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I was trying to understand the derivation of the boundary layer equations at p.145 of http://www.unimasr.net/ums/upload/files/2012/Sep/UniMasr.com_919e27ecea47b46d74dd7e268097b653.pdf. : the derivation is completely given at that page.

I almost figured it all out, but I don't understand (12-8). With the approximations they made, I should get (12-8), but not the last term $\mu\frac{\partial^2v_y}{\partial x^2}$. I don't see how they get this term, when approximating $\tau_{xy} = \mu \frac{\partial^2 v_y}{\partial x^2}$ and $\sigma_{yy} = -P$ does not give the result shown. I wonder if I'm wrong, or the book is just mistaken? I hope someone can help me out here.

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That's obviously a typo. The last term should be $\mu \frac{\partial^2 v_y}{\partial y^2}$. Which would have the same order of magnitude as the rest of terms in the equation. –  user23660 Aug 22 '13 at 3:38
2  
@user23660 You should probably turn that into an answer -- maybe show that it is of the same order of magnitude for completeness. –  tpg2114 Aug 22 '13 at 4:45

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