$(20$ pts$)$ In order to avoid boundary layer interference, engineers design a "boundary layer scoop" with suction to skim off the boundary layer in a large wind tunnel $($see sketch$).$ The scoop is constructed of thin sheet metal. The air is at $20C,$ and flows at $V=62\mathrm{.}5\frac{m}{s}.$ How high $($dimension $h)$ should the scoop be at downstream distance $x=1\mathrm{.}45m$ in order to "skim off" the entire boundary layer?