Section 4: Soil and Water Conservation Engineering
Hydrology
Subtopic: Runoff estimation
Question Statement:
The maximum rainfall with a return period of 25 years is given below for a watershed having a time of concentration of 47.65 minutes:
| Time (min) | 10 | 20 | 30 | 40 | 60 |
|---|---|---|---|---|---|
| Rainfall depth (mm) | 52.50 | 55.00 | 57.50 | 60.00 | 65.00 |
In this watershed, 2.0 km² area has cultivated sandy soil ($C = 0.2$) and the remaining 3.0 km² has cultivated clay soil ($C = 0.7$). The peak rate of runoff from the watershed is:
Options:
(A) 4.29 m³ s⁻¹
(B) 5.41 m³ s⁻¹
(C) 42.99 m³ s⁻¹
(D) 54.13 m³ s⁻¹
Official Answer Key:
D
Step-by-Step Solution & Explanation
Rainfall depth at t=47.65 min (linear interpolation between 40 min:60.00 mm and 60 min:65.00 mm): d = 60.00 + (65.00−60.00)×(47.65−40)/(60−40) = 60.00+1.9125 = 61.91 mm. Intensity, i = d/(t_c in hours) = 61.91/(47.65/60) = 77.96 mm/h. Weighted runoff coefficient: C_w = (2.0×0.2+3.0×0.7)/(2.0+3.0) = 2.5/5.0 = 0.50. Rational formula (A in km², i in mm/h): Q = 0.278·C·i·A = 0.278×0.50×77.96×5.0 = ≈54.13 m³/s.
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