The total depth of the water required by a crop Delta (m) during the entire period the crop is calculated as _______ where B is no. of days, D is Duty in hectares / cumec
- A0.864 × B / D
- B8.64 × B / DCorrect
- C864 × B / D
- D8640 × B / D
Solution
Concept
The relationship between Delta (total water depth), Duty (area irrigated per unit flow), and Base Period (time duration).
Formula
Δ = 8.64 × B / D
Step-by-step solution
1. Let B be the Base Period in days. This is the time from the first watering to the last watering of the crop. 2. Let D be the Duty in hectares per cumec (ha/cumec). This means 1 m³/s of water flow can irrigate D hectares of land. 3. Let Delta (Δ) be the total depth of water in meters (m) required by the crop. 4. Total volume of water supplied = Discharge × Time = (1 m³/s) × (B × 24 × 60 × 60 seconds). 5. Total volume of water supplied = 86,400 × B m³. 6. This volume covers an area of D hectares. Since 1 hectare = 10,000 m², the area is D × 10,000 m². 7. Depth (Δ) = Volume / Area = (86,400 × B) / (D × 10,000). 8. Δ = 8.64 × B / D. Answer: (B) 8.64 × B / D
Explanation
This formula links the time the crop grows (B) with the efficiency of water use (D). If the depth Delta is needed in meters, the constant is 8.64. If Delta is needed in centimeters, the constant becomes 864.
Why the other options are wrong
A: This value is 10 times smaller than the correct constant. C: This is the formula when Delta is required in centimeters (cm), not meters. D: This value is 1000 times larger than the correct constant.
Shortcut
Remember: Delta (m) = 8.64 B/D and Delta (cm) = 864 B/D.
Common mistake
Students often confuse the units and pick 864 when the question asks for the answer in meters.
Correct answer: B) 8.64 × B / D