A

ERODYNAMICS

–

EXAM

19-06-2015

Basic part

1. Calculate the lofting force coefficient of the circular profile knowing that the angle

between the radii joining the profile's center with the stagnations points on its contour is
equal 120 degrees. The reference chord is the profile's diameter.

2. Make a careful scheme of the streamlines patters and the local velocity profiles in the

vicinity of the boundary layer's separation point. Define the displacement thickness and
the momentum thickness. How does the wall friction coefficient change with the distance
from the leading edge in the laminar boundary layer over a flat plate at zero angle of
incidence

3. Make a careful and properly commented plot explaining the mechanism of induced drag

generation. Using the formulae from the lifting line theory calculate the induced angle
and induced drag coefficient of the elliptic wing with the aspect ratio equal 10. The lifting
coefficient of the wing is C

L

=0.4 and the corresponding profile drag is C

D

= 0.06.

4. Define the isentropic process and provide its mathematical formula in terms of pressure

and density. Write the formula for the speed of sound in the Clapeyron gas (involving gas
temperature) and define the Mach number. What is the tip angle of the Mach cone
generated by the small disturbance source moving with the Mach number equal 2?

5. The Prandtl-Glauert correction – explain what it is and explain how it is used.
6. Laminar compressible boundary layer – make careful plots of the velocity and

temperature profiles for the thermally isolated flat plate.

Extended part

7. Write general mathematical formulation of the boundary value problem for 2D stationary

potential flow past an airfoil embedded in the stream uniform at infinity. Describe how the
solution to this problem is constructed so that the Kutta-Youkovsky condition is satisfied
simultaneously.

8. Describe how the induced angle and local angle of attack change along the span of the

wing with rectangular planform. The wing does not have any geometric twist. In which
part of such wing – near the centerplane (or fuselage) or near the tips – the flow separation
appears first while gradually increasing the geometric angle of attack? Explain your
answer.

9. Write the equation for the velocity potential in the small disturbances (linearized) theory.

What simplification are assumed with respect to the full potential theory?

10.

Flap effectiveness in the transonic flow – make a plot of the

L

C



as a function of the

free stream Mach number, together with short description/comment.

Time: 100 minutes

ATTENTION: Students, who passed the mid-term exam solve
only the problems no. 4-6 and 9-10. Time: 50 minutes