Re: Help! 6 equation non-linear system

• To: mathgroup at smc.vnet.net
• Subject: [mg99734] Re: [mg99681] Help! 6 equation non-linear system
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Tue, 12 May 2009 03:11:23 -0400 (EDT)
• Reply-to: hanlonr at cox.net

```eqns = {
190200 ==
999*(V3^2/2) - 999*(V1^2/2) + 33266.7*f3*V3^2 + 166533*f1*V1^2 +
14185.2*V3^2,
180400 ==
999*(V2^2/2) - 999*(V1^2/2) + 199800*f2*V2^2 + 166533*f1*V1^2 +
25874.1*V2^2,
V1 == V2 + V3,
1/Sqrt[f1] == -2*Log[2.7*10^-5 + 1.88*10^-4/(V1*Sqrt[f1])],
1/Sqrt[f2] == -2*Log[2.7*10^-5 + 1.88*10^-4/(V2*Sqrt[f2])],
1/Sqrt[f3] == -2*Log[2.7*10^-5 + 1.88*10^-4/(V3*Sqrt[f3])]};

soln = FindRoot[
eqns, {{V1, 10}, {V2, 5}, {V3, 5}, {f1, 0.05}, {f2, 0.05}, {f3,
0.05}}] // Chop

{V1->6.00943,V2->2.50657,V3->3.50285,f1->0.00433244,f2->0.0053216,f3->\
0.00490493}

eqns /. soln

{True,True,True,True,True,True}

Bob Hanlon

---- Marc <dunh0037 at umn.edu> wrote:

=============
I'm very new to Mathematica, and I'm trying to solve a fairly complex
system involving 3 non-linear implicit equations (Colebrook
equations). I've tried just doing a Solve and NSolve function, but my
Core 2 Duo @ 2.2GHz with 3 GB ram running on XP runs out of memory and
can't produce anything.

Here are my equations:

190200=999*V3^2/2-999*V1^2/2+33266.7*f3*V3^2+166533*f1*V1^2+14185.2*V3^2

180400=999*V2^2/2-999*V1^2/2+199800*f2*V2^2+166533*f1*V1^2+25874.1*V2^2

V1=V2+V3

1/sqrt(f1)=-2*log(2.7*10^-5+1.88*10^-4/(V1*sqrt(f1)))

1/sqrt(f2)=-2*log(2.7*10^-5+1.88*10^-4/(V2*sqrt(f2)))

1/sqrt(f3)=-2*log(2.7*10^-5+1.88*10^-4/(V3*sqrt(f3)))

Variables:

V1: should be in the range 0 < V1 < 20
V2: should be in the range 0 < V2 < 10
V3: should be in the range 0 < V3 < 10
f1: should be in the range 0 < f1 < 0.1
f2: should be in the range 0 < f2 < 0.1
f3: should be in the range 0 < f3 < 0.1

Any help would be greatly appreciated, I'm stuck!!

```

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