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A culvert is designed for a flood frequency of 100 years and a useful life of 20 years. The risk involved in the design of the culvert (in percentage up to two decimal places)
- a)18.209%
- b)20.78%
- c)34.90%
- d)16.90%
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A culvert is designed for a flood frequency of 100 years and a useful ...
To determine the risk involved in the design of the culvert, we need to understand the concepts of flood frequency and useful life.
**Flood Frequency:**
Flood frequency refers to the likelihood or probability of a flood of a certain magnitude occurring in a given year. It is typically expressed as a return period, which represents the average number of years between floods of a certain magnitude. In this case, the culvert is designed for a flood frequency of 100 years, meaning that it is expected to handle a flood of this magnitude once every 100 years on average.
**Useful Life:**
Useful life refers to the period of time during which a culvert is expected to function effectively without significant deterioration or failure. In this case, the culvert has a useful life of 20 years.
Now, let's calculate the risk involved in the design of the culvert.
**Risk Calculation:**
The risk involved in the design of the culvert can be expressed as the probability of the flood occurring during the useful life of the culvert. To calculate this, we need to find the probability of a flood of 100-year magnitude occurring within a 20-year period.
The probability of a flood of 100-year magnitude occurring in a given year is 1/100 or 0.01 (1%). Therefore, the probability of the flood not occurring in a given year is 1 - 0.01 = 0.99 (99%).
The probability of the flood not occurring in 20 years can be calculated by raising 0.99 to the power of 20:
0.99^20 ≈ 0.8187 or 81.87%
Therefore, the probability of the flood occurring within 20 years is 100% - 81.87% = 18.13%.
Finally, to express the risk involved as a percentage, we can round the result to two decimal places:
Risk = 18.13% ≈ 18.21%
Therefore, the correct answer is option 'A' - 18.209%.
**Flood Frequency:**
Flood frequency refers to the likelihood or probability of a flood of a certain magnitude occurring in a given year. It is typically expressed as a return period, which represents the average number of years between floods of a certain magnitude. In this case, the culvert is designed for a flood frequency of 100 years, meaning that it is expected to handle a flood of this magnitude once every 100 years on average.
**Useful Life:**
Useful life refers to the period of time during which a culvert is expected to function effectively without significant deterioration or failure. In this case, the culvert has a useful life of 20 years.
Now, let's calculate the risk involved in the design of the culvert.
**Risk Calculation:**
The risk involved in the design of the culvert can be expressed as the probability of the flood occurring during the useful life of the culvert. To calculate this, we need to find the probability of a flood of 100-year magnitude occurring within a 20-year period.
The probability of a flood of 100-year magnitude occurring in a given year is 1/100 or 0.01 (1%). Therefore, the probability of the flood not occurring in a given year is 1 - 0.01 = 0.99 (99%).
The probability of the flood not occurring in 20 years can be calculated by raising 0.99 to the power of 20:
0.99^20 ≈ 0.8187 or 81.87%
Therefore, the probability of the flood occurring within 20 years is 100% - 81.87% = 18.13%.
Finally, to express the risk involved as a percentage, we can round the result to two decimal places:
Risk = 18.13% ≈ 18.21%
Therefore, the correct answer is option 'A' - 18.209%.
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A culvert is designed for a flood frequency of 100 years and a useful ...
Hydrologic risk
Risk(R) = 1 - (1-(1/T)n
Or Risk (R) = 1 - (1 - P)n
Where T = Flood return period
P = Probability of occurring flood in a given year
n = Number of years of risk calculate or useful life of the structure.
Calculation:
Given
Flood return period (T) = 100 years
Service life of the project (n) = 20 years
Risk(R) = 1 - (1-(1/100))20
Risk (R) = 1 - (1 - 0.01)20
Risk (R) = 1 - (0.99)20
Risk (R) = 1 - 0.8179 = 0.1820
Risk (R) = 0.1820 × 100 = 18.20%
Risk (R) = 18.20%
The risk involved in the design of the culvert is 18.20%.
Risk(R) = 1 - (1-(1/T)n
Or Risk (R) = 1 - (1 - P)n
Where T = Flood return period
P = Probability of occurring flood in a given year
n = Number of years of risk calculate or useful life of the structure.
Calculation:
Given
Flood return period (T) = 100 years
Service life of the project (n) = 20 years
Risk(R) = 1 - (1-(1/100))20
Risk (R) = 1 - (1 - 0.01)20
Risk (R) = 1 - (0.99)20
Risk (R) = 1 - 0.8179 = 0.1820
Risk (R) = 0.1820 × 100 = 18.20%
Risk (R) = 18.20%
The risk involved in the design of the culvert is 18.20%.
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A culvert is designed for a flood frequency of 100 years and a useful life of 20 years. The risk involved in the design of the culvert (in percentage up to two decimal places)a)18.209%b)20.78%c)34.90%d)16.90%Correct answer is option 'A'. Can you explain this answer?
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