$(50$ pts$)$ Air flows through the test section of a small wind

E$1....$

tunnel at average speed $V=7\mathrm{.}5\frac{m}{s}.$ The air is at standard pressure and at $30\mathrm{.}09C,$ and the length, height, and width of the wind tunnel test section are $1\mathrm{.}12m,0\mathrm{.}556m,$ and $0\mathrm{.}725$ m $,$ respectively. The tunnel walls are hydrodynamically smooth. There is a very rapid contraction section, and the boundary layer at the start of the test section can be approximated as zero$-$thickness $($in other words, $=0$ at $x=0,$ where $x$ is taken as zero at the beginning of the test section$).$ Note: Use Sutherland's law for air viscosity.

$($a$)$ Is the boundary layer at the end of the test section walls laminar, transitional, or turbulent? Explain.

$($b$)$ Regardless of your answer to Part $($a$),$ assume that the boundary layer remains laminar over the entire length of the $,$ test section. Estimate the boundary layer thickness, the displacement thickness, and the momentum thickness at the end of the test section. Give your answers in millimeters. Is the boundary layer thin as per the boundary layer approximation?

$($c$)$ Calculate the skin friction force on the top wall of the wind tunnel. Give your answer in newtons.

$($d$)$ Repeat parts $($b$)$ and $($c$)$ for the case of a turbulent boundary layer $($assume the BL is turbulent from $x=0$ to $L).$