Oneeq19a

Name:	Oneeq19a - Compressibility factor from the RK equation - three solutions
Source:	Cutlip, M. B. and Shacham, M, Problem Solving in Chemical
	Engineering with Numerical Methods (2nd Ed), Prentice Hall Inc.,
Reference/s
Model:	1 implicit equation, indep. variable name: z
	Average difficulty level
	Constraints: z>0
	Discontinuities: none in the range of interest
	Initial range: zmin=-0.5, zmax=1.2
Solved by	Shacham, M., POLYMATH 5.1, build 19, April 1, 2001
Model Eqs.	Compressibility factor from the RK equation - three solutions |POLVER05_1
EXCEL FILE	f(z)=z^3-z^2-Q*z-r #
TEXT FILE	P = 200 #
POLYMATH FILE	Pc=33.5 #
	T= 631*2 #
	Tc=126.2 #
	Pr=P/Pc #
	Tr=T/Tc #
	Asqr=0.4278*Pr/(Tr^2.5) #
	B=0.0867*Pr/Tr #
	Q=B^2+B-Asqr #
	r=Asqr*B #
	p=(-3*Q-1)/3 #
	q=(-27*r-9*Q-2)/27 #
	R=(p/3)^3+(q/2)^2 #
	V=if(R>0)then((-q/2+sqrt(R))^(1/3))else(0) #
	WW=if(R>0)then(-q/2-sqrt(R))else(0) #
	psi1 = if(R<0)then(arccos(sqrt((q^2/4)/(-p^3/27))))else(0) #
	W = if(R>0)then(sign(WW)*(abs(WW))^(1/3))else(0) #
	z1 = if(R<0)then(2*sqrt(-p/3)*cos((psi1/3)+2*3.1416*0/3)+1/3)else(0) #
	z2 = if(R<0)then(2*sqrt(-p/3)*cos((psi1/3)+2*3.1416*1/3)+1/3)else(0) #
	z3 = if(R<0)then(2*sqrt(-p/3)*cos((psi1/3)+2*3.1416*2/3)+1/3)else(0) #
	z0=if(R>0)then(V+W+1/3)else(0) #
	z(min)=-.5, z(max)=1.2
Variable/function values	Variable	Value	f(x)
	z	0.35	-9.6270E-02
	P	200
	Pc	33.5
	T	1262
	Tc	126.2
	Pr	5.970149254
	Tr	10
	Asqr	0.008076552
	B	0.051761194
	Q	0.046363864
	r	0.000418052
	p	-0.379697197
	q	-0.089946747
	R	-4.83753E-06
	V	0
	WW	0
	psi1	0.048870067
	W	0
	z1	1.044760488
	z2	-0.032420632
	z3	-0.012336754
	z0	0
Root1	Variable	Value	f(x)
	z	-0.03241692071380	-6.10E-16
	P	200
	Pc	33.5
	T	1262
	Tc	126.2
	Pr	5.970149254
	Tr	10
	Asqr	0.00807655154040
	B	0.05176119402990
	Q	0.04636386369680
	r	0.00041805195140
	p	-0.37969719703020
	q	-0.08994674725770
	R	-0.00000483752560
	V	0.00000000000000
	WW	0.00000000000000
	psi1	0.048870067
	W	0.00000000000000
	z1	1.044760488
	z2	-0.032420632
	z3	-0.012336754
	z0	0.00000000000000
Root2	Variable	Value	f(x)
	z	-0.01234360708030	-1.28E-13
	(The other variables have the same value as in Root1)
Root3	Variable	Value	f(x)
	z	1.04476050281300	3.7405E-18
	(The other variables have the same value as in Root1)
Function plot