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Name: |
Threeq8 - Pipe and Pump Network |
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Source: |
Carnahan, B. and Wilkes, J.O., Digital
Computing and |
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Numerical Methods,John
Wiley, New York, 1973 |
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Reference/s |
Engineering with Numerical Methods, Prentice Hall Inc., 1999 |
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Model: |
3 implicit equations, indep. variables p4,
Q24 and Q34 |
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Lower difficulty level |
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Constraints: p>0, Q24>=0 and Q34>=0 |
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Discontinuities: none |
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Initial estimates: 1. p4=50, Q24=100, Q34=100;
2. p4=50, Q24=-100, Q34=100; |
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3. p4=50, Q24=-100, Q34=-100; 4. p4=50, Q24=100,
Q34=-100; |
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Solved by |
Shacham, M., POLYMATH 5.1, build 19, April
5, 2001 |
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Model Eqs. |
Pipe and Pump Network |POLVER05_3 |
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EXCEL
FILE |
f(p4)=70*32.3-p4*(144*32.2/62.35)+k45*(Q24+Q34)^2
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TEXT
FILE |
f(Q24)=(p4-p2)*(144*32.2/62.35)+k24*Q24^2
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POLYMATH
FILE |
f(Q34)=(p4-p3)*(144*32.2/62.35)+k34*Q34^2
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p2=156.6-0.00752*Q24^2 # |
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p3=117.1-0.00427*Q34^2 # |
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D34=2.067/12 # |
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D24=1.278/12 # |
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D45=2.469/12 # |
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fF=0.015 # |
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pi=3.1416 # |
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k24=2*fF*125/((60*7.48)^2*(pi*D24^2/4)^2*D24)
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k34=2*fF*125/((60*7.48)^2*(pi*D34^2/4)^2*D34)
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k45=2*fF*145/((60*7.48)^2*(pi*D45^2/4)^2*D45)
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p4(0)=50 |
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Q24(0)=100 |
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Q34(0)=100 |
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Variable/function values |
Variable |
Value |
f(x) |
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p4 |
50 |
2.3407E+03 |
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Q24 |
100 |
1.9694E+04 |
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Q34 |
100 |
1.7587E+02 |
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p2 |
81.4 |
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p3 |
74.4 |
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D34 |
0.1723 |
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D24 |
0.1065 |
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D45 |
0.2058 |
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fF |
0.0150 |
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pi |
3.1416 |
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k24 |
2.2029 |
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k34 |
0.1990 |
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k45 |
0.0950 |
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Solution 1 |
Variable |
Value |
f(x) |
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p4 |
57.12556038475 |
1.1369E-12 |
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Q24 |
51.75154563498 |
8.1855E-12 |
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Q34 |
92.91811138918 |
1.3642E-12 |
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p2 |
136.45976698340 |
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p3 |
80.23377893896 |
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D34 |
0.1723 |
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D24 |
0.1065 |
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D45 |
0.2058 |
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fF |
0.0150 |
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pi |
3.1416 |
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k24 |
2.20290484696 |
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k34 |
0.19904332800 |
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k45 |
0.09495165682 |
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Infeasible solution 1 |
Variable |
Value |
f(x) |
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p4 |
33.85347741000 |
5.6843E-14 |
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Q24 |
-57.48733479292 |
-1.8190E-12 |
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Q34 |
109.47131250920 |
4.5475E-13 |
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Infeasible solution 2 |
Variable |
Value |
f(x) |
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p4 |
57.12556053860 |
4.5475E-13 |
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Q24 |
-51.75154635713 |
-6.3665E-12 |
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Q34 |
-92.91811127982 |
6.8212E-13 |
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Infeasible solution 3 |
Variable |
Value |
f(x) |
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p4 |
33.85347740990 |
-2.2737E-13 |
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Q24 |
57.48733479339 |
3.6380E-12 |
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Q34 |
-109.47131250920 |
-9.0949E-13 |