Question Bank • QB_SWCE_HYD_004 NAT • 2 Marks

Section 4: Soil and Water Conservation Engineering

Hydrology

Subtopic: Infiltration – indices and equations

Question Statement:

In Horton's infiltration capacity equation $f_t = f_c + (f_0 - f_c) e^{-k t}$, the initial infiltration capacity is $f_0 = 10.0\text{ cm/h}$, ultimate steady infiltration capacity is $f_c = 2.0\text{ cm/h}$, and the decay constant is $k = 1.20\text{ h}^{-1}$. The infiltration capacity $f_t$ at $t = 2.0\text{ hours}$ in $\text{cm/h}$ is ________ (round off to 2 decimal places).

Answer Key:

2.73

Step-by-Step Solution & Explanation

From Horton's equation: $f_t = f_c + (f_0 - f_c) e^{-k t}$ Substituting given values: • $f_0 = 10.0\text{ cm/h}$ • $f_c = 2.0\text{ cm/h}$ • $k = 1.20\text{ h}^{-1}$ • $t = 2.0\text{ h} \implies k t = 2.40$ $e^{-2.40} \approx 0.090718$ $f_t = 2.0 + (10.0 - 2.0) \times 0.090718 = 2.0 + 8.0 \times 0.090718 = 2.0 + 0.7257 = 2.7257\text{ cm/h} \approx 2.73\text{ cm/h}$
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