the canal must supply and the base period: D = 8.64 B / Δ.
Formula
D = 8.64 × B / Δ (D in ha/cumec, B in days, Δ in m)
Step-by-step solution
1. Total water needed by crop = 60 cm. 2. Effective rainfall = 15 cm. 3. Net irrigation water (Δ) = 60 − 15 = 45 cm = 0.45 m. 4. Base period B = 15 days. 5. D = 8.64 × 15 / 0.45 = 129.6 / 0.45 = 288 ha/cumec.
Explanation
Rain gives 15 cm of water, so the canal must give only 45 cm. Using D = 8.64 B / Δ with B = 15 days and Δ = 0.45 m, the duty at field head is 288 ha/cumec. No losses are assumed, so this is also the field duty.
Why the other options are wrong
B, C and D come from wrong arithmetic or rounding. Only 8.64 × 15 / 0.45 = 288 gives the exact value.
Shortcut
Use net depth: 8.64 × 15 / 0.45 = 288.
Common mistake
Using full 60 cm without subtracting rainfall gives D = 216 ha/cumec. Also, Δ must be in metres, not cm.
Correct answer: A) 288 ha/cumec