Section 4: Soil and Water Conservation Engineering
Hydrology
Subtopic: Drought and its classification
Question Statement:
The infiltration capacity of a basin is described by the Horton's equation, I = 2 + e^(−3t), where I is in cm h⁻¹ and the duration, t is in hours. If the duration of the storm event is 2 hours, the depth of the infiltration in the last 1 hour of the storm event in mm is
Options:
(A) 5
(B) 10
(C) 20
(D) 25
Official Answer Key:
C
Step-by-Step Solution & Explanation
Cumulative infiltration depth in the last 1 hour (from t=1h to t=2h) = ∫₁² I dt = ∫₁² (2+e⁻³ᵗ) dt = [2t − (1/3)e⁻³ᵗ]₁²
= (4 − (1/3)e⁻⁶) − (2 − (1/3)e⁻³) = 2 − (1/3)(e⁻⁶−e⁻³) = 2 − (1/3)(0.00248−0.04979) = 2+0.01577 = 2.0158 cm ≈ 20.2 mm. Rounding to the nearest option, Answer: (C) 20. (Verified by direct numerical integration.)
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