LEP
1.4.08
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Lift and drag (resistance to flow)
Related topics
Resistance to pressure, frictional resistance, drag coefficient,
turbulent flow, laminar flow, Reynolds number, dynamic pressure, Bernoulli equation.
Aerofoil, induced resistance, circulation, angle of incidence,
polar diagram.
Principle
A) Objects of different cross-section and shape are placed in
a laminar air stream. The drag is examined as a function of
the flow velocity and the geometry of the objects.
B) A rectangular plate or an aerofoil in a stream of air experiences a buoyant force (lift) and a resistance force (drag).
These forces are determined in relation to area, rate of flow
and angle of incidence.
Equipment
Aerodynamic models, set of 14
Aerofoil model
Pitot tube, prandtl type
Precision manometer
Holder with bearing points
Double shaft holder
Precision pulley
Spring balance 0.2 N
Vernier caliper
Blower, mains voltage 220 V
Power regulator
Pipe probe
02787.00
02788.00
03094.00
03091.00
02411.00
02780.00
11201.02
03065.01
03010.00
02742.93
32247.93
02705.00
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Universal clamp with joint
Support base -PASSSupport rod -PASS-, sqare, l = 1000 mm
Barrel base -PASSRight angle clamp -PASSRod with hook
Stand tube
Rod, pointed
Silk thread, l = 200 m
Rule, plastic, l = 200 mm
Rubber tubing, i.d. 7 mm
37716.00
02005.55
02028.55
02006.55
02040.55
02051.00
02060.00
02302.00
02412.00
09937.01
39282.00
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Tasks
A) Determination of the drag as a function of:
1. the cross-section of different bodies,
2. the flow velocity,
3. determination of the drag coefficients cw for objects of
various shape.
B ) Determination of the lift and the drag of flat plates as a function of:
1. the plate area
2. the dynamic pressure
3. the angle of incidence (polar diagram)
4. Determination of the pressure distribution over the aerofoil
for various angles of incidence.
Fig. 1: Experimental set up for determining the resistance to flow.
PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
21408-00
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LEP
1.4.08
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Lift and drag (resistance to flow)
Fig. 2 : Drag of an object as a function of its cross-sectional
area A (q = 0.85 hPa).
Fig. 3 : Drag of an object as a function of the dynamic pressure.
A) Set-up and procedure
The experimental set up is as shown in Fig. 1. The dynamic
pressure is measured with the Prandtl tube, and the air velocity calculated from equation (2). This measurement must be
repeated several times during the test. The double shaft holder must be clamped loosely between the pivot points and
adjusted horizontally and vertically. The objects whose resistance is to be measured are statically balanced; to do this it is
convenient to use the pointed rod as a reference point. As the
anticipated resistance forces are very slight, the balance must
be very carefully adjusted. The compensation force is produced by way of the precision pulley, using the spring balance.
If, in the compensated state, the objects do not return to equilibrium when deflected by hand this is because the double
shaft holder is held too loosely between the pivot points (surface friction) or is held too tightly (squeezing effect) and must
be corrected accordingly.
This value FR is appropriately expressed by the dynamic pressure q of the incident flow
Theory and evaluation
The force F acting on a body around which air is circulating
is:
F = p da ,
(1)
A
where A is the peripheral area of the body. The surface forces
p are the normal and shearing stresses. These include the
pressure p and the frictional forces. If the direction of the flow
velocity v is applied in the x direction, then Fx is the drag FR.
q
r 2
·v
2
(2)
( = density of the medium)
and by a typical area fp (e g. the cross-sectional area of the
body perpendicular to the flow). Equation (1) can thus be
written
FR cw fp · r
v2
.
2
The drag coefficient cw can be expressed by a surface integral.
In the case of smooth objects it is to a great extent independent of the Reynolds number
Re vd
,
where d is a typical parameter, e.g. the width of the object in
the stream of air, and :
m
,
r
is the kinematic viscosity (m is the viscosity).
