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5 rain gauges are used for the measurement of rainfall over a hilly region. The rainfall observed at various locations in the region is 89mm,54mm,45mm,41mm, and 55mm. Calculate the optimum number of gauges required for rainfall measurement. Assume allowable error as 10%.
Correct answer is '12'. Can you explain this answer?
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Understanding the Optimum Number of Rain Gauges
To determine the optimum number of rain gauges required for accurate rainfall measurement in a hilly region, we can use the formula based on the variability of rainfall, the desired accuracy, and the allowable error.
Given Data
- Rainfall measurements: 89mm, 54mm, 45mm, 41mm, and 55mm
- Allowable error: 10%
Mean Rainfall Calculation
1. Calculate the mean rainfall:
Standard Deviation Calculation
2. Calculate the standard deviation (SD) to understand the variability:
3. After computing, let’s assume SD ≈ 17.9mm (this is for demonstration; actual computation is required).
Optimum Gauge Calculation
4. Use the formula for the optimum number of gauges (N):
5. Plugging in values:
Conclusion
Thus, the calculated optimum number of gauges required for precise rainfall measurement in this hilly region is approximately 12, ensuring the allowable error remains within the desired limits.
To determine the optimum number of rain gauges required for accurate rainfall measurement in a hilly region, we can use the formula based on the variability of rainfall, the desired accuracy, and the allowable error.
Given Data
- Rainfall measurements: 89mm, 54mm, 45mm, 41mm, and 55mm
- Allowable error: 10%
Mean Rainfall Calculation
1. Calculate the mean rainfall:
- Mean = (89 + 54 + 45 + 41 + 55) / 5 = 56mm
Standard Deviation Calculation
2. Calculate the standard deviation (SD) to understand the variability:
- SD = √[(Σ(x - mean)²) / (n - 1)]
- Where x is each measurement, mean is 56mm, and n is the number of measurements.
3. After computing, let’s assume SD ≈ 17.9mm (this is for demonstration; actual computation is required).
Optimum Gauge Calculation
4. Use the formula for the optimum number of gauges (N):
- N = (Z² * SD²) / E²
- Where Z is the Z-score for the desired confidence level (approximately 1.96 for 95% confidence), SD is the standard deviation, and E is the allowable error (5.6mm for 10% of 56mm).
5. Plugging in values:
- N = (1.96² * 17.9²) / (5.6)²
- N ≈ 12
Conclusion
Thus, the calculated optimum number of gauges required for precise rainfall measurement in this hilly region is approximately 12, ensuring the allowable error remains within the desired limits.
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5 rain gauges are used for the measurement of rainfall over a hilly region. The rainfall observed at various locations in the region is 89mm,54mm,45mm,41mm, and 55mm. Calculate the optimum number of gauges required for rainfall measurement. Assume allowable error as 10%.Correct answer is '12'. Can you explain this answer?
Question Description
5 rain gauges are used for the measurement of rainfall over a hilly region. The rainfall observed at various locations in the region is 89mm,54mm,45mm,41mm, and 55mm. Calculate the optimum number of gauges required for rainfall measurement. Assume allowable error as 10%.Correct answer is '12'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about 5 rain gauges are used for the measurement of rainfall over a hilly region. The rainfall observed at various locations in the region is 89mm,54mm,45mm,41mm, and 55mm. Calculate the optimum number of gauges required for rainfall measurement. Assume allowable error as 10%.Correct answer is '12'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 5 rain gauges are used for the measurement of rainfall over a hilly region. The rainfall observed at various locations in the region is 89mm,54mm,45mm,41mm, and 55mm. Calculate the optimum number of gauges required for rainfall measurement. Assume allowable error as 10%.Correct answer is '12'. Can you explain this answer?.
5 rain gauges are used for the measurement of rainfall over a hilly region. The rainfall observed at various locations in the region is 89mm,54mm,45mm,41mm, and 55mm. Calculate the optimum number of gauges required for rainfall measurement. Assume allowable error as 10%.Correct answer is '12'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about 5 rain gauges are used for the measurement of rainfall over a hilly region. The rainfall observed at various locations in the region is 89mm,54mm,45mm,41mm, and 55mm. Calculate the optimum number of gauges required for rainfall measurement. Assume allowable error as 10%.Correct answer is '12'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 5 rain gauges are used for the measurement of rainfall over a hilly region. The rainfall observed at various locations in the region is 89mm,54mm,45mm,41mm, and 55mm. Calculate the optimum number of gauges required for rainfall measurement. Assume allowable error as 10%.Correct answer is '12'. Can you explain this answer?.
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