Drag Force in Flow Over a Body

TITLE Drag force in flow over body OBJECTIVE To measure the drag coefficient CD, over the range of velocities in the test section for hemispherical (open end facing flow and open end facing down stream). THEORY Drag is the component of force on a body acting parallel to the direction of relative motion. The drag force, FD, was written in the functional form FD = f1 (d, V, μ, ρ). Application of the Buckingham Pi theorem resulted in two dimensionless П parameters that written in function form as FD  ρVd = f 2  1  µ ρV 2 d 2 2

   -----------------(1.0)

Note that d2 is proportional to the cross-sectional area (A = лd2/4) and therefore we could write  ρVd   = f 3 (Re) = f 3  -------(1.1) 1 µ  2  ρV A 2 FD

Although Eq. 1.1 was obtained for sphere, the form of equation is valid for incompressible flow over any body; the characteristic length used in the Reynolds Number depends on body shape. The drag coefficient, CD, any body defined as

CD =

FD 1 ρV 2 A 2

-------------(1.2)

APPARATUS Wind tunnel and accessories

Figure 1 Wind tunnel

Figure 2 Hemisphere body

Figure 4 b streamline body

Figure 5 Holder/connecting rod

EXPERIMENTAL PROCEDURES 1. The diameter of hemispherical is measured. This measurement will be use to calculate the Reynolds Number and projected area of hemisphere. 2. The hemispherical body is fitted to the balance arm, open end facing flow first then open end facing downstream and finally airfoil body. 3. The inclined gage is set to zero, and the reading from drag scale is taken. 4. The blower fan is switch on and set the velocity to 8m/s. 5. The reading was taken from the drag scale. 6. The velocity is increased to 8, 10, 12, 14, 16; 18 and 20 m/s, and step 5 is repeated. 7. Then change the hemispherical body to open end facing downstream. 8. Then step 3 to 6 is repeated and data are taken. 9. Finally change the end facing downstream to streamlined body. Repeat the same step. 10. After done the streamlined body experiment, then placed only the connecting rod into wind tunnel. 11. Then step 3 to 6 is repeated and data are taken. 12. Reynolds no. and coefficient of drag of streamline object and hemispherical are calculated. 13. The Graph of Reynolds no. vs. drag coefficient is sketch for both hemispherical and streamline object.

DATA FROM EXPERIMENT Open End Facing Upstream

Figure 1 Open end facing upstream

Velocity (m/s) Force (N)

8 10 12 14 16 18 0.16 0.28 0.44 0.74 0.94 1.21 Table 1 Drag force, FD for open end facing upstream

20 1.48

Open End Facing Downstream

Figure 2 Open end facing downstream Velocity (m/s) 8 10 12 14 16 18 Force (N) 0.05 0.12 0.17 0.24 0.31 0.39 Table 2 Drag force, FD for open end facing downstream

20 0.48

Figure 3 Streamlined body

Velocity (m/s) Force (N)

8 10 12 14 16 0.03 0.05 0.09 0.12 0.14 Table 3 Drag force, FD for streamlined body

18 0.18

20 0.25

18 0.10

20 0.13

Holder/Connecting Rod

Figure 4 Holder/connecting rod

Velocity (m/s) Force (N)

8 10 12 14 16 0.02 0.03 0.04 0.05 0.09 Table 4 Drag force, FD for holder/connecting rod

RESULT AND CALCULATION

FD

Velocity (m/s) Upstream 0.16 8 0.28 10 0.44 12 0.74 14 0.94 16 1.21 18 1.48 20

CD

FD

CD

Upstream

Downstream

Downstream

CD NET

Re

1.2281

0.05 0.12 0.17 0.24 0.31 0.39 0.48

0.3838

0.8443

35912.4

0.5895

0.7859

44890.5

0.5799

0.9211

53868.6

0.6015

1.2532

62846.7

0.5949

1.2089

71824.8

0.5913

1.2433

80802.9

0.5894

1.2282

89781.0

1.3754 1.5010 1.8547 1.8038 1.8346 1.8176

Table 4 Data calculated from experiment Velocity

FD

CD

(m/s)

Streamlined body

streamlined body

Re

8

0.03 0.05 0.09 0.12 0.14 0.18 0.25

0.2303

35912.4

0.2456

44890.5

0.3070

53868.6

0.3008

62846.7

0.2686

71824.8

0.2729

80802.9

0.3070

89781.0

10 12 14 16 18 20

Table 5 Data calculated from experiment

Graph

CD NET (hemisphere) vs Velocity 1,4 1,2

CD NET

1 0,8 0,6 0,4 0,2 0 0

5

10

15

20

25

Velocity (m/s)

Graph 1 Graph CD NET (hemisphere) vs Velocity

CD NET (hemisphere) vs Re 1,4 1,2

CD NET

1 0,8 0,6 0,4 0,2 0 0,0

20000,0

40000,0

60000,0

80000,0

100000,0

Re

Graph 2 Graph CD NET (hemisphere) vs Re

CD (streamline body) vs Velocity

CD (streamline body)

