| hardycross {hydraulics} | 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 [ |
n_iter |
integer identifying the number of iterations to perform. |
units |
character vector that contains the system of units [options are
|
ret_units |
If set to TRUE the value(s) returned for pipe flows are of
class |
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}{\pi^{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:
\Delta{Q_i} = -\frac{\sum_{j=1}^{p_i} K_{ij}Q_j|Q_j|}{\sum_{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 \Delta{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
See Also
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")