Section 4: Soil and Water Conservation Engineering
Hydrology
Subtopic: Infiltration – indices and equations
Question Statement:
A watershed of 4.8 km² generates 4.3 cm runoff from a rain storm of 4-hour duration. The measured rainfall intensities for this storm in successive 30-minute durations are given below:
| Time interval (min) | 0-30 | 30-60 | 60-90 | 90-120 | 120-150 | 150-180 | 180-210 | 210-240 |
|---|---|---|---|---|---|---|---|---|
| Rainfall intensity (cm h⁻¹) | 1.6 | 4.8 | 3.2 | 3.4 | 2.2 | 5.0 | 4.2 | 1.2 |
The value of $\Phi$-index for the watershed in cm h⁻¹ will be:
Options:
(A) 6.5
(B) 5.3
(C) 2.4
(D) 2.1
Official Answer Key:
C
Step-by-Step Solution & Explanation
• The Φ-index is the constant infiltration/abstraction rate such that rainfall intensity in excess of Φ, summed over all intervals where it exceeds Φ, equals the total measured runoff.
• Total rainfall depth = Σ(intensity × 0.5 h) = (1.6+4.8+3.2+3.4+2.2+5.0+4.2+1.2) × 0.5 = 25.6 × 0.5 = 12.8 cm.
• Trying Φ = 2.4 cm/h: intervals with intensity > 2.4 are 4.8, 3.2, 3.4, 5.0, 4.2 (5 intervals of 0.5 h each); intervals with 1.6, 2.2, 1.2 (≤ 2.4) contribute no runoff.
• Runoff = Σ(intensity – Φ)×0.5 for the 5 qualifying intervals = [(4.8+3.2+3.4+5.0+4.2) – 2.4×5]×0.5 = [20.6 – 12.0]×0.5 = 8.6×0.5 = 4.3 cm.
• This matches the given runoff of 4.3 cm exactly, confirming Φ = 2.4 cm/h.
• Final Answer: (C) 2.4
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