Irrigation planning: A tube well delivers 4 m^3/hour and operates 20 hours per day during the season. If the irrigation interval is 20 days and the required depth per irrigation is 7 cm, what is the maximum command area (in m^2)?
Civil Engineering
GATE Exam Questions
Difficulty: Easy
Choose an option
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A1.71 × 10^4 m^2
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B1.14 × 10^4 m^2
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C22.9 × 10^4 m^2
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D2.29 × 10^4 m^2
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E3.20 × 10^4 m^2
Answer
Correct Answer: 2.29 × 10^4 m^2
Explanation
Introduction / Context:Command area calculations translate discharge and operating schedule into the land area that can be adequately irrigated at a specified interval and depth. This is essential for sizing well fields and planning water distribution.
Given Data / Assumptions:
- Discharge Q = 4 m^3/hour.
- Operating time = 20 hours/day.
- Irrigation interval = 20 days.
- Depth per irrigation = 7 cm = 0.07 m.
Concept / Approach:
Total volume available per interval equals discharge × operating time over the interval. Command area A = Volume / required depth. Uniform application and negligible losses are assumed.
Step-by-Step Solution:
Compute daily volume: V_day = 4 * 20 = 80 m^3/day.Compute interval volume: V = 80 * 20 = 1600 m^3.Depth requirement: d = 0.07 m.Area: A = V / d = 1600 / 0.07 = 22857.14 m^2 ≈ 2.29 × 10^4 m^2.Verification / Alternative check:
Units check: m^3 / m = m^2 → correct. Result matches option D.
Why Other Options Are Wrong:
- Values smaller or larger than 2.29 × 10^4 m^2 result from arithmetic errors (wrong interval volume or depth conversion).
Common Pitfalls:
- Forgetting to convert 7 cm to 0.07 m.
- Multiplying instead of dividing by depth when computing area.
Final Answer:
2.29 × 10^4 m^2