Question

What would be the estimated peak rate of runoff (\(\text{m}^3\text{/s}\)) from a 100 ha catchment having value of runoff coefficient (C) as 0.3 and intensity of rainfall for duration equal to time of concentration as 120 mm/hr?

• A. \(12\text{ m}^3\text{/s}\)
• B. \(30\text{ m}^3\text{/s}\)
• C. \(10\text{ m}^3\text{/s}\)
• D. \(3\text{ m}^3\text{/s}\)

Hint:

Standard Rational Formula: $Q = \frac{CIA}{360} = \frac{0.3 \times 120 \times 100}{360} = 10\text{ m}^3\text{/s}$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The Rational Formula is widely used to estimate peak stormwater discharge from small agricultural and urban watersheds when rainfall duration equals the time of concentration.
Key Formula or Approach:
\[ Q_p = \frac{C \cdot I \cdot A}{360} \]
where \(Q_p\) is peak runoff (\(\text{m}^3\text{/s}\)), \(C\) is runoff coefficient, \(I\) is rainfall intensity (mm/hr), and \(A\) is drainage area (ha).

Step 2: Detailed Explanation:
Given data:
- Catchment area: \(A = 100\text{ ha}\)
- Runoff coefficient: \(C = 0.3\)
- Rainfall intensity: \(I = 120\text{ mm/hr}\)
Applying the Rational Method:
\[ Q_p = \frac{C \times I \times A}{360} \]
\[ Q_p = \frac{0.3 \times 120 \times 100}{360} = \frac{3600}{360} = 10\text{ m}^3\text{/s} \]

Step 3: Final Answer:
Therefore, the estimated peak rate of runoff is \(10\text{ m}^3\text{/s}\), corresponding to option (C).