Question

The wing of the Fairchild Republic A-10A twin-jet close-support airplane is approximately rectangular with a wingspan (the length perpendicular to the fl ow direction) of 17.5 m and a chord (the length parallel to the fl ow direction) of 3 m. The airplane is fl ying at standard sea level with a velocity of 200 m/s. If the fl ow is considered to be completely laminar, calculate the boundary layer thickness at the trailing edge and the total skin friction drag. Assume that the wing is approximated by a fl at plate. Assume incompressible fl ow.

Answer 1

An airplane flying across the sky experience drag force determined by the factors including the speed of flight, coefficient of skin friction and the reference surface area

The boundary layer thickness is approximately 0.233 cm

The total skin friction drag, is approximately 265 N

Reason:

First part:

Given parameters are;

Chord length, L = 3 m

Velocity of the plane, V = 200 m/s

Density of the air, ρ = 1.225 kg/m³

Viscosity of the air, μ = 1.81 × 10⁻⁵ kg/(m·s)

The Reynolds number is given as follows;

$R_{eL} = \dfrac{\rho \times V \times L}{\mu}$

Therefore;

$R_{eL} = \dfrac{1.255 \times 200 \times 3}{1.81 \times 10^{-5}} = 4.16022099448 \times 10^7 \approx 4.16 \times 10^7$

Boundary layer thickness, $\delta_L$, for laminar flow, is given as follows;

$\dfrac{ \delta_L }{L}=\dfrac{5.0}{\sqrt{R_{eL} } }$

${ \delta_L }=\dfrac{5.0 \times L}{\sqrt{R_{eL} } }$

Which gives;

${ \delta_L }=\dfrac{5.0 \times 3}{\sqrt{4.16 \times 10^{7}} } \approx 2.33 \times 10^{-3 }$

The boundary layer thickness, $\delta_L$ ≈ 2.33 × 10⁻³ m = 0.233 cm

Second Part

The total skin friction is given as follows;

$Dynamic \ pressure, q = \dfrac{1}{2} \cdot \rho \cdot V^2$

Therefore;

$q = \dfrac{1}{2} \times 1.225 \times 200^2 = 24,500$

The dynamic pressure, q = 24,500 N/m²

Skin friction drag coefficient, $C_D$, is given as follows;

$C_D = \dfrac{1.328}{\sqrt{R_{eL} } }$

Therefore;

$C_D = \dfrac{1.328}{\sqrt{4.16 \times 10^7 } } \approx 2.06 \times 10^{-4}$

Skin friction drag, $D_f$, is given as follows;

$D_f$ = q × $C_D$ × A

Where;

A = The reference area

∴ $D_f$ = 24,500 N/m² × 2.06 × 10⁻⁴ × 3 m × 17.5 m = 264.9675 N ≈ 265 N

The total skin friction drag, $D_f$ ≈ 265 N

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