In the relation Δ = 8.64 B/D, if D is the duty in hectare/cumec and B is the number of days of base period, then Δ is the
- Adepth of water in cm
- Bduty in m
- Cdepth of water in mCorrect
- Drotation period
Solution
Concept
Delta is the total depth of water given to a crop. With D in ha/cumec and B in days, Δ = 8.64 B/D gives Δ in metres.
Formula
Δ = 8.64 B/D (Δ in m, B in days, D in ha/cumec)
Step-by-step solution
1. A flow of 1 cumec for B days gives a volume of 1 × 86400 × B m³. 2. This water irrigates D hectares = D × 104 m². 3. Depth Δ = 86400 B / (D × 104) = 8.64 B/D. 4. Volume in m³ divided by area in m² gives Δ in m.
Explanation
One cumec flowing for B days gives 86400B m³ of water. Spreading it over D hectares (D × 104 m²) gives a depth of 8.64B/D. Since the units are m³/m², Δ is in metres.
Why the other options are wrong
A: To get Δ in cm the constant would be 864, not 8.64. B: Duty is D (ha/cumec), not Δ. D: Rotation period is a different time quantity, not a depth.
Shortcut
8.64 means metres; 864 means centimetres.
Common mistake
Mixing up the constants 8.64 (m) and 864 (cm).
Correct answer: C) depth of water in m