borehole <- function(xx)
{
  ##########################################################################
  #
  # BOREHOLE FUNCTION
  #
  # Authors: Sonja Surjanovic, Simon Fraser University
  #          Derek Bingham, Simon Fraser University
  # Questions/Comments: Please email Derek Bingham at dbingham@stat.sfu.ca.
  #
  # Copyright 2013. Derek Bingham, Simon Fraser University.
  #
  # THERE IS NO WARRANTY, EXPRESS OR IMPLIED. WE DO NOT ASSUME ANY LIABILITY
  # FOR THE USE OF THIS SOFTWARE.  If software is modified to produce
  # derivative works, such modified software should be clearly marked.
  # Additionally, this program is free software; you can redistribute it 
  # and/or modify it under the terms of the GNU General Public License as 
  # published by the Free Software Foundation; version 2.0 of the License. 
  # Accordingly, this program is distributed in the hope that it will be 
  # useful, but WITHOUT ANY WARRANTY; without even the implied warranty 
  # of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 
  # General Public License for more details.
  #
  # For function details and reference information, see:
  # http://www.sfu.ca/~ssurjano/
  #
  ##########################################################################
  #
  # OUTPUT AND INPUT:
  #
  # y  = water flow rate
  # xx = c(rw, r, Tu, Hu, Tl, Hl, L, Kw)
  #
  ##########################################################################
  
  rw <- xx[1]
  r  <- xx[2]
  Tu <- xx[3]
  Hu <- xx[4]
  Tl <- xx[5]
  Hl <- xx[6]
  L  <- xx[7]
  Kw <- xx[8]
  
  frac1 <- 2 * pi * Tu * (Hu-Hl)
  
  frac2a <- 2*L*Tu / (log(r/rw)*rw^2*Kw)
  frac2b <- Tu / Tl
  frac2 <- log(r/rw) * (1+frac2a+frac2b)
  
  y <- frac1 / frac2
  return(y)
}