Exercise $1$

Consider an airplane patterned after the twin$-$engine Beechcraft Queen Air executive transport

flying at an altitude of $9Km$ where the ambient air temperature, density, and dynamic viscosity

coefficient are $T=229K,=0\mathrm{.}4663K\frac{g}{m^3},$ and $=1\mathrm{.}5{10}^{-5}N.\frac{s}{m^2},$ respectively. The airplane

weight is $38,220N$ with wing planform area $27\mathrm{.}3m^2,$ chord length $1\mathrm{.}8m,$ aspect ratio $7\mathrm{.}5,$ Oswald

efficiency factor $0\mathrm{.}9,$ and parasite drag coefficient $C_{d_o}=0\mathrm{.}03.$ The plane is flying at a velocity of

$294k\frac{m}{h}$ with wing velocity profile given by

$u=750y+2\mathrm{.}5**{10}^{-6}{y}^3\frac{m}{s}$

$1-$calculate the shear stress produced and the skin friction drag the wing

$2-$regardless of pressure drag, determine the thrust required for steady level flight

$3-$calculate the flight mach number

$4-$considering the transition Reynolds number $Re=5{10}^5$ discuss the flow around the wing and determine the characteristic length at which the flow turns into turbulent flow if any.

$5-$calculate the minimum thrust required for steady flight and its corresponding velocity.