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Student Support Forum: 'Solve nonlinear algberic euations' topicStudent Support Forum > General > Archives > "Solve nonlinear algberic euations"

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Author Comment/Response
Bill Simpson
07/08/13 4:56pm

Solve is terrible with trig problems, Reduce is better, but only with exact problems.

Change approximate numbers to exact,
Change pi to Pi,
Simplify the system of equations,
Replace \[Theta]2 with \[Theta]1,
Use Reduce instead of Solve

In[1]:= \[Rho]0 = 127/100;
p0 = 1013*10^2;
p1 = 3*p0;
\[Gamma] = 14/10;
\[Phi]1 = 30*(Pi/180);
sys = Simplify[{
\[Rho]0*u0*Sin[\[Phi]1] == \[Rho]1*u1* Sin[\[Phi]1 - \[Theta]1],
p0 + \[Rho]0*(u0*Sin[\[Phi]1])^2 == p1 + \[Rho]1*(u1*Sin[\[Phi]1 - \[Theta]1])^2,
\[Rho]0*Tan[\[Phi]1] == \[Rho]1*Tan[\[Phi]1 - \[Theta]1],
\[Gamma]*(p0/((\[Gamma] - 1)*\[Rho]0)) + (1/2)*(u0*Sin[\[Phi]1])^2 == \[Gamma]*(p1/((\[Gamma] - 1)*\[Rho]1)) + (1/2)*(u1*Sin[\[Phi]1 - \[Theta]1])^2,
\[Rho]1*u1*Sin[\[Phi]2] == \[Rho]2*u2*Sin[\[Phi]2 - \[Theta]2],
p1 + \[Rho]1*(u1*Sin[\[Phi]2])^2 == p2 + \[Rho]2*(u2*Sin[\[Phi]2 - \[Theta]2])^2,
\[Rho]1*Tan[\[Phi]2] == \[Rho]2*Tan[\[Phi]2 - \[Theta]2],
\[Gamma]*(p1/((\[Gamma] - 1)*\[Rho]1)) + (1/2)*(u1*Sin[\[Phi]2])^2 == \[Gamma]*(p2/((\[Gamma] - 1)*\[Rho]2)) + (1/2)*(u2*Sin[\[Phi]2 - \[Theta]2])^2}]

Out[6]= {127 u0 == 200 u1 \[Rho]1 Sin[1/6 (\[Pi] - 6 \[Theta]1)],
127 u0^2 == 400 (202600 + u1^2 \[Rho]1 Sin[1/6 (\[Pi] - 6 \[Theta]1)]^2),
300 \[Rho]1 Tan[1/6 (\[Pi] - 6 \[Theta]1)] == 127 Sqrt[3],
127 u0^2 + (2836400 (-381 + 100 \[Rho]1))/\[Rho]1 == 508 u1^2 Sin[1/6 (\[Pi] - 6 \[Theta]1)]^2,
u2 \[Rho]2 Sin[\[Theta]2 - \[Phi]2] + u1 \[Rho]1 Sin[\[Phi]2] == 0,
p2 + u2^2 \[Rho]2 Sin[\[Theta]2 - \[Phi]2]^2 ==
303900 + u1^2 \[Rho]1 Sin[\[Phi]2]^2, \[Rho]2 Tan[\[Theta]2 - \[Phi]2] + \
\[Rho]1 Tan[\[Phi]2] == 0,
(7 p2)/\[Rho]2 + u2^2 Sin[\[Theta]2 - \[Phi]2]^2 == 2127300/\[Rho]1 + u1^2 Sin[\[Phi]2]^2}

In[7]:= Reduce[sys, {\[Rho]1, u0, u1, \[Theta]1, \[Rho]2, u2, p2, phi2}]

Out[7]= ...LargeComplicatedResultAfterAFewSeconds...

Study that and see what you can discover.

Simplify may or may not help with parts of that.

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Subject (listing for 'Solve nonlinear algberic euations')
Author Date Posted
Solve nonlinear algberic euations Ritwik Ghoshal 07/08/13 05:25am
Re: Solve nonlinear algberic euations Bill Simpson 07/08/13 4:56pm
Re: Re: Solve nonlinear algberic euations Ritwik Ghoshal 07/10/13 02:03am
Re: Re: Re: Solve nonlinear algberic euations Bill Simpson 07/10/13 4:35pm
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