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Rayleigh Flow - Integration By Parts

  1. Mar 29, 2008 #1
    Hello,

    This is not a question regarding a homework problem, but a step in class the professor did not show how to calculate.

    1. The problem statement, all variables and given/known data

    I am taking a course on Viscous Flow, and for Rayleigh flow after applying the similiarity solution : [tex]\eta=(y/(2*\sqrt{\gamma*t}))[/tex]

    The x-momentum equation is given by [tex]f^{''}+2*\eta*f^{'}=0[/tex]

    He states that "after integrating by parts the following solution is obtained"

    [tex]f=C_{1}*\int(exp(-\eta^{2})*d\eta)+C_{2}[/tex] (integral is from 0 to [tex]\eta)[/tex]

    I probably should, but I don't understand how to integrate the original governing equation by parts and obtain that solution. I have reviewed my old calculus books and cannot find any type of example which is similar. Can anyone shed any light?
     
  2. jcsd
  3. Mar 29, 2008 #2

    Dick

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    Science Advisor
    Homework Helper

    Call g=f'. Then the ode is dg/d(eta)+2*eta*g=0. Now just solve for g by separation of variables. Finally integrate g to get f. I'm not sure I would call that 'integration by parts'.
     
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