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Mathematics Algebra Equation Solving Wolfram Language

Elimination of 3 equations

Jakob Obi

Posted 10 years ago

Guys, i am a bloody greenhorn in Mathematica. but i want to eliminate following 3 equations and thus come up with a solution for the variable v. Eq1 = [CapitalNu] == (\[Rho]Vd)/\[Mu] Eq2 = f == 24/\[CapitalNu](1 + 0.27 \[CapitalNu])^0.43 + c1(1 - exp (-0.04\[CapitalNu]^0.38)) Equ3 = f == (4gd(\[CapitalTheta] - \[Rho])/(3\[Rho]v^2)) Thus, Equation 1 should be inserted into Equation 2. Then Equation 2 shall be inserted into Equation 3 and then this should be solver for v. Can somebody show me how to do this? I have no idea and I am pretty desperade already. I have added the file in the attachment :) Can the Equations even be solved for v? Thanks Guys, Jakob Attachments:

POSTED BY: Jakob Obi

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Bill Simpson

Posted 10 years ago

I'm going to use -> instead of == in a couple of places. That will allow me to replace one symbol with another expression using /. In[1]:= Glg1 = \[CapitalNu] -> (\[Rho]Vd)/\[Mu] Out[1]= \[CapitalNu] -> (d V \[Rho])/\[Mu] In[2]:= Glg2 = f -> 24/\[CapitalNu](1+0.27 \[CapitalNu])^0.43+c1(1-exp (-0.04\[CapitalNu]^0.38)) /. Glg1 Out[2]= f -> (24 \[Mu] (1+(0.27 d V \[Rho])/\[Mu])^0.43)/(d V \[Rho])+c1 (1+0.04 exp ((d V \[Rho])/\[Mu])^0.38) In[3]:= Glg3 = f == (4gd(\[CapitalTheta] - \[Rho])/(3\[Rho]v^2)) /. Glg2 Out[3]= (24 \[Mu] (1+(0.27 d V \[Rho])/\[Mu])^0.43)/(d V \[Rho])+c1 (1+0.04 exp ((d V \[Rho])/\[Mu])^0.38) == (4 d g (\[CapitalTheta] - \[Rho]))/(3 v^2 \[Rho]) In[5]:= Solve[Out[3], v] Out[5]= { {v -> (-10.dSqrt[1.gV\[CapitalTheta] - 1.gV\[Rho]])/Sqrt[75.c1dV\[Rho] + 3.c1dexpV\[Rho]((dV\[Rho])/\[Mu])^(19/50) + 248.46916762851927\[Mu](100. + (27.dV\[Rho])/\[Mu])^(43/100)]}, {v -> (10.dSqrt[1.gV\[CapitalTheta] - 1.gV\[Rho]])/Sqrt[75.c1dV\[Rho] + 3.c1dexpV\[Rho]((dV\[Rho])/\[Mu])^(19/50) + 248.46916762851927\[Mu](100. + (27.dV\[Rho])/\[Mu])^(43/100)] }} You can look up Rule, another way of writing ->, and ReplaceAll, another way of writing /., in the help system and study the examples. See if you can make a little sense of what I've shown.

I'm going to use -> instead of == in a couple of places. That will allow me to replace one symbol with another expression using /.

In[1]:= Glg1 = \[CapitalNu] -> (\[Rho]*V*d)/\[Mu]

Out[1]= \[CapitalNu] -> (d V \[Rho])/\[Mu]

In[2]:= Glg2 = f -> 24/\[CapitalNu]*(1+0.27 \[CapitalNu])^0.43+c1*(1-exp (-0.04*\[CapitalNu]^0.38)) /. Glg1

Out[2]= f -> (24 \[Mu] (1+(0.27 d V \[Rho])/\[Mu])^0.43)/(d V \[Rho])+c1 (1+0.04 exp ((d V \[Rho])/\[Mu])^0.38)

In[3]:= Glg3 = f == (4*g*d*(\[CapitalTheta] - \[Rho])/(3*\[Rho]*v^2)) /. Glg2

Out[3]= (24 \[Mu] (1+(0.27 d V \[Rho])/\[Mu])^0.43)/(d V \[Rho])+c1 (1+0.04 exp ((d V \[Rho])/\[Mu])^0.38) ==
   (4 d g (\[CapitalTheta] - \[Rho]))/(3 v^2 \[Rho])

In[5]:= Solve[Out[3], v]

Out[5]= {
  {v -> (-10.*d*Sqrt[1.*g*V*\[CapitalTheta] - 1.*g*V*\[Rho]])/Sqrt[75.*c1*d*V*\[Rho] +
      3.*c1*d*exp*V*\[Rho]*((d*V*\[Rho])/\[Mu])^(19/50) + 248.46916762851927*\[Mu]*(100. +
      (27.*d*V*\[Rho])/\[Mu])^(43/100)]}, 
  {v -> (10.*d*Sqrt[1.*g*V*\[CapitalTheta] - 1.*g*V*\[Rho]])/Sqrt[75.*c1*d*V*\[Rho] +
      3.*c1*d*exp*V*\[Rho]*((d*V*\[Rho])/\[Mu])^(19/50) + 248.46916762851927*\[Mu]*(100. +
      (27.*d*V*\[Rho])/\[Mu])^(43/100)]
  }}

You can look up Rule, another way of writing ->, and ReplaceAll, another way of writing /., in the help system and study the examples. See if you can make a little sense of what I've shown.

POSTED BY: Bill Simpson

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