Green-Ampt cylindrical horizontal flow time

This function models saturated outward radial flow from a circular saturated surface horizontally into a soil profile. The assumptions are the same as in the Green-Ampt equation, except that there is no effect of gravity because all flow is assumed to be horizontal. The equation includes \(r_f\), which is the radius to the edge of the front from the center of the cylinder:

$$t = \frac{\Delta \theta}{4 (h_b - h_0)} \Big[r_b^2 + r_f^2 (2 \ln \frac{r_f}{r_b} - 1) \Big]$$

It is straightforward to convert between cumulative infiltration \(F_c\) and \(r_f\):

$$F_c = \pi (r_f^2 - r_b^2) \Delta \theta$$

and the reverse:

$$r_f = \sqrt{ \frac{F_c}{\pi \Delta \theta} + r_b^2}$$

Usage

get_greenampt_cyl_horiz_time(theta_0, theta_s, F_c, Ksat, h_b, h_0, r_b)

Arguments

theta_0

Soil volumetric water content prior to event

theta_s

Soil porosity

F_c

cumulative radial infiltration through the cylinder (units of area or L^2)

Ksat

Saturated hydraulic conductivity

h_b

Hydraulic head at soil surface boundary

h_0

Hydraulic head in soil prior to event

r_b

radius from the centroid to the free water--soil boundary

Value

Returns the time at which a cumulative amount of infiltration occurs.

Examples

library(units)
r_b <- set_units(2, "ft") # length
theta_0 <- 0.2 # unitless
theta_s <- 0.35 # unitless
F_c <- set_units(10, "ft^2") # units of length^2
Ksat <- set_units(0.2, "cm/h") # length / time
h_b <- set_units(6, "ft") # hydraulic head (length)
h_0 <- set_units(-10, "cm") # hydraulic head (length)
times <- get_greenampt_cyl_horiz_time(theta_0, theta_s, F_c, Ksat, h_b, h_0, r_b)