Talk:Falkner–Skan boundary layer

Error in the Falkner-Skan similarity variable

It seems to me that the $\eta$ similarity variable is ill defined here. If we take the book of Schlichting and Gersten (Boundary Layer Theory, 2017) p. 172 for the Wedge flow, eq. 7.33, we see that for $m=1$ we have $U(x)=ax$, which using 7.33 yields a similarity variable that becomes independent of $x$ (stagnation point). It clearly is not the case in the formulation of this wikipedia article, due to the formulation of the boundary layer thickness :

$\delta (x)\;=\;{\sqrt {\frac {2\nu L}{U_{0}(m+1)}}}\left({\frac {x}{L}}\right)^{(1+m)/2}\quad ,$

which is not independent of $x$ for $m=1$. After some algebra, it seems to me that the correct formulation is

$\delta (x)\;=\;{\sqrt {\frac {2\nu L}{U_{0}(m+1)}}}\left({\frac {x}{L}}\right)^{(1-m)/2}\quad ,$

so that we fall back on the expression of Schlichting, which corresponds to

$\delta (x)\;=\;{\sqrt {\frac {2\nu x}{u_{e}(x)(m+1)}}}\quad .$

This probably changes other expressions in the development that follows. Locarnitude (talk) 15:08, 6 March 2025 (UTC)

Good catch. I rechecked it and you are correct, the (x/L) exponent should be (1-m)/2, not (1+m)/2. Please make the correction. David Weyburne (talk) 14:23, 7 March 2025 (UTC)

Since this change hadn't been made yet, I've gone ahead and made this correction. The other expressions in the article do not appear to have been affected by this, but it is possible I may have missed something. Michigangoose (talk) 17:14, 20 March 2025 (UTC)