TO:
FROM:
DATE:
Dr. Sawyers
John Doe, Joe Smith
8 December, 2008
SUBJECT: Results of wind tunnel testing
On Friday, December 5, we performed an experiment to measure the drag coefficient of two
simple shapes: a flat circular disk and a concave hemisphere. The original data sheet showing
the airspeed (in mph) and the drag force (in lbf) is attached.
In order to compare to published values, the drag coefficient CD and Reynolds number Re were
calculated using the following equations:
CD 
Re 
FD
1 V 2 A
2
VD

(1)
(2)
where FD is the measured drag force,  is the density of air, V is the airspeed, A is the frontal
area of the shape, D is the diameter, and  is the viscosity of air. The diameter of the circular
disk was 0.071 m, while the diameter of the concave hemisphere was 0.075 m. The density and
viscosity were assumed to be  = 1.204 kg/m3 and  = 1.825x10-5 kg/m-s. Sample calculations
for Equations 1 and 2, including unit conversions, are attached.
The published values of drag coefficient for the two shapes considered in this experiment were
found in Fluid Mechanics: Fundamentals and Applications, by Cengel and Cimbala (Table
11.2 on pp.574-5):
 Thin circular disk: CD = 1.1
 Concave hemisphere (parachute): CD = 1.3
As shown in Figures 1 and 2 (attached), the drag coefficients obtained from the experiment were
fairly close to the published values, with a maximum error of 17% for the flat disk and 11% for
the concave hemisphere. As expected, the drag coefficient of the concave hemisphere was
consistently higher than that of the flat disk.
We believe the results of this experiment will be useful in designing a suitable parachute. If you
wish to discuss our findings further, or have any questions, feel free to contact us at
abc@def.edu.
Attachments:
- Tabular and Graphical Results
- Sample Data
- Experimental Data
Results for a Thin Circular Disk
Table 1: Drag coefficient of a thin circular disk.
Speed
(mph)
50.2
60.1
70.1
80.3
91.0
Speed
(m/s)
22.4
26.9
31.3
35.9
40.7
Re
()
1.1E+05
1.3E+05
1.5E+05
1.7E+05
1.9E+05
Drag
(lbf)
0.29
0.40
0.58
0.88
1.02
Drag
(N)
1.29
1.78
2.58
3.91
4.54
C_D
()
1.07
1.03
1.10
1.27
1.15
error
(%)
2.6
6.6
0.2
17.4
5.0
2.0E+05
2.5E+05
1.5
Drag Coefficient, C D
1.4
1.3
1.2
1.1
Theoretical Value: CD = 1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.0E+00
5.0E+04
1.0E+05
1.5E+05
Reynolds Number, Re
Figure 1: Drag coefficient of a thin circular disk.
The dashed line shows the published value.
Results for a Concave Hemisphere
Table 2: Drag coefficient of a concave hemisphere.
Speed
(mph)
50.2
60.1
70.1
80.3
91.0
Speed
(m/s)
22.4
26.9
31.3
35.9
40.7
Re
()
1.1E+05
1.3E+05
1.6E+05
1.8E+05
2.0E+05
Drag
(lbf)
0.37
0.50
0.77
0.99
1.37
Drag
(N)
1.65
2.22
3.42
4.40
6.09
C_D
()
1.23
1.16
1.31
1.28
1.38
error
(%)
5.5
10.9
0.8
1.2
6.5
1.5
1.4
Theoretical Value: CD = 1.3
Drag Coefficient, C D
1.3
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.0E+00
5.0E+04
1.0E+05
1.5E+05
2.0E+05
Reynolds Number, Re
Figure 2: Drag coefficient of a concave hemisphere.
The dashed line shows the published value.
2.5E+05
Experimentally Determining Drag Coefficients
1. Using the force balance in the Aerolab wind tunnel, measure the drag (axial force) acting on a flat circular
surface (diameter D = 0.071 m) at the following nominal airspeeds:
Nominal Airspeed
(mph)
Measured Airspeed
(mph)
Drag Force
(lbf)
50
60
70
80
90
2. Repeat part 1 using the concave hemispheric surface (diameter D = 0.075 m):
Nominal Airspeed
(mph)
Measured Airspeed
(mph)
Drag Force
(lbf)
50
60
70
80
90
3. Plot the drag coefficient as a function of Reynolds number for each shape. Recall that the definitions of C D and
Re are:
F
VD
C D  1 D2
Re 

V A
2
The area used to calculate the drag coefficient is the frontal area of the shape. The properties of air at room
temperature are  = 1.204 kg/m3 and  = 1.825x10-5 kg/m-s (from Fluid Mechanics: Fundamentals and
Applications, by Cengel and Cimbala).
4. The theoretical values of CD for a thin flat disk and for a concave hemisphere should be available in most
undergraduate Fluid Mechanics books. For each shape, create a table showing the Reynolds number, the
experimental drag coefficient, and the percent difference between the experimental and theoretical values of C D:

theoretical  exp erimental
 100%
theoretical
5. On Wednesday, December 10, each group should submit a memo report describing the results of the experiment
(see page 83 of Beer & McMurray for examples). Note that a memo report does not have to fit on a single page.
 Don’t forget to include a citation for the reference from which you obtained the theoretical C D values.
Rather than using footnotes or endnotes, you may simply include the title and authors’ names directly in the
text of the memo, as was done in part 3 above.
 The graphs and tables described above should be included as attachments.
 You should also attach one neatly handwritten sheet of sample calculations.
 Attach this data sheet showing the original values collected in the lab.