#' @title Function FL liquid pressure recovery factor
#' @description for a control valve without attached fittings
#' @param x valve position
#' @param b steepness
#' @param d upper value
#' @param e the effective dose
#' @param fls liquid pressure recovery full open (max between fl and Flp/Fp)
#' @return fl liquid pressure recovery factor for
#'
#' @export
#'
fl_function <- function( x, b, d, e, fls ){
sigma_value <- 1/(fls^2) - 1
kv_kvs <- drm_LL3(x, b, d, e)
fl <- sqrt(1/(sigma_value * kv_kvs + 1))
return(fl)
}
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