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SUBJECT: AMEE401 – AERODYNAMICS
DATE: 27/10/11
TIME: 1 Hr
INSTRUCTIONS TO CANDIDATES:
Answer 2 out of 3 questions from Part A and all questions from Part B.
All necessary work must be shown and any assumptions must be stated clearly.
Simple calculators may be used. Wherever
needed:
 H 2O  1000 kg/m3 , H 2O  1.15  10-3 Pa  s,  air  1.225 kg/m 3 , air  1.79 *105 kg/(m×s)
g=9.81 m/s2 , patm  1.01  105 N/m 2 , 1.0 in= 0.0254 m, 1 ft=12 in, ideal gas law p   RT
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PART A [60 marks]
QUESTION 1 [30 Points]
The drag coefficient can be assumed to depend only on the Reynolds number. If a
1:2 scale model of a car is tested in a pressurized wind tunnel:
a. What would be the required density of the air in the tunnel so that the
model has the same drag coefficient with the prototype?
b. Find the relation between the force on the prototype with the force on the
model.
QUESTION 2 [30 Marks]
a. Explain the meaning of Drag force and give the expression of the dimensionless
Drag coefficient.
b. Explain the meaning of Lift force and give the expression of the dimensionless Lift
coefficient.
c. In the Figure below identify the Drag force, the Lift Force, and show the direction
of the total shear force.
QUESTION 3 [30 Points]
Two smooth spheres are attached to a thin rod that is free to rotate in the horizontal
plane about point O as shown in the Figure. The rod is held stationary until the air
speed reaches 15.24 m/ s . Which direction will the rod rotate (clockwise or
counterclockwise) when the holding force is released? Explain your answer.
PART B [40 marks]
QUESTION 5 [40 Points]
A small spherical air-bubble is rising in still water (see Figure).
a. Determine the drag and the buoyancy forces acting on the bubble given
that the drag coefficient of a sphere is CD 
b.
c.
d.
e.
24
for Re  1 .
Re
Determine the total force acting on the bubble. Neglect the weight of the
bubble.
Using Newton’s 2nd law of motion, i.e.
dU
F  ma  m
dt
where m is the mass of the bubble, determine the differential equation
governing the bubble motion.
dx
Given that 
 log a  x  , solve the resulting differential equation
a x
and obtain an equation for U .
Determine the time required such that the bubble reaches 99% of its
terminal velocity
U
Figure: Rising air-bubble in a container