Show that near wall $\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}\text{x}}<mn>0</mn>$ in a Boundary Layer $($BL$)$ over a flat surface for any pressure gradient. Hence:

i$.$ Prove that transverse velocity $($v$)$ is such that BL is deflected away from the wall.

ii$.$ Show that in the neighbourhood of flat surface, the transverse velocity

$(v)$ is proportional to $y^2.$