$1$ Forces & Moments

Problem $1\mathrm{.}1.$ Enumerate the primary origins of forces and moments in the field of aerodynamics.

Problem $1\mathrm{.}2.$ What is the differences between inviscid and viscous flows

Problem $1\mathrm{.}3.$ What is the differences between incompressible and compressible flows

Problem $1\mathrm{.}4.$ What is Mach number? How this Mach number can be used to describe flow conditions?

Problem $1\mathrm{.}5.$ A wing section of an airplane is flying at a Mach number of $M_{}=0\mathrm{.}2$ under standard sea level conditions, as depicted in Figure $1.$ The wing has surface angles ${}_{LE}=10$ and ${}_{TE}=5$ respectively. At this flying speed, the static pressures on the upper surface of the wing section are $P_1=9\mathrm{.}8{10}^{4}Pa$ and $P_2=1{10}^{5}Pa,$ while on the lower surface they are $P_3=P_4=1\mathrm{.}01{10}^{5}Pa.$ At sea level, the air density and temperature are $1\mathrm{.}225k\frac{g}{m^3}$ and $15C$ respectively. The gas constant is $287\frac{J}{kg.K},$ and the atmospheric lapse rate is $1\mathrm{.}4.$

$1$

Determine:

$($a$)$ the axial force

$($b$)$ the normal force

$($c$)$ the lift force at $=0$

$($d$)$ the drag force at $=0$

$($e$)$ the lift coefficient at $=0$

$($f$)$ the drag coefficient at $=0$

$($g$)$ the lift$-$to$-$drag ratio, $\frac{C_l}{C_d}$

$($h$)$ the pitching moment coefficient about the quarter chord, $M_{\frac{c}{4}}$ where $x=\frac{c}{4}$ and $y=0$

$($i$)$ the location of the centre of pressure, $x_{cp}$