Seveneq4

Name:	Seveneq4 - Water Distribution Network
Source:	Ingels, D. M. and Powers, J. E., Chem. Eng. Progress. 60(2), 65(1964)
Reference/s	Cutlip, M. B. and Shacham, M, Problem Solving in Chemical
	Engineering with Numerical Methods, Prentice Hall Inc., 1999
Model:	7 implicit equations, indep. variables q12, q14, q23, q43, q35, q65, q46
	Lower difficulty level
	Constraints:none
	Discontinuities: none
	Initial estimates: 1.(1000, 500, 600, 200, 300, 100, 400), 2.(-1000, -500, -600, -200, -300, -100,- 400);
	3.(0, 0, 0, 0, 0, 0, 0, 0, 0) 4.(10, 10, 10, 10, 10, 10, 10, 10, 10);
Solved by	Shacham, M., POLYMATH 5.1, build 19, April 22, 2001
Model Eqs.	Water Distribution Network |POLVER05_3
EXCEL FILE	f(q12)=1400-q12-q14 #
TEXT FILE	f(q14)=dp12+dp23-dp43-fc*q14^2*1000/(8^5) #
POLYMATH FILE	f(q23)=q12-420-q23 #
	f(q43)=q43+q23-420-q35 #
	f(q35)=q35+q65-420 #
	f(q65)=q46-140-q65 #
	f(q46)=dp43+dp35-fc*0.2572*q65^2-fc*0.1286*q46^2 #
	fc=8.7*10^(-4) #
	dp12=fc*2000*q12*q12/(12^5) #
	dp23=fc*1000*q23*q23/(8^5) #
	dp43=fc*2000*q43^2/(8^5) #
	dp35=fc*1000*q35^2/(6^5) #
	q12(0)=1000
	q14(0)=500
	q23(0)=600
	q43(0)=200
	q35(0)=300
	q65(0)=100
	q46(0)=400
Variable/function values	Variable	Value	f(x)
	q12	1000	-100
	q14	500	7.7892
	q23	600	-20
	q43	200	80
	q35	300	-20
	q65	100	160
	q46	400.000	-7.9453
	fc	0.001
	dp12	6.993
	dp23	9.558
	dp43	2.124
	dp35	10.0694
Solution	Variable	Value	f(x)
	q12	872.751598594702	0
	q14	527.248401405298	-4.4409E-15
	q23	452.751598594702	0
	q43	252.590830181724	-5.6843E-14
	q35	285.342428776427	5.6843E-14
	q65	134.657571223573	0
	q46	274.657571223573	0
	fc	0.00087
	dp12	5.32628405493795
	dp23	5.44238552020724
	dp43	3.38793035387858
	dp35	9.10952449128423