Bernoulli’s Theorem Aerodinamics Forces Nondimensional Coefficients Wind Tunnel

1. Aerodinamics Forces
Focus
1 Bernoulli’s Theorem
2 Aerodinamics Forces
3 Nondimensional Coefficients
4 Wind Tunnel
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2. Aerodinamics Forces
Bernoulli’s Theorem
Bernoulli’s theorem states that the sum of kinetic energy
1/2qV2 and potential energy (pressure p) is constant and
which can be expresed as follows
1
2
qV2
+ p = constant , (1)
excluding the forces of gravity.
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3. Aerodinamics Forces
Bernoulli’s Theorem
T2
+ Velocity
- Pressure
- Velocity
+ Pressure
T1 TV
Td
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4. Aerodinamics Forces
Bernoulli’s Theorem
The flows can be considered as two pipes, an upper one
T1 toward the ventral side of the plate and a lower one T2
toward the dorsal side.
In the dorsal part the airflow is forced to travel to rejoin the
exiting streamlines with an increase in speed and a loss of
pressure energy.
In the ventral part, the trajectories are shorter, due to lower
velocity, and the area Tv of local pressure is greater.
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5. Aerodinamics Forces
Aerodinamics Forces
V
R
-P
F
j
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6. Aerodinamics Forces
Nondimensional Coefficients
The component of the resultant parallel to airflow is the
drag R
CR = f (Re) =
R
1
2
qSV2
, (2)
with S the projected frontal area.
The component normal to the flow is the downforce −P
and its nondimensional coefficient −CP:
CP = f (Re) = −
P
1
2
qSV2
, (3)
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7. Aerodinamics Forces
Center of pressure
C
R
-P
F
j
Xp
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8. Aerodinamics Forces
Center of pressure
The point where the line of action of aerodinamics force F
encounters the body is called the center of pressure. It is
located at a distance XP from the leading edge, which
varies according to the angle of attack, so that the
nondimensional ratio Xp/C, with chord C, varies from 0 to
0.5 for angles to attack from 0
◦
to 90
◦
.
The curvature, in the plate, creates an angle j between the
slope of the tailing edge and the chord line.
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9. Aerodinamics Forces
NACA Profile 4412
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10. Aerodinamics Forces
NACA Profile 4412
V
R
-P
F
i
i −Cp CR
3.6 0.00 0.007
0.0 0.28 0.012
−2.0 0.43 0.019
−4.0 0.58 0.028
−6.0 0.73 0.041
−8.0 0.88 0.056
−10.0 1.02 0.076
−12.0 1.15 0.096
−14.0 1.28 0.121
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11. Aerodinamics Forces
Wind Tunnel
V
V=0Laminar
Turbulent
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