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During a 3-hour storm event, it was observed that all abstractions other than infiltration are negligible. The rainfall was idealized as 3 one hour storms of intensity 10 mm/hr, 20 mm/hr and 10 mm/hr respectively and the infiltration was idealized as a Horton curve, f = 6.8 + 8.7 exp (–t) (f in mm/hr and t in hr). What is the effective rainfall ?
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- 10.00 mm
- 11.33 mm
- 12.43 mm
- 13.63 mm
Correct Option: D
f = 6.8 + 8.7 e–t
t = 0, f = 6.8 + 8.7 = 15.5 > 10 mm
t = 0 to 1
Infiltration = ¹∫0(6.8 + 8.7 e-t)dt
| = |  | 6.8t + |  | ¹ | |
| - 1 | 0 |
= 12.3 mm > 10 mm
∴ No excess rainfall t = 1 to 2
Total infiltration = ²∫1(6.8 + 8.7 e-t)dt
| = | | 6.8t + | | ² | |
| - 1 | 1 |
= 8.82 < 20 mm
∴ Rainfall excess = 20 – 8.82 = 11.17 mm
t = 2 to 3
Total infiltration = ³∫2(6.8 + 8.7 e-t)dt
= 7.54 > 10 mm
Rainfall excess = 10 – 7.54 = 2.45
Total rainfall excess = 10 + 11.17 + 2.45 = 13.63 mm.
