3. Laminar Flow over a Wing (30%) A trapezoidal wing with geometry shown below i

Question

3. Laminar Flow over a Wing (30%) A trapezoidal wing with geometry shown below is flying at U 50m/s, in air of density p 0.8kg/m3 and dynamic viscosity = 1.6 × 10-5kg/ms. Approximate this wing as a flat plate at zero angle of attack, with no cross-flow, so that the Blasius solution is valid. 3m 12m a) Determine the drag, D, and the drag coefficient, CD = Dusa S), on the wing. Note, s is the planform area of the wing. b) Imagine now that the wing is flying sideways (e.g. to the left in the figure above). Calculate the part. Explain why a difference arises.

Explanation / Answer

3. given blasius solution is true

a.

so from blasius solution

draqg force on the plate

F = 1.328*sqroot(rho*mu*l*U^3)

here

rho = density of air = 0.8 kg/m^3

mu = dynamic viscosity of air = 1.6*10^-5 kg/s

l = lenth of wing = 3 m

U = 50 m/s

F = 2.9095 N = D

Now, Cd = 2D/rho*U^2*S

S = 0.5(3)(6 + 12) = 27 m^2

hence

Cd = 1.077*10^-4

b.

for the wing flying sideways

l = (12 + 6)/2 = 9 m

hence

F = 5.0394 N

Cd = 1.8654*10^-4

the values are different because of change in length of the wing due to change in orientation

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