MCG 3345 FLUID MECHANICS II
Midterm
Examination
Duration: 1 hr.
11 March 1998
Professor S. Tavoularis
Closed Book and No
tes. Only Basic Calculators Permitted.
1. A contemporary of Galileo dropped simultaneously two hollow brass balls from the top of the
leaning tower of Pisa. Both balls had a diameter of 100 mm and a weight of 2.0 N but the first ball was
highly polishe
d and smooth, while the second one was cast crudely and retained substantial roughness.
There was no wind at the time of the experiment. The density of air is 1.2 kg/m
3
and its kinematic
viscosity is 15×10

6
m
2
/s. The gravitational acceleration is 9.81 m/s
2
and the volume of a sphere is
D
3
/6, where
D
is its diameter. The tower can be considered as sufficiently high for the balls to reach
their terminal velocity.
a) Compute the speed of the smooth ball when it reached the ground.
(Marks : 30%)
b) Explain in detail which ball would have
reached the ground first.
(20%)
c) If the smooth ball were given a clockwise spin, which it maintained throughout the fall, sketch its
likely trajectory. Explain the rational for this sketch.
(10%)
2. Explain what are "wing tip vortices", why they are formed and how they affect the lift and drag on
the wing of an aircraft. Sketch the wing tip vortices behind an aircraft.
(40%)
3. Provide definitions
for the drag and lift coefficients. These coefficients contain a certain area.
Explain how this area would be determined for bodies of different shapes.
(10%)
Total (including a 10% bonus): 110%
MCG 3345 FLUID MECHANICS II
Midterm Examination
Duration: 50 min.
2 March 2000
Professor S. Tavoularis
Closed Book and Notes. Calculators Permitted.
1. The measured pressure distrib
ution along the upper surface of an airfoil has been fitted by the
expression
p
(
x
/
c
)/
p
o
=1

9.2(
x/c
) + 8.5(
x/c
)
2
,
where
p
o
is the stagnation pressure and
c
is the airfoil chord length. Explain qualitatively whether it is
possible for the flow over this a
irfoil to separate, and, if so, identify the most likely location for
separation.
(Marks: 20)
2. a) On the same graph, sketch the lift coefficients vs. angle of attack of i) a symmetric airfoil, ii) a
cambered airfoil, iii) a symmetric airfoil with it
s trailing edge flap deflected downward, and iv) a
symmetric airfoil with its trailing edge flap deflected upward. Do not provide explanations.
(20)
b) An airplane is flying horizontally at constant speed, when the pilot deflects the trailing edge flaps
of
both wings downward, while maintaining the speed of the airplane unchanged. Explain whether there
will be any changes in i) the altitude of the aircraft and ii) the flight efficiency, as determined by fuel
consumption per km travelled.
(15)
3. Descr
ibe whether the terminal velocities of a falling i) spherical grain of pollen, ii) metallic sheet
with its flat side vertical and iii) metallic sheet with its flat side horizontal would change as a result of
the addition of surface roughness.
(15)
4.
Describe in detail, using sketches as required, how a soccer
player must execute a "corner kick" in order to score directly,
namely to place the ball into the goal (see sketch at right).
(20)
5. Provide two distinct examples of disastrous effects o
f flow

induced vibration. Provide two examples
of how an engineer may avoid this problem.
(20)
Total Marks (including a 10% bonus): 110%
MCG 3345 FLUID MECHANICS II
Midterm Examination
Duration: 60 min.
14 March 2002
Professor S. Tavoularis
Closed Book and Notes. No calculators Permitted.
1. Consider incompressible flow in a two

dimensional converging duct, as shown in Figure 1. The flow
entering the duct has a uniform velocity
u
1
.
a.
Neglecting frictional and gravitational effects, compute the acceleration of a fluid partic
le that
at a given time occupies the central position A in the duct.
(Marks: 20)
b.
Now assume that the flow has friction. Sketch the likely velocity variation in the cross

section
that includes point A. Is it possible for this flow to separate from the wall?
Explain your
answer.
(20)
2. Consider wind flow past two cylindrical beams, one with a circular cross

section and another with a
square cross

section, as shown in Figure 2.
a.
Sketch likely patterns of flow separation from these objects and explain whether th
e value of
wind velocity would have a significant effect on the separation patterns and on the
corresponding drag coefficients. Provide sketches, as required.
(25)
b.
Which of the two objects is likely to have i) a higher drag coefficient and ii) a higher fre
quency
of vortex shedding? Justify your answer.
(10)
3. Sketch the lift coefficient of a two

dimensional, cambered airfoil vs. the angle of attack, for both
positive and negative angles. Explain what is the angle of zero lift. Identify the maximum lift
coe
fficient on your sketch and sketch a likely streamline pattern past the airfoil under conditions of
maximum lift. Describe one method by which you can increase the maximum lift of a wing.
(35)
Total (including a 10% bonus) 110%
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