A catchment area of 10 km² has recorded a rainfall of 25 mm/h. Assuming a runoff co-efficient of 0.3, the peak discharge from the catchment using the rational method is:
- A18.36 cumec
- B26.56 cumec
- C24.6 cumec
- D20.83 cumecCorrect
Solution
Concept
Rational method: peak runoff Q = C i A / 3.6 when i is in mm/h and A is in km².
Formula
Qp = C × i × A / 3.6 (Qp in m³/s, i in mm/h, A in km²)
Step-by-step solution
1. Data: A = 10 km², i = 25 mm/h, C = 0.3. 2. Use Qp = C × i × A / 3.6. 3. Qp = 0.3 × 25 × 10 / 3.6. 4. Qp = 75 / 3.6 = 20.83 m³/s. 5. Answer: 20.83 cumec, option (D).
Explanation
The rational method gives peak runoff from rainfall intensity, catchment area and runoff coefficient. With i in mm/h and A in km², we divide by 3.6 to get the answer in m³/s. So Q = 0.3 × 25 × 10 / 3.6 = 20.83 cumec.
Why the other options are wrong
A (18.36), B (26.56) and C (24.6) do not match C i A / 3.6. They come from wrong unit conversion or arithmetic errors.
Shortcut
C × i × A = 75. Then 75 / 3.6 ≈ 20.8.
Common mistake
Using 360 (for A in hectares) instead of 3.6 (for A in km²), or forgetting the conversion factor.
Correct answer: D) 20.83 cumec