- 2082 Bhadra · 12 marks
Flood hydrograph from 2-h UH, 5.2 cm rainfall
Short answer
Total rainfall 5.2 cm over 6 h with φ-index 0.2 cm/h yields net excess 4.0 cm, divided equally into three 2-h blocks of 1.333 cm. Superpose given 2-h UH ordinates with baseflow 15 m³/s; peak flood discharge 655.0 m³/s at 12 h.
Calculate the flood discharge from the outlet of the catchment if the total rainfall of 5.2 cm occurred at an interval of 6 hours using the following 2 UH. Assume base flow = 15 cumes and infiltration index of 0.2 cm/hr.
| Time (hr) | 0 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2hr-UH (cumes) | 0 | 30 | 55 | 90 | 130 | 170 | 180 | 110 | 60 | 35 | 20 | 0 |
Reading of the problem. A total rainfall of 5.2 cm falls in 6 hours. The UH is 2-h, so the storm is taken as three consecutive 2-h periods with equal rain.
Rainfall excess
- Total loss = = 0.2 × 6 = 1.2 cm
- Total excess = 5.2 − 1.2 = 4.0 cm
- Per 2-h period: 4.0 / 3 = 1.333 cm (rain per period = 5.2/3 = 1.733 cm; loss per period = 0.4 cm)
Superposition
| t (h) | UH (m³/s) | 1.33333 cm × UH | 1.33333 cm × UH | 1.33333 cm × UH | Base | Q (m³/s) |
|---|---|---|---|---|---|---|
| 0 | 0.00 | 0.0 | 0.0 | 0.0 | 15.0 | 15.0 |
| 2 | 30.00 | 40.0 | 0.0 | 0.0 | 15.0 | 55.0 |
| 4 | 55.00 | 73.3 | 40.0 | 0.0 | 15.0 | 128.3 |
| 6 | 90.00 | 120.0 | 73.3 | 40.0 | 15.0 | 248.3 |
| 8 | 130.00 | 173.3 | 120.0 | 73.3 | 15.0 | 381.7 |
| 10 | 170.00 | 226.7 | 173.3 | 120.0 | 15.0 | 535.0 |
| 12 | 180.00 | 240.0 | 226.7 | 173.3 | 15.0 | 655.0 |
| 14 | 110.00 | 146.7 | 240.0 | 226.7 | 15.0 | 628.3 |
| 16 | 60.00 | 80.0 | 146.7 | 240.0 | 15.0 | 481.7 |
| 18 | 35.00 | 46.7 | 80.0 | 146.7 | 15.0 | 288.3 |
| 20 | 20.00 | 26.7 | 46.7 | 80.0 | 15.0 | 168.3 |
| 22 | 0.00 | 0.0 | 26.7 | 46.7 | 15.0 | 88.3 |
| 24 | 0.00 | 0.0 | 0.0 | 26.7 | 15.0 | 41.7 |
| 26 | 0.00 | 0.0 | 0.0 | 0.0 | 15.0 | 15.0 |
Answer: peak flood ≈ 655.0 m³/s at t = 12 h (the last column gives the flood hydrograph; it returns to the 15 m³/s base flow after t = 26 h).
✓ Answer checked by Claude Sonnet 5.5
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