GATE 2023 CE (CE1) – Question 61
In Horton's equation fitted to the infiltration data for a soil, the initial infiltration capacity is 10 mm/h; final infiltration capacity is 5 mm/h; and the exponential decay constant is 0.5 /h. Assuming that the infiltration takes place at capacity rates, the total infiltration depth (in mm) from a uniform storm of duration 12 h is _____ (round off to one decimal place).
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Correct answer: 69.65 to 70.35
Explanation
Horton's equation is $f = f_c + (f_0 - f_c)e^{-kt}$. The total depth is $F = \int_0^{12}f\,dt = f_ct + \frac{f_0 - f_c}{k}(1 - e^{-kt}) = 5 \times 12 + \frac{5}{0.5}(1 - e^{-6}) = 60 + 10 \times 0.99752 = 69.98 \approx 70.0$ mm.