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MathGroup Archive 2005

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can anyone solve this equation?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg57986] can anyone solve this equation?
  • From: Chris Chiasson <chris.chiasson at gmail.com>
  • Date: Thu, 16 Jun 2005 05:35:43 -0400 (EDT)
  • Reply-to: Chris Chiasson <chris.chiasson at gmail.com>
  • Sender: owner-wri-mathgroup at wolfram.com

Dear MathGroup Gurus,

Can anyone solve the following equation (for theta_4)?

The assumptions are in this cell (use ctrl+shift+e, paste it into the
notebook, and then use ctrl+shift+e again):

Cell["\<\
$Assumptions=Flatten[Append[{True},{(#1>=0&)/@{\[Alpha]},
(#1>0&)/@{r,numcyl,Displacement\[UnderBracket]Base,SBRatio,P\[UnderBracket]0,P\
\[UnderBracket]7,T\[UnderBracket]Intake,T\[UnderBracket]7},
(#1>1&)/@{R\[UnderBracket]ConRodCrankArm,CR\[UnderBracket]Base,k\[UnderBracket]Air\
\[UnderBracket]c,k\[UnderBracket]Air\[UnderBracket]e}}]];\
\>","Input"]

The equation is in the cell below (I need the solution for theta
underbracket four):

Cell["\<\
(1/(2*(-1+CR\[UnderBracket]Base)*numcyl))*(Displacement\[UnderBracket]Base*(1+CR\
\[UnderBracket]Base-R\[UnderBracket]ConRodCrankArm+
CR\[UnderBracket]Base*R\[UnderBracket]ConRodCrankArm+Cos[\[Theta]\[UnderBracket]4]-CR\
\[UnderBracket]Base*Cos[\[Theta]\[UnderBracket]4]+
Sqrt[R\[UnderBracket]ConRodCrankArm^2-Sin[\[Theta]\[UnderBracket]4]^2]-
CR\[UnderBracket]Base*Sqrt[R\[UnderBracket]ConRodCrankArm^2-Sin[\[Theta]\[UnderBracket]4]^2]))==\

