Engineering Design Chapter 1a
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Transcript Engineering Design Chapter 1a
Piping Systems
mass mass Energy Energy Conservation Laws
;
IN
OUT
IN
OUT
for CV & st eady st at e
Ein,i Eout , j Eout ,k Ein,l if Ein , Eout on both side of Eq.
i
j
k
l
J m 2 Energy
Energy
J
e h head 2 ;
H Head m
m ass
N
kg s Weight
W pump
P V2
L V2
V2
V2
h H g ; ; gz ;
hp ; f
;K
; Cf T
; etc.
2
m
D 2
2
2
h
in,i
i
hout , j hout ,k
j
k
VD QD
4 Q
hin,l ; Re
D
A
l
circle
VD
shape
Cf T
Power Q P Q( h) m h ; f f (Re, ) ; K K
D
size,Re
Piping Systems- Example 1-1
or (a)
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
or (b)
Example 1-1 (Continue)
May be used to find any variable
if 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
Given
No pump
Re & fT
Solution
Satisfying conservation of mass and energy equations
we may solve or “guess and check” any piping problem …!
Hardy-Cross Method & Program
Qb 0
b
0
• For every node in a pipe network:
•
Iteration #
Since a node pressure must be unique,
then net pressure loss head around any loop
must be zero:
Eq.1
must be
h
f j 0 Eq.2
j
• If we assume Qb0 to satisfy Eq. 1, the Eq. 2 will not be satisfied.
• So we have to correct Qb0 for Qloop, so that Eq. 2 is satisfied,
i.e.:
Expressall h f j h f j (Q) as functionof Q . Since h 0f j 0 , then
j
previous
h next
(
Q
Q
)
h
(Q)
fj
fj
next
i
Q
dhfprevious
j
dQ
Q ; h next
0 Qloop Q
fj
j
Qi Qloop ...continue until convergence
Q
L
loop 1
2
loop
tol
Hardy-Cross Method & Program (2)
...loops
...pipes
Example 1-13 (cont.)
Hardy-Cross subroutine
...guess (LX1)
…while tolerance is not satisfied
…correction (LX1)
…new Qs (PX1)=(PXL)(LX1)
…result (PX1)
The results
after Hardy-Cross
iterations
Example 1-13
Loop 1
Loop 2
This 3rd loop is not independent (no new pipe in it)
2 loops
T
1 1 0
0 1 1
“Connection” matrix N
1 0
N 1 1
0 1
3 pipes
Example 1-13 (cont.)
" Connection" matrix:
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 & device
heads
Derivative of h(Q)
About constant
Qi guesses from conservation of mass
2 loops
3 pipes
“Connection” matrix N
...loops
...pipes
Example 1-13 (cont.)
Hardy-Cross subroutine
...guess
…while tolerance is not satisfied
Since assumed Q>0
…correction
…new Qs
…result
The results
after Hardy-Cross
iterations