Question

A water resources project with an expected life of 25 years has to be designed for an acceptable risk of 5% against a design flood. The return period for the design flood (in years) is ........... (rounded off to the nearest integer).

• A. 488
• B. 485
• C. 490
• D. 495

Hint:

When calculating the return period, ensure that the risk and expected life are correctly substituted into the formula. The return period is the inverse of the probability of exceedance.

Answer 1

The Correct Option is A

The return period \( T \) is calculated using the formula: \[ {Risk} = 1 - \left(1 - \frac{1}{T}\right)^n, \] where:
- \( n = 25 \) years (the expected life of the project),
- Risk = 5%.
Substituting the values into the formula:
\[ 0.05 = 1 - \left(1 - \frac{1}{T}\right)^{25}. \] Solving for \( T \), we get: \[ T = \frac{1}{1 - (0.95)^{1/25}} \approx 488 \, {days}. \] Thus, the return period is approximately 488 days, which corresponds to option (A).