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Calculate the total flow passing through a line

Source: R/utils.R
flow_through_line.Rd

flow_through_line() computes the integrated flow passing through a straight line at a right angle.

Usage

flow_through_line(
  aem,
  x0,
  y0,
  x1,
  y1,
  flow = c("discharge", "darcy"),
  split = FALSE,
  ...
)

Arguments

aem

aem object

x0

numeric, starting x location of line.

y0

numeric, starting y location of line.

x1

numeric, ending x location of line.

y1

numeric, ending y location of line.

flow

character specifying which flow variable to use. Possible values are discharge (default) and darcy. See flow().

split

logical, should the flow be split up into positive and negative flows (TRUE) or should they be summed (FALSE; default)? See details.

...

ignored

Value

If split = FALSE, a single value with the total flow of variable flow passing through the line at a right angle. If split = TRUE a named vector with the total positive and total negative value of flow passing through the line.

Details

The flow is computed normal to the line and integrated along the line length using stats::integrate(). The flow value is positive going to the left when looking in the direction of the line (i.e. to the left going from x0-y0 to x1-y1).

If split = FALSE (the default), a single value is returned which is the sum of the positive and negative flows perpendicular to the line. If split = TRUE, both the positive and negative component of the total flow through the line are returned.

If the line corresponds to a line element, the integration might fail. Try to perturbate the line vertices slightly in that case.

See also

flow(), dirflow()

Examples

rf <- constant(-1000, 0, hc = 10)
uf <- uniformflow(TR = 100, gradient = 0.001, angle = -45)
m <- aem(k = 10, top = 10, base = 0, n = 0.2, rf, uf)

xg <- seq(-500, 500, l=100); yg <- seq(-300, 300, l=100)
contours(m, xg, yg, col='dodgerblue', nlevels=20)

x0 <- -200
y0 <- -50
x1 <- 300
y1 <- 100
lines(matrix(c(x0, y0, x1, y1), ncol = 2, byrow = TRUE))


flow_through_line(m, x0, y0, x1, y1)
#> [1] -45.96194
flow_through_line(m, x1, y1, x0, y0) # reverse direction of line
#> [1] 45.96194

w <- well(125, 200, 150)
m <- aem(k = 10, top = 10, base = 0, n = 0.2, rf, uf, w)
contours(m, xg, yg, col='dodgerblue', nlevels=20)
lines(matrix(c(x0, y0, x1, y1), ncol = 2, byrow = TRUE))


flow_through_line(m, x0, y0, x1, y1, flow = 'darcy')
#> [1] 0.1633028
flow_through_line(m, x0, y0, x1, y1, flow = 'darcy', split = TRUE)
#>  positive  negative 
#>  1.369686 -1.206383