Seveneq3b

Name:	Seveneq3b - Flow Distribution in a Pipeline Network - Calculated Friction Factor
Source:	Cutlip, M. B. and Shacham, M, Problem Solving in Chemical
	Engineering with Numerical Methods, Prentice Hall Inc., 1999
Reference/s
Model:	7 implicit equations, indep. variables q01, q12, q13, q24, q23, q34, q45
	Lower difficulty level
	Constraints:none
	Discontinuities: Undefined for qij<=0
	Initial estimates: 1.(0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1) 2.(-0.1, -0.1, -0.1, -0.1,-0.1, -0.1, -0.1);
	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.	Flow Distribution in a Pipeline Network - Calculated Friction Factor |POLVER05_3
EXCEL FILE	f(q01)=q01-q12-q13 #
TEXT FILE	f(q12)=q12-q24-q23 #
POLYMATH FILE	f(q13)=q23+q13-q34 #
	f(q24)=q24+q34-q45 #
	f(q23)=k01*q01^2+k12*q12^2+k24*q24^2+k45*q45^2+deltaPUMP #
	f(q34)=k13*q13^2-k23*q23^2-k12*q12^2 #
	f(q45)=k23*q23^2+k34*q34^2-k24*q24^2 #
	rho=997.08 #
	D=0.154 #
	pi=3.1416 #
	mu=8.937e-4 #
	deltaPUMP=-15.e5 #
	ed=4.6e-5/D #
	fF01=1/(16*(log(ed/3.7-5.02*pi*D*mu/(4*q01*rho)*log(ed/3.7 +14.5*pi*D*mu/(4*q01*mu))))^2) #
	fF12=1/(16*(log(ed/3.7-5.02*pi*D*mu/(4*q12*rho)*log(ed/3.7 +14.5*pi*D*mu/(4*q12*rho))))^2) #
	fF24=1/(16*(log(ed/3.7-5.02*pi*D*mu/(4*q24*rho)*log(ed/3.7 +14.5*pi*D*mu/(4*q24*rho))))^2) #
	fF45=1/(16*(log(ed/3.7-5.02*pi*D*mu/(4*q45*rho)*log(ed/3.7 +14.5*pi*D*mu/(4*q45*rho))))^2) #
	fF13=1/(16*(log(ed/3.7-5.02*pi*D*mu/(4*q13*rho)*log(ed/3.7 +14.5*pi*D*mu/(4*q13*rho))))^2) #
	fF23=1/(16*(log(ed/3.7-5.02*pi*D*mu/(4*q23*rho)*log(ed/3.7 +14.5*pi*D*mu/(4*q23*rho))))^2) #
	fF34=1/(16*(log(ed/3.7-5.02*pi*D*mu/(4*q34*rho)*log(ed/3.7 +14.5*pi*D*mu/(4*q34*rho))))^2) #
	k01=32*fF01*rho*100/(pi^2*D^5) #
	k12=32*fF12*rho*300/(pi^2*D^5) #
	k24=32*fF24*rho*1200/(pi^2*D^5) #
	k45=32*fF45*rho*300/(pi^2*D^5) #
	k13=32*fF13*rho*1200/(pi^2*D^5) #
	k23=32*fF23*rho*300/(pi^2*D^5) #
	k34=32*fF34*rho*1200/(pi^2*D^5) #
	q01(0)=0.1
	q12(0)=0.1
	q13(0)=0.1
	q24(0)=0.1
	q23(0)=0.1
	q34(0)=0.1
	q45(0)=0.1
Variable/function values	Variable	Value	f(x)
	q01	0.1	-0.1
	q12	0.1	-0.1
	q13	0.1	0.1
	q24	0.1	0.1
	q23	0.1	1.2756E+06
	q34	0.1	8.7962E+05
	q45	0.100	4.3981E+05
	rho	997.080
	D	0.154
	pi	3.142
	mu	0.001
	deltaPUMP	-1500000
	ed	2.9870E-04
	fF01	3.6624E-03
	fF12	3.9280E-03
	fF24	3.9280E-03
	fF45	3.9280E-03
	fF13	3.9280E-03
	fF23	3.9280E-03
	fF34	3.9280E-03
	k01	1.3669E+07
	k12	4.3981E+07
	k24	1.7592E+08
	k45	4.3981E+07
	k13	1.7592E+08
	k23	4.3981E+07
	k34	1.7592E+08
Solution	Variable	Value	f(x)
	q01	0.110237410418775	-6.9389E-18
	q12	0.073312448014583	3.4694E-18
	q13	0.036924962404192	0
	q24	0.055534266884471	4.16E-17
	q23	0.017778181130112	0
	q34	0.054703143534304	1.1350E-09
	q45	0.110237410418774	8.15E-10
	rho	997.08
	D	0.154
	pi	3.1416
	mu	0.0008937
	deltaPUMP	-1500000
	ed	0.000298701298701
	fF01	0.003671115732774
	fF12	0.003991182117464
	fF24	0.004062318148155
	fF45	0.003911224372972
	fF13	0.004196830275841
	fF23	0.004547355921332
	fF34	0.004066622211574
	k01	13701643.97525590
	k12	44688667.20193340
	k24	181940666.64801900
	k45	43793392.33632400
	k13	187965115.07645600
	k23	50916061.81735610
	k34	182133434.45672300
Additional information	Initial guesses 2 and 3 do not satisfy the constraints