R/verruijt_s.R

In ToonVanDaele/hydranalytic: A Collection of Some Analytic Hydrological Equations

#' Verruijt - drawdown
#'
#' @description drawdown in an unconfed aquifer with stationary flow and
#' recharge (Verruijt, 1970). page 55 equation 5.20
#'     When r > r0 the drawdown (s) is set to 0.
#'     When the drawdown (s) is larger than the aquifer thickness (D) the
#'     drawdown is set equal to the the thickness and a warning message is
#'     returned.
#'
#' Verruijt A. (1970). Theory of Groundwater Flow. London: Macmillan.
#'
#' @param Q abstraction (L^3/T)
#' @param D saturated thickness (L)
#' @param Kh horizontal conductivity (L/T)
#' @param Rech recharge (L/T)
#' @param r distance at which to calculate the drawdown(L)
#' @param r0 radius of influence(L)
#'
#' @export
#'
#' @return s drawdown (L)

#------------------------------------------------------------------------------
verruijt_s <- function(r, r0, Q, D, Kh, Rech) {


  s <- ifelse(r < r0,
              ifelse(D^2 - (Q / (pi * Kh)) * log(r0 / r) - (Rech / (2 * Kh))  * (r^2 - r0^2) > 0,
                     D - (D^2 - (Q / (pi * Kh)) * log(r0 / r) - (Rech / (2 * Kh))  * (r^2 - r0^2))^0.5,
                     D),
              0)

  return(s)
}