The parameters in Horton’s infiltration equation [f(t)

Home » Hydrology » Hydrology miscellaneous » Question

The parameters in Horton’s infiltration equation [f(t) = f_c + (f_o – f_c)^e–kt] are given as, f_o = 7.62 cm/ hour, fc = 1.34 cm/ hour and k = 4.182/hour. For assumed continuous ponding the cumulative infiltration at the end of 2 hours is

1. 2.68 cm
2. 1.50 cm
3. 1.34 cm
4. 4.18 cm

Correct Option: D

ƒ_t = ƒ_c + (ƒ₀ – ƒ_c) e^–kt
ƒ_t = 1.34 + (7.62 – 1.34) e^–4.182×t
= 1.34 + 6.28 e^–4.82t
2 hours of infiltration
⇒ ∫²₂ƒ_tdt ∫²₀(1.34 + 6.28.e^–4.182t)dt

= 1.34 × 2[t]²₀ +	6.28	[e^{-4.182t]²₀}
	-4.182

= 1.34 × 2 -	6.28	(e^{-4.182×2 - e^-4.182×0)}
	-4.182

= 4.18 cm