PROBLEM $5\mathrm{.}1$

For boundary layer flow over the wing of a commercial aircraft is modeled as a straight flat plate with an approximate boundary layer velocity profile of

$u(y)=V_{}sin(\frac{y}{2}),0y$

The air stream velocity is $350f\frac{t}{sec}$ at $40,000ft,$ and the location of interest is $x=10ft.$ Assume standard air properties apply.

Boundary condition verification:

$($a$)$ Verify that this velocity profile satisfies the no$-$slip condition. $)=(0$

$($b$)$ Verify this velocity profile matches the free stream velocity at the edge of the boundary layer. at $y=)$

$($c$)$ Verify the smooth transition at the edge of the boundary layer. at $($:$y=\}$