Laboratory 3

```Laboratory 2
Drag Measurements in a Subsonic Wind Tunnel
OBJECTIVES
This experiment illustrates several concepts and principles concerning drag
forces acting upon bodies. These concepts will be demonstrated by the
measurement of drag for two sizes of smooth spheres at various wind speeds in a
subsonic wind tunnel. The results will be presented in both dimensional and
nondimensional terms. This experiment will allow the observation of the effects
of boundary layer transition on drag for flow over a sphere and determination of
the critical Reynolds number.
Section 9.1 in your fluid mechanics text [1] should be studied before undertaking
this laboratory exercise.
BACKGROUND
DRAG
A body immersed in a flowing fluid is acted upon by both pressure and viscous
forces from the flow. The sum of the forces (pressure and viscous) that acts
parallel to the free-stream direction is termed drag. Body forces, such as
buoyancy or weight may also act on the body; however, drag forces are limited
by definition to those forces produced by the dynamic action of the flowing fluid.
The pressure forces are a function of the form or shape or the body and
contribute to the "form drag." The viscous resistance contributes to the viscous
drag or "skin-friction" drag. Our intuition would tell us that the drag force
should increase with increasing fluid velocity. One purpose of the present
experiment is to measure these changes over a range of wind speeds.
TRANSITION EFFECTS (Note: The assigned background reading is essential here!)
The drag force on a sphere experiences a marked reduction when the flow in the
boundary layer upstream of the separation point undergoes transition from
laminar to turbulent flow (see Figure 2.1). This boundary layer transition causes
a delay in the separation point resulting in a reduction of the form drag. Figure
2.1 shows the pressure coefficient for the case of a laminar boundary layer (a)
and for the case where the boundary layer experiences transition to turbulence
2-1
upstream of the separation point (b). The Reynolds number associated with this
transition is known as the critical Reynolds number.
2-2
cp  0
cp  0
U
P
 P  P 
c p   2  
U  / 2 
Figure
(a)3 .1:Flow of Viscous Fluid Past a Cylinde r Show ing
Laminar Bounda ry La yer Sepa ration from the F ront
Portion: A) Pa ttern of Streamlines , B) Pressure
Distribution
cp  0
cp  0
cp  0
U
cp  0
P U 
P
 P  P 
 
2

U  /2 
c p  

(b)
P  P 
c   2  
Figure 3.2:Flow of Visc ous F luid Pas pt a C
yl inde
Showing
/ 2r 
U
Turbu le nt Bounda ry Layer Sepa rat ion from t he R ear
Po rt ioof
n:Viscous
A ) Patt
ern
ofcoefficient
Stream
lines,
Pr es
su
Figure
3 .1:Flow
Fluid
Past
a Cylinde
r Show
ingre
Figure
2.1 Streamlines
and
pressure
for B)
flow
over
a sphere.
D is trib ut ion
Laminar Bounda ry La yer Sepa ration from the F ront
Portion: A) Pa ttern of Streamlines , B) Pressure
Distribution
2-3
To measure Vo a Pitot tube is used in conjunction with a digital manometer. By
determining the difference between the total and static pressures, the free-stream
velocity may be determined using equation (2.3).
Vo  2gh
w

(2.3)
where,
g  acceleration due to gravity (32.174 ft/sec2 )
h  pressure difference ( ft of air)
 w  density of water (62.4 lb/ft 3 )
  density of air (lb/ft 3 )
PROCEDURE:
An AEROLAB subsonic wind tunnel, 2 smooth spheres (diameter 2.92in and
3.70in) , a digital manometer and a pitot tube will be available for use in this
laboratory exercise. To perform the exercise, follow the following steps.
1. Calculate the nominal pressure drop associated with a given wind speed.
Record these values in the worksheet provided.
2. Turn control panel on.
3. Install 0.75 inch diameter calibration barrel on the sting balance.
4. Adjust angle of attack of sting assembly to 30, and zero the value of the
5. Hang a 0.5 and 1 kg weight on the calibration barrel, and record the new
axial force readout value for both inputs. This data may then be used to
establish the calibration for the axial force measurement.
6. Remove calibration barrel from the sting balance, readjust angle of attack
to 0o, and install first sphere (NOTE: Do not over-tighten the set-screw).
7. Remove all tools and loose objects from the test section and close the
viewing window.
2-4
8. Turn on wind tunnel, and adjust air speed to the maximum value. Reduce
air speed to zero, and again zero the axial force readout.
9. Now it is time to take data. Set the wind speed to 45 MPH and record
10. Repeat step 8 for air speeds of 60, 80, 100, 120, and 130 (or maximum wind
tunnel velocity) mph. If the critical Reynolds number, where the
transition to turbulence in the boundary layer is reached, you will observe
a decrease in the drag force for increasing wind speed. Through careful
observation of the sphere you should be able to determine an accurate
value of the critical Reynolds number. Comment on the stability of the
flow at this Reynolds number.
11. Repeats steps 7 through 9 for the second sphere.
12. Shut off wind tunnel.
Fl ow
St r ai ght ener s
1 f t . by 1 f t .
Tes t Sec t i on
Fan
Out l et
I nl et
Cont r ol
Figure 2.2
Box
Schematic of AEROLAB apparatus.
2-5
ASSIGNMENT
Write a formal lab report-due in one (1) week at the beginning of the lab period.
1. Plot the drag force as a function of wind speed for each sphere.
Explore various plot formats (log-log, etc.) to see if a functional
relationship between drag and wind speed can be discerned.
2. Plot the drag coefficient as a function of Reynolds number for the two spheres
on the same plot. Comment on the results.
3. Estimate the drag force on a 17.5 mm sphere at a wind speed of 90 m/sec.
4. Evaluate the accuracy of the drag coefficient by comparison with
published values.
5. Discuss the significance of the critical Reynolds number.
REFERENCE
1.
Munson, B.R., Young, D.F., and T.H. Okiishi, Fundamentals of Fluid
Mechanics, 4th Ed. 2002, John Wiley and Sons, Inc.
NOMENCLATURE
Ap
= area of the test shape projected in the free-stream
[ft2]
direction
Cd
= Drag coefficient
[dimensionless]
d
= cross-sectional width of object
[ft]
Fd
= axial force
[lbf]
g
= Gravitational acceleration constant
[ft/s2]
h
[in h20]
Red
= Reynolds number
[dimensionless]
Recrit = Reynolds number associated with boundary layer
[dimensionless]
transition
Vo
= Free-stream velocity
[ft/s]

= free-stream density of air
[lbm/ft3]
2-6
w
= free-stream density of water
[lbm/ft3]

= kinematic viscosity
[ft2/s2]
2-7
DATA SHEETS FOR DRAG EXPERIMENT
Speed MPH
Air Density (lb/ft3)
Pitot Tube
Pressure Difference (in.H2O)
45
60
80
100
120
130
Sphere
Axial Force, counts
45
MPH
60
MPH
80
MPH
100
MPH
1
2
2-8
120
MPH
130
MPH
Max
Acheivable
Velocity
inches H20
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