 Hiemenz flow

The steady planar stagnation point boundary layer with outer velocity $(Ax,-Ay)$ has the similarity solution $u=Ax{f}^{\prime }(\eta )$, $v=-\sqrt{A\nu }f(\eta )$, $\eta =y\sqrt{A/\nu }$. The Prandtl boundary-layer equation becomes $f^{\prime \prime \prime }+f{f}^{\prime \prime }-(f^{\prime }{)}^2+1=0$, with $f(0)=f^{\prime }(0)=0$ and $f^{\prime }(\infty )=1$. Its thickness is of order $\sqrt{\nu /A}$, independent of horizontal distance. Normal dynamic pressure corrections are of smaller order than the tangential driving pressure.