Table 1: Drag coefficents of various objects.
0.45
cw
2
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0.37
1.17
0.92
0.24
0.21
0.71
0.14
0.07
1.12
PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
LEP
1.4.08
-00
Lift and drag (resistance to flow)
Fig. 4 : Drag coefficient of rough object as a function of the
Reynolds number.
For air at 278 K and 1013 mbar,
v 1.3 · 10 5
m2
.
s
For stationary flow in an incompressible medium, the law of
conservation of energy gives us
p0 r 2
v = const = p
2
(Bernoulli equation)
The dynamic pressure
q
r 2
v
2
is thus
q = p – p0
and can be measured as a pressure difference, using the
Prandtl tube.
B) Set-up and procedure
The dynamic pressure is measured with the Prandtl tube, and
the air velocity is calculated from equation (2). The air velocity
must be checked frequently.
Fig. 1a: Experimental set up for determining the lift and drag acting for determining the pressure distribution over the aerofoil.
PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
21408-00
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LEP
1.4.08
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Lift and drag (resistance to flow)
The double shaft holder must be clamped loosely in the pivot
points and adjusted horizontally and vertically. The rectangular plates are statically counterbalanced; it is convenient to
use the pointed rod as a reference point. Since the anticipated
lift and drag forces are very slight, the balance must be very
carefully adjusted. Using the spring balances, the lift and
(using the precision pulley) the drag are compensated and
measured. If, after compensation, the plates do not return to
equilibrium when deflected by hand, the double shaft holder is
gripped too loosely in the pivot points (surface friction) or too
tightly (squeezing effect), and must be corrected accordingly.
FR cw · fp ·
r 2
v
2
FA ca · fp ·
r 2
v
2
For small angles of incidence and for irrotational flow we
have, for an aerofoil of infinite length,
cw = 0
and ca is approximately equal to
In the range between 27° and 35° approximately, pronounced
turbulence occurs so that these angles of incidence are unsuitable for carrying out a test.
ca 2p · a a To measure the pressure distribution over the aerofoil (Fig. 1a)
a piece of rubber tubing is slipped over the pipe probe. In
order to obtain better contact with the measurement positions
this tubing must be turned back at the contact point and
moistened.
where: t = chord, f = camber.
Theory and evaluation
If the direction of the flow velocity v lies along the x direction,
then Fx is the drag FR and Fy is the lift FA (see eq. (1) and (2)):
2f
b,
t
In the case of the finite aerofoil, a separation area is formed at
the trailing edge if the angle of incidence is small. The turbulence produced induces a resistance (coefficient of resistance
cre) which is related to the lift:
cre c2a · fp
p · b2
.
where b is the distance between the supports.
Fig. 1b: Experimental set up for determining the lift and drag acting on the rectangular plate.
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PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
LEP
1.4.08
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Drag (resistance to flow)
Fig. 5: Drag and lift in relation to dynamic pressure for an
angle of incidence of 20° and a plate area of 17.5 cm2.
Fig. 7: Lift FA and resistance FR of a flat plate as a function of
the angle of incidence.
Since a certain frictional resistance as well as the resistance
due to partial separation of the flow still exist, the following is
obtained
c2a · fp
cw = cwo +
p · b2
With larger angles of incidence, the flow changes from laminar
to turbulent so that the drag increases and the lift decreases.
Fig. 6: Drag and lift in relation to the plate area for an angle of
incidence of 20° and a dynamic pressure of 0.35 hPa.
The lift is usually plotted against the drag (polar diagram).
Fig. 8: Lift FA as a function of the drag FR of a plate for different angles of incidence with a dynamic pressure of
0.25 hPa and a plate area of 35.1 cm2.
PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
21408-00
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LEP
1.4.08
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Lift and drag (resistance to flow)
Fig. 9: Pressure distribution over the aerofoil for different angles of incidence with a dynamic pressure of 0.8 hPa
o = top side of the aerofoil,
x = under side of the aerofoil.
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PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen