piping systems. piping systems- example 1-1 or (a)or (b) type i (explicit) problem : given: l i, d...
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Piping Systems
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shape;)(Re,;)(
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Eq. of sideboth on , if
statesteady & CVfor
Lawson Conservati
OUT
Energy
IN
Energy;
OUT
mass
IN
mass
Piping Systems- Example 1-1
or (a)
or (b)
Type I (explicit) problem :Given: Li, Di, Qi; Find Hi
Type II (implicit) problem :Given: Li, Di, Hi; Find Qi
Type III (implicit) problem :Given: Li, Hi Qi; Find Di
Example 1-1 (Continue)
May be used to find any variableif the others are given, i.e.
for any type of problem (I, II, III)
Example 1-2 with MathCAD
For inlet (0.78)& exit (1), p.18
For valve (55) &elbows (2*30),NOTE: K=CfT
Re & fT
No pumpGiven
Solution
Satisfying conservation of mass and energy equationswe may solve or “guess and check” any piping problem …!
Hardy-Cross Method & Program
• For every node in a pipe network:
• Since a node pressure must be unique, then net pressure loss head around any loop must be zero:
2.0 Eqhj
bemustf j
• If we assume Q
to satisfy Eq. 1, the Eq. 2 will not be satisfied.
• So we have to correct Qfor Qloop, so that Eq. 2 is satisfied,
i.e.:
tolQQQQ
QQhQdQ
dhQhQQh
hQhh
L
looplooploopi
nexti
loopj
nextf
previousfprevious
fnextf
jfff
j
j
jj
jjj
1
2
0
econvergencuntile...continu
0;)()(
then,0 Since.Q offunction as)( all Express
1.00 EqQ
Iteration #
Hardy-Cross Method & Program (2)
Example 1-13 (cont.)H
ardy
-Cro
ss s
ubro
utin
e
...loops...pipes
...guess (LX1)
…correction (LX1)
…while tolerance is not satisfied
…new Qs (PX1)=(PXL)(LX1)…result (PX1)
The resultsafter Hardy-Cross
iterations
Example 1-13
Loop 1
Loop 2
This 3rd loop is not independent (no new pipe in it)
Example 1-13 (cont.)
T
N
110
011
10
11
01
:matrix "Connection"
“Con
nect
ion”
mat
rix
N
2 loops
3 pi
pes
Example 1-13 (cont.)
d’s
L’s
units & g
Pump and reservoirs
dhd/dQ derivative
roughnesses
Kin. viscosity
Example 1-13 (cont.)
Re & fT
Laminar & turbulent f
No minor losses
Example 1-13 (cont.)
Loss & deviceheads
Derivative of h(Q)
Qi guesses from conservation of mass
“Connection” matrix N2 loops
3 pipes
About constant
Example 1-13 (cont.)
The resultsafter Hardy-Cross
iterations
...loops...pipes
...guess
…correction
…while tolerance is not satisfied
…new Qs…result
Har
dy-C
ross
sub
rout
ine
Since assumed Q>0
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