R/hydrailic_functions.R

In ratral/wcontrolvalve: Meta Analysis Plunger Valves

#' @title  Velocity in a pipe
#'
#' @description This function calculates the velocity of the fluid in a
#'   circular pipe.
#'
#' @author Dr. Raúl Trujillo Álvarez \email{dr.ing.trujillo@gmail.com}
#'
#' @param flow cubic meter per second [m³/s]
#' @param dn diameter in meter [m]
#'
#' @return velocity in meter per second [m/s]
#' @export
#'
#' @examples
#' velocity(flow = 0.4, dn = 0.2)

  velocity <- function(flow, dn){
    velocity <- flow/((pi*dn^2)/4)
    return(velocity)
  }

#' @title  Reynolds number
#'
#' @description The Reynolds number (Re) is an important dimensionless quantity in fluid
#' mechanics used to help predict flow patterns in different fluid flow situations.
#'
#' @author Dr. Raúl Trujillo Álvarez \email{dr.ing.trujillo@gmail.com}
#'
#' @param flow cubic meter per second (m³/s)
#' @param dn diameter in meter (m)
#' @param temp temp is in °C
#'
#' @return reynolds number dimensionless quantity
#' @export
#'
#' @examples
#' reynolds_number(flow = 0.157, dn = 0.3,   temp = 20)
#' reynolds_number(flow = 3.72,  dn = 1.2,   temp = 14)
#' reynolds_number(flow = 0.042, dn = 0.150, temp = 14.5)
#'
  reynolds_number  <- function(flow,dn,temp = 15.6){
    reynolds <- (4*flow)/(pi*dn*kinematic_viscosity(temp)*1e-6)
    return(reynolds)
  }


#' @title Colebrook–White equation (Darcy friction factor formula)
#' @description The phenomenological Colebrook–White equation
#' (or Colebrook equation) expresses the Darcy friction factor f as a function
#' of Reynolds number Re and pipe relative roughness ε/Dh, fitting the data
#' of experimental studies of turbulent flow in smooth and rough pipes.
#' The equation can be used to (iteratively) solve for the Darcy–Weisbach
#' friction factor f.
#' [https://en.wikipedia.org/wiki/Darcy_friction_factor_formulae#Colebrook%E2%80%93White_equation]
#'
#' @param flow cubic meter per second (m³/s)
#' @param dn diameter in meter (m)
#' @param roughness roughness in (m)
#' @param temp temp is in °C
#'
#' @return the output from \code{\link{uniroot}} for the calculation of the
#'   root from the ecuation of Colebrook-White
#' @export
#' @examples
#' friction_colebrook(flow = 0.042, dn = 0.150, roughness = 1.5e-6, temp = 14.5)
#'
  friction_colebrook <- function(flow, dn, roughness, temp = 15.6){
    re <- reynolds_number(flow,dn,temp)
    r_roughness <- roughness/dn
    (-2*log10((r_roughness/3.7)-(5.02/re)*log10(r_roughness-(5.02/re)*log10(r_roughness/3.7+13/re))))^(-2)
  }

#' @title Darcy–Weisbach equation
#' @description In fluid dynamics, the Darcy–Weisbach equation is an empirical
#' equation, which relates the head loss, or pressure loss, due to friction
#' along a given length of pipe to the average velocity of the fluid flow
#' for an incompressible fluid.
#' The Darcy–Weisbach equation contains a dimensionless friction factor,
#' known as the Darcy friction factor. This is also variously called the
#' Darcy–Weisbach friction factor, friction factor, resistance coefficient,
#' or flow coefficient.
#' [https://en.wikipedia.org/wiki/Darcy%E2%80%93Weisbach_equation]
#' @author Dr. Raúl Trujillo Álvarez \email{dr.ing.trujillo@gmail.com}
#' @param flow cubic meter per second (m3/s)
#' @param pipe_length length of pipe  (m)
#' @param dn inner diameter of pipe  (m)
#' @param roughness internal roughness of the pipe in (m)
#' @param temp temperature in °C
#'
#' @return head loss (m)
#' @export
#'
#' @examples
#' darcy_weisbach( flow = 0.042,
#'                 pipe_length = 970,
#'                 dn = 0.150,
#'                 roughness = 1.5e-6,
#'                 temp = 14.5)
#'
    darcy_weisbach <- function(flow, pipe_length, dn, roughness, temp = 15.6){

      friction <- friction_colebrook (flow, dn, roughness, temp)
      v <- velocity(flow, dn)
      darcy <- friction*(pipe_length/dn)*((v^2)/(2*9.807))
      return(darcy)
    }


#' Minor Losses
#' @description Although they often account for a major portion of the head loss,
#' especially in process piping, the additional losses due to entries and exits,
#' fittings and valves are traditionally referred to as minor losses.
#' These losses represent additional energy dissipation in the flow, usually
#' caused by secondary flows induced by curvature or recirculation.
#' The minor losses are any head loss present in addition to the head loss for
#' the same length of straight pipe.
#' allows for easy integration of minor losses into the Darcy-Weisbach equation.
#' Zeta is the sum of all of the loss coefficients in the length of pipe, each
#' contributing to the overall head loss. Although Zeta appears to be a constant
#' coefficient, it varies with different flow conditions.
#' Factors affecting the value of K include: the exact geometry of the component
#' in question; the flow Reynolds Number; proximity to other fittings, etc.
#' (Tabulated values of K are for components in isolation - with long straight
#'  runs of pipe upstream and downstream.)
#' @param flow cubic meter per second (m3/s)
#' @param dn inner diameter of pipe  (m)
#' @param zeta loss coefficient
#'
#' @return minor losses in meter
#' @export
#'
#' @examples
#'  minor_losses( flow = 0.042,
#'                 dn = 0.150,
#'                 zeta = 3)

    minor_losses <- function(flow, dn, zeta){
      v <- velocity(flow, dn)
      losses <- zeta * ((v^2)/(2*9.807))
    }


#' Flow Calculation
#' @description Pressure Drop in Pipe with Losses (Determine flow)
#' @param pipe_length length of pipe  (m)
#' @param dn inner diameter of pipe  (m)
#' @param roughness internal roughness of the pipe in (m)
#' @param zeta loss coefficient
#' @param dp pressure diff.
#' @param temp temperature in °C
#' @importFrom stats uniroot
#'
#' @return flow in m3/s
#' @export
#'
flow_calculation <- function(pipe_length, dn, roughness, zeta, dp, temp = 15.6){

  root <- uniroot( function(x){ darcy_weisbach(x, pipe_length, dn, roughness, temp) +
                                minor_losses(x, dn, zeta) - dp } ,
                   lower = 0.0001,
                   upper = 10,
                   tol   = 1e-10)
  return(root$root)
}