- #1
apennine
- 2
- 0
Hello,
This is not a question regarding a homework problem, but a step in class the professor did not show how to calculate.
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?
This is not a question regarding a homework problem, but a step in class the professor did not show how to calculate.
Homework Statement
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?