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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