Boundary layer theory

  • Thread starter juice34
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  • #1

Homework Statement


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

Homework Equations

[tex]\prod[/tex]


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.
 
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Answers and Replies

  • #2
also note initally the first equation was the navier stokes equation, then i substituted in the stream function.
 
  • #3
Finally got the solution
 

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