= Conical sink boundary layer
{title2=$\delta=\sqrt{\nu/A}\,x^{3/2}$}
An axisymmetric sink inside a cone has outer speed $U=-A/x^2$. With local distance $x$ along the wall and normal distance $y$, leading continuity is $u_x+u/x+v_y=0$ because the circumference is proportional to $x$. Balancing convection with normal viscous diffusion gives the displayed thickness. With streamfunction $\Psi=-\sqrt{A\nu}x^{1/2}F(y/\delta)$, $xu=\Psi_y$ and $xv=-\Psi_x$, the similarity equation is $F'''-FF''/2+2(1-F'^2)=0$, with $F(0)=F'(0)=0$ and $F'(\infty)=1$. The displacement-flux correction scales as $\sqrt{A\nu}\,R^{1/2}$, and the corresponding outer velocity correction as $\sqrt{A\nu}\,R^{-3/2}$.
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