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!!