If a 10% risk of flooding is acceptable over the next 10 years, what design return period should be selected__________________?
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Answer: C. 1/(1-0.9°10)
Explanation
Flood risk probability formulas relate acceptable risk r, design life n, and return period t. The exact binomial risk equation transforms to solve for the return period t parameter. Algebraic rearrangement yields the exact mathematical expression presented in option C. Return period represents the statistical average time interval between floods of a given magnitude. Hydrological risk is the probability that a flood of specified size will occur at least once in n years. Engineers balance economic costs against acceptable flood risk probabilities when sizing structures.
Dam spillways and urban drainage systems are designed using specific return period flood thresholds. Risk analysis helps municipalities quantify infrastructure vulnerability to extreme weather events. Probability calculations ensure public safety while optimizing capital investment in flood defenses. Option A provides an incorrect mathematical structure lacking proper probability exponents. Option B fails to represent the correct algebraic inversion required for return period formulas. Option D includes an erroneous plus sign in the denominator violating binomial probability rules.
- Subject
- Engineering
- Category
- Civil Engineering
- Topic
- —
- Difficulty
- medium
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