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Boundary layer theory

  1. Mar 9, 2010 #1
    1. The problem statement, all variables and given/known data
    The problem is write this

    d[tex]\Psi[/tex]/dy(d^2[tex]\Psi[/tex]/dxdy)-d[tex]\Psi[/tex]/dx(d^2[tex]\Psi[/tex]/dy^2=-[tex]\nu[/tex](d^3[tex]\Psi[/tex]/dy^3)

    in the form of -ff''=f'''
    where

    [tex]\Psi[/tex](x,y)=-sqrt(V*[tex]\nu[/tex]*x)f([tex]\eta[/tex])

    f([tex]\eta[/tex])=integral(from 0 to [tex]\eta[/tex])([tex]\Pi[/tex]')*([tex]\overline{\eta}[/tex])*d([tex]\overline{\eta}[/tex]) where [tex]\overline{\eta}[/tex] is a dummy variable

    2. Relevant equations[tex]\prod[/tex]


    3. The attempt at a solution
    I have just tried taking the derivatives using maple but to no avail. Please help! Also note that the small v is a multiplier and nothing is raised to the power. Please excuse my formatting.
     
    Last edited: Mar 9, 2010
  2. jcsd
  3. Mar 9, 2010 #2
    also note initally the first equation was the navier stokes equation, then i substituted in the stream function.
     
  4. Mar 9, 2010 #3
    Finally got the solution
     
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