0,3500 0,3000 0,2500 0,2000 0,1500 0,1000 0,0500 0,0000 0

5

10

15

20

25

Velocity (m/s)

Graph 3 Graph CD (streamline body) vs Velocity

CD (streamline body) vs Re

CD (streamline body)

0,3500 0,3000 0,2500 0,2000 0,1500 0,1000 0,0500 0,0000 0,0

20000,0

40000,0

60000,0

80000,0

100000,0

Re

Graph 4 Graph CD (streamline body) vs Re

Sample of Calculation

Air density in lab ρ=

P RT

ρ=

105000 286 .9 × 297 .5

ρ=1.23 kg m 3

Projected area of hemisphere A=

πd 2 4

=

π (0.065 ) 2 4

=3.318 ×10

−3

m2

CD for open end facing upstream D = 0.065m V = 8 m/s ρ = 1.23 kg/m3

CD =

FD 1 ρV 2 A 2

0.16 1 ×1.23 × 8 2 × (3.31 ×10 −3 ) 2 = 1.2281

CD = CD

CD for open end facing downstream D = 0.065m

V = 8 m/s ρ = 1.23 kg/m3 CD =

FD 1 ρV 2 A 2

0.05 1 ×1.23 × 8 2 × (3.31 ×10 −3 ) 2 = 0.383

CD = CD

CD Net CD Net = (CD for open end facing upstream) – (CD for open end facing downstream) = 1.2281- 0.3838 = 0.8443 CD for streamline body D = 0.065m V = 8 m/s ρ = 1.23 kg/m3 CD =

FD 1 ρV 2 A 2

0.03 1 ×1.23 × 8 2 × (3.31 ×10 −3 ) 2 = 0.2303

CD = CD

Reynolds Number, Re Re =

ρVD µ

1.23 ×8 ×0.065 17 .81 ×10 −6 Re = 35912.4 Re =

Percentage of error of CD for open end facing upstream CDtheory = 1.2

CDexp = 1.6307 (average)

Percentage of error, %

=

C D exp −C D theoretica

l

C D exp

×100 %

1.6307 −1.2 ×100 % 1.6307 = 26 .4% =

Percentage of error of CD for open end facing downstream CDtheory = 0.4

CDexp= 0.56 (average)

Percentage of error, %

=

C D exp −C D theoretica

l

C D exp

×100 %

0.56 − 0.4 ×100 % 0.56 = 28 .5% =

Percentage of error of CD for streamline body CDtheory = 0.04

CDexp = 0.2760 (average)

Percentage of error, % =

C D exp −C D theoretica C D exp

l

×100 %

0.2760 − 0.04 ×100 % 0.8433 = 85 .50 % =

DISCUSSION The drag coefficient values can be calculated after obtaining the drag force. The drag force can be taken by the experiment. The Reynolds number, Re, also can be obtained using a formula and the data from the experiment.

Re =

From the graph drag coefficient, CD

Net

ρVD µ

against Reynolds number, Re for hemisphere

object that has been plotted, we can see that the highest drag coefficient C D = 1.2532 occur at Re = 62846.7. At this point the velocity of air act to the body is 14 m/s. But then the drag coefficient decrease dramatically to 0.7859 when the weight and drag force increase. After the drag drop down the value of drag coefficient sometimes is increase and sometimes is decrease. From the both graph we can conclude that the drag coefficient C D increase when the Reynolds number decreasing from big to small numbers. After the drag coefficient CD was increase the Reynolds number also increased. So its mean that the value of drag is depend on their Reynolds number. The average of CD obtained from experiment is 1.6307 for open end facing upstream 0.56 for open end facing downstream and streamline body 0.2760. Compare to the theoretical value, the drag coefficient, CD for open end facing upstream is 1.2 while for open end facing downstream is 0.4 and streamline body is 0.04. The percentage of error of CD for the open end facing upstream is 26.4% then open end facing downstream is 28.5% and finally for streamline body is 85.50%. From the percentage of error calculated, it is not much differ than the theoretical value. The error due to parallax error occurs in this experiment while taking the reading and also the error because of apparatus itself such as the air goes out from the hole around the holder that connected to the drag scale. Also the balancing of the hemisphere body maybe unwell balanced. CONCLUSION The objective of the experiment achieved. The percentage of error between theoretical value and experimental value is not much differing. There is no big difference between

velocity and Reynolds number and can be concluded similarly same. The parallax error occur in this experiment is not constant that’s make the reading become difficult. The drag coefficient profile on the graph for open end facing flow and open end facing down stream is differ from each other due to streamlines and bluntness of the air flowing towards the hemisphere. It is also due to the laminar and turbulent flow that occur during the process that takes place at different Reynolds number From the experiment also it can be concluded that the higher the drag coefficient the higher the drag force involves. For 103