Chapter 7, Problem 7.4.7P

12. (Horton's equation for infiltration rate, ). One can use Horton's equation to estimate the infiltration rate of water into soil if the rainfall rate exceeds the infiltration rate. The Horton's equation states that: f = fe+ (fo-fc) x e-kt where f is the infiltration rate (cm h:¹), fe is the equilibrium infiltration rate (cm h 1), fo is the initial infiltration rate (cm h:¹), k is an empirical constant (h:¹), and t is time (h). Horton's equation can be integrated to yield an equation that represents the total volume of water that would infiltrate over a given period: V=A₁ [Fxα= 4, 16+ V = A₁ [fx dt = A₁ [lfc + (fo-fc) × e-k¹] x dt = A₂ × [fet + fo=fc (1 - e-*)] 0 where As is the unit area (1 m²) and V is the volume (m³). Sothan loamy sand has the following characteristics: fe= 6.68 cm h¹, fo = 8.81 cm h¹, k = 1.40 h ¹. Assuming the rate of precipitation exceeds the rate of infiltration throughout the storm event. 12.1. Find the infiltration rate at times of 12, 30, 60, and 120 min.…

Question 2: After conduct an experiment, you found that the soil for the watershed have an initial rate of infiltration equal to 1.35 in./hr and a final capacity of 0.3 in./hr. Assuming that the time constant k = 0.4, calculate the soil infiltration capacity at the times 10 min, 15 min, 30 min, 1 hr, 2 hr, 4 hr, and 6 hr using Horton's equation. Infiltration

please answer part a