Model Answer
0 min readIntroduction
Hydrological data analysis is fundamental in water resource management, particularly crucial for the planning and construction of large infrastructure projects like dams. Prior to dam construction, comprehensive studies are undertaken to assess water availability, flood risks, and sediment transport. These studies rely heavily on statistical analysis of historical river flow data to ensure the dam's safety and optimal operation. Understanding the central tendency (mean), dispersion (standard deviation), and relative variability (coefficient of variation) of river flow is essential for informed decision-making in water resource engineering. This analysis helps in designing appropriate spillways, storage capacity, and operational strategies for the dam.
Data Analysis of River Flow
Let's assume the following river flow data (in litres per minute) is provided in the table (as the question refers to a table but doesn't provide the data, we will create a sample dataset for demonstration):
| River Flow (Litres/Minute) |
|---|
| 4800 |
| 5000 |
| 5200 |
| 5500 |
| 5800 |
| 6000 |
| 6200 |
| 6500 |
| 6800 |
| 7000 |
1. Calculating the Mean
The mean (average) river flow is calculated as the sum of all flow values divided by the number of values.
Mean (μ) = (4800 + 5000 + 5200 + 5500 + 5800 + 6000 + 6200 + 6500 + 6800 + 7000) / 10 = 59800 / 10 = 5980 litres/minute
2. Calculating the Standard Deviation
The standard deviation (σ) measures the dispersion of the data around the mean. It is calculated as the square root of the variance.
First, calculate the variance (σ2):
- Calculate the difference between each data point and the mean.
- Square each of these differences.
- Sum the squared differences.
- Divide the sum by the number of data points minus 1 (for sample standard deviation).
Variance (σ2) = Σ(xi - μ)2 / (n-1)
Variance = [(-180)2 + (-980)2 + (-780)2 + (-480)2 + (-180)2 + (20)2 + (220)2 + (520)2 + (820)2 + (1020)2] / 9
Variance = (32400 + 960400 + 608400 + 230400 + 32400 + 400 + 48400 + 270400 + 672400 + 1040400) / 9
Variance = 3900000 / 9 = 433333.33
Standard Deviation (σ) = √Variance = √433333.33 ≈ 658.3 litres/minute
3. Calculating the Coefficient of Variation
The coefficient of variation (CV) is a standardized measure of dispersion, expressed as a percentage. It is calculated as the standard deviation divided by the mean.
CV = (σ / μ) * 100 = (658.3 / 5980) * 100 ≈ 11.01%
4. Portion of Water Flow Less Than 5200 Litres per Minute
From the given data, we can directly count the number of flow values less than 5200 litres per minute. There are three values (4800, 5000, and 5200) that are less than 5200.
Portion of water flow less than 5200 litres/minute = (Number of values less than 5200 / Total number of values) * 100 = (3 / 10) * 100 = 30%
Conclusion
In conclusion, the mean river flow is 5980 litres per minute, with a standard deviation of approximately 658.3 litres per minute and a coefficient of variation of 11.01%. This indicates a moderate level of variability in the river flow. Furthermore, 30% of the observed water flow occurs at less than 5200 litres per minute. These statistical parameters are crucial for the safe and efficient design and operation of the proposed dam, informing decisions related to storage capacity, spillway design, and flood control measures.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.