(Displacement\[UnderBracket]Base*(2^k\[UnderBracket]Air\[UnderBracket]c*(-1+\
CR\[UnderBracket]Base)*(P\[UnderBracket]Intake/P\[UnderBracket]Exit)^(1/k\[UnderBracket]Air\
\[UnderBracket]c)*q\[UnderBracket]LHV*
(c\[UnderBracket]P\[UnderBracket]e+c\[UnderBracket]v\[UnderBracket]e*\[Alpha])*Cos[\[Theta]\
\[UnderBracket]1]+2^k\[UnderBracket]Air\[UnderBracket]c*c\[UnderBracket]v\[UnderBracket]e*q\
\[UnderBracket]LHV*\[Alpha]*
(2-(P\[UnderBracket]Intake/P\[UnderBracket]Exit)^(1/k\[UnderBracket]Air\[UnderBracket]c)+(P\
\[UnderBracket]Intake/P\[UnderBracket]Exit)^(1/k\[UnderBracket]Air\[UnderBracket]c)*
R\[UnderBracket]ConRodCrankArm-(P\[UnderBracket]Intake/P\[UnderBracket]Exit)^(1/k\
\[UnderBracket]Air\[UnderBracket]c)*
Sqrt[R\[UnderBracket]ConRodCrankArm^2-Sin[\[Theta]\[UnderBracket]1]^2]+\
CR\[UnderBracket]Base*(P\[UnderBracket]Intake/P\[UnderBracket]Exit)^
(1/k\[UnderBracket]Air\[UnderBracket]c)*(-1-R\[UnderBracket]ConRodCrankArm+Sqrt[R\
\[UnderBracket]ConRodCrankArm^2-Sin[\[Theta]\[UnderBracket]1]^2]))+
c\[UnderBracket]P\[UnderBracket]e*(-2*(1+\
AF)*c\[UnderBracket]v\[UnderBracket]e*(P\[UnderBracket]Intake/P\[UnderBracket]Exit)^(1/k\[UnderBracket]\
Air\[UnderBracket]c)*T\[UnderBracket]Intake*(1+\[Alpha])*
(1+CR\[UnderBracket]Base-R\[UnderBracket]ConRodCrankArm+CR\[UnderBracket]Base*R\
\[UnderBracket]ConRodCrankArm+Cos[\[Theta]\[UnderBracket]1]-
CR\[UnderBracket]Base*Cos[\[Theta]\[UnderBracket]1]+Sqrt[R\[UnderBracket]ConRodCrankArm^2-\
Sin[\[Theta]\[UnderBracket]1]^2]-
CR\[UnderBracket]Base*Sqrt[R\[UnderBracket]ConRodCrankArm^2-\
Sin[\[Theta]\[UnderBracket]1]^2])^k\[UnderBracket]Air\[UnderBracket]c+
2^k\[UnderBracket]Air\[UnderBracket]c*q\[UnderBracket]LHV*(2-(P\[UnderBracket]Intake/P\
\[UnderBracket]Exit)^(1/k\[UnderBracket]Air\[UnderBracket]c)+
(P\[UnderBracket]Intake/P\[UnderBracket]Exit)^(1/k\[UnderBracket]Air\[UnderBracket]c)*R\
\[UnderBracket]ConRodCrankArm-
(P\[UnderBracket]Intake/P\[UnderBracket]Exit)^(1/k\[UnderBracket]Air\[UnderBracket]c)*Sqrt[R\
\[UnderBracket]ConRodCrankArm^2-Sin[\[Theta]\[UnderBracket]1]^2]+
CR\[UnderBracket]Base*(P\[UnderBracket]Intake/P\[UnderBracket]Exit)^(1/k\[UnderBracket]Air\
\[UnderBracket]c)*(-1-R\[UnderBracket]ConRodCrankArm+
Sqrt[R\[UnderBracket]ConRodCrankArm^2-Sin[\[Theta]\[UnderBracket]1]^2])))))/((-1+CR\
\[UnderBracket]Base)*c\[UnderBracket]P\[UnderBracket]e*numcyl*
(2^k\[UnderBracket]Air\[UnderBracket]c*(-1+CR\[UnderBracket]Base)*(P\[UnderBracket]Intake/P\
\[UnderBracket]Exit)^(1/k\[UnderBracket]Air\[UnderBracket]c)*q\[UnderBracket]LHV*Cos[\[Theta]\
\[UnderBracket]1]-
2*(1+AF)*c\[UnderBracket]v\[UnderBracket]e*(P\[UnderBracket]Intake/P\[UnderBracket]Exit)^(1/k\
\[UnderBracket]Air\[UnderBracket]c)*T\[UnderBracket]Intake*(1+\[Alpha])*
(1+CR\[UnderBracket]Base-R\[UnderBracket]ConRodCrankArm+CR\[UnderBracket]Base*R\
\[UnderBracket]ConRodCrankArm+Cos[\[Theta]\[UnderBracket]1]-
CR\[UnderBracket]Base*Cos[\[Theta]\[UnderBracket]1]+Sqrt[R\[UnderBracket]ConRodCrankArm^2-\
Sin[\[Theta]\[UnderBracket]1]^2]-
CR\[UnderBracket]Base*Sqrt[R\[UnderBracket]ConRodCrankArm^2-\
Sin[\[Theta]\[UnderBracket]1]^2])^k\[UnderBracket]Air\[UnderBracket]c+
2^k\[UnderBracket]Air\[UnderBracket]c*q\[UnderBracket]LHV*(2-(P\[UnderBracket]Intake/P\
\[UnderBracket]Exit)^(1/k\[UnderBracket]Air\[UnderBracket]c)+
(P\[UnderBracket]Intake/P\[UnderBracket]Exit)^(1/k\[UnderBracket]Air\[UnderBracket]c)*R\
\[UnderBracket]ConRodCrankArm-
(P\[UnderBracket]Intake/P\[UnderBracket]Exit)^(1/k\[UnderBracket]Air\[UnderBracket]c)*Sqrt[R\
\[UnderBracket]ConRodCrankArm^2-Sin[\[Theta]\[UnderBracket]1]^2]+
CR\[UnderBracket]Base*(P\[UnderBracket]Intake/P\[UnderBracket]Exit)^(1/k\[UnderBracket]Air\
\[UnderBracket]c)*(-1-R\[UnderBracket]ConRodCrankArm+
Sqrt[R\[UnderBracket]ConRodCrankArm^2-Sin[\[Theta]\[UnderBracket]1]^2]))))\
\>","Output",
CellLabel->"Out[40]="]

Thank you for your time,
-- 
Chris Chiasson
http://chrischiasson.com/
1 (810) 265-3161


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