Seveneq3a

Name: Seveneq3a - Flow Distribution in a Pipeline Network - Constant 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: none

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 - Constant 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 #

fF=0.005 #

rho=997.08 #

D=0.154 #

pi=3.1416 #

deltaPUMP=-15.e5 #

k01=32*fF*rho*100/(pi^2*D^5) #

k12=32*fF*rho*300/(pi^2*D^5) #

k24=32*fF*rho*1200/(pi^2*D^5) #

k45=32*fF*rho*300/(pi^2*D^5) #

k13=32*fF*rho*1200/(pi^2*D^5) #

k23=32*fF*rho*300/(pi^2*D^5) #

k34=32*fF*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 2.0457E+06

q34 0.1 1.1197E+06

q45 0.100 5.5984E+05

fF 0.005

rho 997.080

D 0.154

pi 3.142

deltaPUMP -1500000

k01 1.8661E+07

k12 5.5984E+07

k24 2.2394E+08

k45 5.5984E+07

k13 2.2394E+08

k23 5.5984E+07

k34 2.2394E+08

Solution 1 Variable Value f(x)

q01 0.098136927428176 6.9389E-18

q12 0.064819554408160 -3.4694E-18

q13 0.033317373020015 0

q24 0.049372394599739 0

q23 0.015447159808421 0

q34 0.048764532828436 -2.9104E-11

q45 0.098136927428176 -1.16E-10

fF 0.005

rho 997.08

D 0.154

pi 3.1416

deltaPUMP -1500000

k01 18661416.54556850

k12 55984249.63670540

k24 223936998.54682100

k45 55984249.63670540

k13 223936998.54682100

k23 55984249.63670540

k34 223936998.54682100

Solution 2 Variable Value f(x)

q01 -0.098136927428176 -6.9389E-18

q12 -0.064819554408160 3.4694E-18

q13 -0.033317373020015 6.94E-18

q24 -0.049372394599739 0

q23 -0.015447159808421 0

q34 -0.048764532828436 -2.9104E-11

q45 -0.098136927428176 1.16E-10

fF 0.005

rho 997.08

D 0.154

pi 3.1416

deltaPUMP -1500000

k01 18661416.54556850

k12 55984249.63670540

k24 223936998.54682100

k45 55984249.63670540

k13 223936998.54682100

k23 55984249.63670540

k34 223936998.54682100

Name:	Seveneq3a - Flow Distribution in a Pipeline Network - Constant 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: none

	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 - Constant 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)=k01q01^2+k12q12^2+k24q24^2+k45q45^2+deltaPUMP #
	f(q34)=k13q13^2-k23q23^2-k12*q12^2 #
	f(q45)=k23q23^2+k34q34^2-k24*q24^2 #
	fF=0.005 #
	rho=997.08 #
	D=0.154 #
	pi=3.1416 #
	deltaPUMP=-15.e5 #
	k01=32fFrho100/(pi^2D^5) #
	k12=32fFrho300/(pi^2D^5) #
	k24=32fFrho1200/(pi^2D^5) #
	k45=32fFrho300/(pi^2D^5) #
	k13=32fFrho1200/(pi^2D^5) #
	k23=32fFrho300/(pi^2D^5) #
	k34=32fFrho1200/(pi^2D^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	2.0457E+06
	q34	0.1	1.1197E+06
	q45	0.100	5.5984E+05
	fF	0.005
	rho	997.080
	D	0.154
	pi	3.142
	deltaPUMP	-1500000
	k01	1.8661E+07
	k12	5.5984E+07
	k24	2.2394E+08
	k45	5.5984E+07
	k13	2.2394E+08
	k23	5.5984E+07
	k34	2.2394E+08

Solution 1	Variable	Value	f(x)
	q01	0.098136927428176	6.9389E-18
	q12	0.064819554408160	-3.4694E-18
	q13	0.033317373020015	0
	q24	0.049372394599739	0
	q23	0.015447159808421	0
	q34	0.048764532828436	-2.9104E-11
	q45	0.098136927428176	-1.16E-10
	fF	0.005
	rho	997.08
	D	0.154
	pi	3.1416
	deltaPUMP	-1500000
	k01	18661416.54556850
	k12	55984249.63670540
	k24	223936998.54682100
	k45	55984249.63670540
	k13	223936998.54682100
	k23	55984249.63670540
	k34	223936998.54682100

Solution 2	Variable	Value	f(x)
	q01	-0.098136927428176	-6.9389E-18
	q12	-0.064819554408160	3.4694E-18
	q13	-0.033317373020015	6.94E-18
	q24	-0.049372394599739	0
	q23	-0.015447159808421	0
	q34	-0.048764532828436	-2.9104E-11
	q45	-0.098136927428176	1.16E-10
	fF	0.005
	rho	997.08
	D	0.154
	pi	3.1416
	deltaPUMP	-1500000
	k01	18661416.54556850
	k12	55984249.63670540
	k24	223936998.54682100
	k45	55984249.63670540
	k13	223936998.54682100
	k23	55984249.63670540
	k34	223936998.54682100