hardycross: Applies the Hardy-Cross method to solve for pipe flows in a...
In hydraulics: Basic Pipe and Open Channel Hydraulics

hardycross

R Documentation

Applies the Hardy-Cross method to solve for pipe flows in a network.

Description

This function uses the Hardy-Cross method to iteratively solve the equations for conservation of mass and energy in a water pipe network. The input consists of a data frame with the pipe characteristics and lists of the pipes in each loop (listed in a clockwise direction) and the initial guesses of flows in each pipe (positive flows are in a clockwise direction).

Usage

hardycross(
  dfpipes = dfpipes,
  loops = loops,
  Qs = Qs,
  n_iter = 1,
  units = c("SI", "Eng"),
  ret_units = FALSE
)

Arguments

`dfpipes`	data frame with the pipe data. Format is described above, but must contain a column named _ID_.
`loops`	integer list defining pipes in each loop of the network.
`Qs`	numeric list of initial flows for each pipe in each loop [m^3/s or ft^3/s]
`n_iter`	integer identifying the number of iterations to perform.
`units`	character vector that contains the system of units [options are `SI` for International System of Units and `Eng` for English (US customary) units.
`ret_units`	If set to TRUE the value(s) returned for pipe flows are of class `units` with units attached to the value. [Default is FALSE]

Details

The input data frame with the pipe data must contain a pipe ID column with the pipe numbers used in the loops input list. There are three options for input column of the pipe roughness data frame:

Column Name	Approach for Determining K
ks	f calculated using Colebrook equation, K using Darcy-Weisbach
f	f treated as fixed, K calculated using Darcy-Weisbach
K	K treated as fixed

In the case where absolute pipe roughness, ks (in m or ft), is input, the input pipe data frame must also include columns for the length, L and diameter, D, (both in m or ft) so K can be calculated. In this case, a new f and K are calculated at each iteration, the final values of which are included in the output. If input K or f columns are provided, values for ks are ignored. If an input K column is provided, ks and f are ignored. If the Colebrook equation is used to determine f, a water temperature of 20^{o}C or 68^{o}F is used.

The number of iterations to perform may be specified with the n_iter input value, but execution stops if the average flow adjustment becomes smaller than 1 percent of the average flow in all pipes.

The Darcy-Weisbach equation is used to estimate the head loss in each pipe segment, expressed in a condensed form as h_f = KQ^{2} where:

K = \frac{8fL}{π^{2}gD^{5}}

If needed, the friction factor f is calculated using the Colebrook equation. The flow adjustment in each loop is calculated at each iteration as:

Δ{Q_i} = -\frac{∑_{j=1}^{p_i} K_{ij}Q_j|Q_j|}{∑_{j=1}^{p_i} 2K_{ij}Q_j^2}

where i is the loop number, j is the pipe number, p_i is the number of pipes in loop i and Δ{Q_i} is the flow adjustment to be applied to each pipe in loop i for the next iteration.

Value

Returns a list of two data frames:

dfloops - the final flow magnitude and direction (clockwise positive) for each loop and pipe
dfpipes - the input pipe data frame, with additional columns including final Q

Examples


#              A----------B --> 0.5m^3/s
#              |\   (4)   |
#              | \        |
#              |  \       |
#              |   \(2)   |
#              |    \     |(5)
#              |(1)  \    |
#              |      \   |
#              |       \  |
#              |        \ |
#              |   (3)   \|
# 0.5m^3/s --> C----------D

#Input pipe characteristics data frame. With K given other columns not needed
dfpipes <- data.frame(
ID = c(1,2,3,4,5),                     #pipe ID
K = c(200,2500,500,800,300)            #resistance used in hf=KQ^2
)
loops <- list(c(1,2,3),c(2,4,5))
Qs <- list(c(0.3,0.1,-0.2),c(-0.1,0.2,-0.3))
hardycross(dfpipes = dfpipes, loops = loops, Qs = Qs, n_iter = 1, units = "SI")

hydraulics documentation built on Dec. 7, 2022, 1:11 a.m.