Section 4: Soil and Water Conservation Engineering
Hydrology
Subtopic: Runoff estimation
Question Statement:
The observed rainfall of a 12 h duration event is given in the table below:
| Time (h) | 0 | 2 | 4 | 6 | 8 | 10 | 12 |
|---|---|---|---|---|---|---|---|
| Cumulative rainfall (cm) | 0 | 0.64 | 2.64 | 5.64 | 6.00 | 6.80 | 10.80 |
If the $\Phi$-index of the storm is 0.46 cm/h, the total direct runoff of the event in mm will be ______
Official Answer Key:
62.4 to 62.4
Step-by-Step Solution & Explanation
Break the cumulative rainfall into 2-hour increments: 0.64, 2.00, 3.00, 0.36, 0.80, 4.00 cm. Loss per 2-h interval at φ=0.46 cm/h is 0.46×2 = 0.92 cm. Direct runoff is generated only in intervals where rainfall exceeds this loss (rainfall < loss produces no runoff in that interval, per the φ-index method): interval 1 (0.64<0.92: no runoff), interval 2 (2.00−0.92=1.08), interval 3 (3.00−0.92=2.08), interval 4 (0.36<0.92: no runoff), interval 5 (0.80<0.92: no runoff), interval 6 (4.00−0.92=3.08). Total direct runoff = 1.08+2.08+3.08 = 6.24 cm = 62.4 mm, matching the accepted band exactly.
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