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

-----------------(1.0)

Note that d2 is proportional to the cross-sectional area (A = лd2/4) and therefore we could

write

-------(1.1)

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

-------------(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) 8 10 12 14 16 18 20

Force (N) 0.16 0.28 0.44 0.74 0.94 1.21 1.48

Table 1 Drag force, FD for open end facing upstream

Open End Facing Downstream

Figure 2 Open end facing downstream

Velocity (m/s) 8 10 12 14 16 18 20

Force (N) 0.05 0.12 0.17 0.24 0.31 0.39 0.48

Table 2 Drag force, FD for open end facing downstream

Figure 3 Streamlined body

Velocity (m/s) 8 10 12 14 16 18 20

Force (N) 0.03 0.05 0.09 0.12 0.14 0.18 0.25

Table 3 Drag force, FD for streamlined body

Holder/Connecting Rod

Figure 4 Holder/connecting rod

Velocity (m/s) 8 10 12 14 16 18 20

Force (N) 0.02 0.03 0.04 0.05 0.09 0.10 0.13

Table 4 Drag force, FD for holder/connecting rod

RESULT AND CALCULATION

Velocity (m/s)

FD

Upstream

CD

Upstream

FD

Downstream

CD

Downstream CD NET Re

8 0.16 1.2281 0.05 0.3838 0.8443 35912.4

10 0.28 1.3754 0.12 0.5895 0.7859 44890.5

12 0.44 1.5010 0.17 0.5799 0.9211 53868.6

14 0.74 1.8547 0.24 0.6015 1.2532 62846.7

16 0.94 1.8038 0.31 0.5949 1.2089 71824.8

18 1.21 1.8346 0.39 0.5913 1.2433 80802.9

20 1.48 1.8176 0.48 0.5894 1.2282 89781.0

Table 4 Data calculated from experiment

Velocity

(m/s)

FD

Streamlined body

CD

streamlined body Re

8 0.03 0.2303 35912.4

10 0.05 0.2456 44890.5

12 0.09 0.3070 53868.6

14 0.12 0.3008 62846.7

16 0.14 0.2686 71824.8

18 0.18 0.2729 80802.9

20 0.25 0.3070 89781.0

Table 5 Data calculated from experiment

Graph

CD NET (hemisphere) vs Velocity

0

0,2

0,4

0,6

0,8

1

1,2

1,4

0 5 10 15 20 25

Velocity (m/s)

CD

NE

T

Graph 1 Graph CD NET (hemisphere) vs Velocity

CD NET (hemisphere) vs Re

0

0,2

0,4

0,6

0,8

1

1,2

1,4

0,0 20000,0 40000,0 60000,0 80000,0 100000,0

Re

CD

NE

T

Graph 2 Graph CD NET (hemisphere) vs Re

CD (streamline body) vs Velocity

0,0000

0,0500

0,1000

0,1500

0,2000

0,2500

0,3000

0,3500

0 5 10 15 20 25

Velocity (m/s)

CD

(str

eam

lin

e b

od

y)

Graph 3 Graph CD (streamline body) vs Velocity

CD (streamline body) vs Re

0,0000

0,0500

0,1000

0,1500

0,2000

0,2500

0,3000

0,3500

0,0 20000,0 40000,0 60000,0 80000,0 100000,0

Re

CD

(str

eam

lin

e b

od

y)

Graph 4 Graph CD (streamline body) vs Re

Sample of Calculation

Air density in lab

Projected area of hemisphere

CD for open end facing upstream

D = 0.065m

V = 8 m/s

ρ = 1.23 kg/m3

CD for open end facing downstream

D = 0.065m

V = 8 m/s

ρ = 1.23 kg/m3

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

Reynolds Number, Re

Percentage of error of CD for open end facing upstream

CDtheory = 1.2 CDexp = 1.6307 (average)

Percentage of error, %

Percentage of error of CD for open end facing downstream

CDtheory = 0.4 CDexp= 0.56 (average)

Percentage of error, %

Percentage of error of CD for streamline body

CDtheory = 0.04 CDexp = 0.2760 (average)

Percentage of error, %

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.

From the graph drag coefficient, CD Net against Reynolds number, Re for hemisphere

object that has been plotted, we can see that the highest drag coefficient CD = 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 CD 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<Re<3×105 the drag coefficient is approximately

constant. In this range the entire rear of the sphere has a low pressure turbulent wake and

most of the drag is caused by the front-rear pressure asymmetry.

In summarize, the drag, which contains portions due to friction (viscous) effects and

pressure effects, is written in terms of dimensionless drag coefficients, CD. It also shown

that the drag coefficient, CD, is a function of shape and Reynolds Number, Re.

REFERENCES

Fundamentals of Fluid Mechanics, 4th Edition, Wiley

Bruce R. Munson, Donald F. Young, Theodore H. Okiishi

Fluid Mechanics 3rd Edition

J.F Douglas, J.M Gaslorek, J.A Swaffield

Introduction to Fluid Mechanics 6th Edition, Wiley International Edition

Robert W. Fox, Alan T. Mcdonald, Philip J. Pritchard

TITLE

Flow Pass a Circular Cylinder

Objective

The objective of this experiment is to study the pressure profile and flow characteristics for flow around a circular cylinder.

Theoretical background

The structure and development of viscous flow over a cylinder is described in figure 9.17a below. The development of the boundary layer and changes in velocity profile from the stagnation point at A until flow separation at point E are described in Figure 9.17b. these changes are closely linked to the change of pressure gradient from A to F. negative pressure gradient tends to maintain laminar boundary layer, while positive pressure gradient will accelerate it to turbulent and (subsequently) reverse flow resulting in flow separation.Figure 9.17c compare the pressure distributions (it is customary to plot the coefficient of pressure) around the cylinder between low Re number and high Re flow and high Re flows and of that predicted by inviscid flow theory.

Experimental procedure

1. A 2-inch diameter circular cylinder of are placed at across 300 mm x 300 mm test section of a wind tunnel as schematically shown below.

V

P∞

2. 20 pressure tapping hole are drill at equidistance over half of the circumference of the cylinder in older to measure pressure around the cylinder.

3. These holes are connected using flexible tube to the multitube manometer for pressure measurement.

θ

Tabular form for velocity at 10m/s

Location Angle, θ(degree)

Manometer Height(mm)

h - h∞

(mm)P - P∞

(pa)CP = P - P∞

1/2ρV1 0 226 3 0.023 5.867x10-4

2 0 227 4 0.031 7.908x10-4

3 0 229 6 0.046 1.174x10-3

4 0 232 9 0.069 1.176x10-3

5 0 236 13 0.100 2.251x10-3

6 0 240 17 0.131 3.342x10-3

7 0 244 21 0.162 4.133x10-3

8 0 245 22 0.169 4.311x10-3

9 0 244 21 0.162 4.133x10-3

10 0 242 19 0.146 3.724x10-3

11 0 240 17 0.131 3.342x10-3

12 0 242 19 0.146 3.724x10-3

13 0 242 19 0.146 3.724x10-3

14 0 242 19 0.146 3.724x10-3

15 0 242 19 0.146 3.724x10-3

16 0 242 19 0.146 3.724x10-3

17 0 242 19 0.146 3.724x10-3

18 0 242 19 0.146 3.724x10-3

19 0 242 19 0.146 3.724x10-3

Graph coefficient of pressure against location

Sample calculation:

Location 1 at velocity 10 m/s

θ = 0N

h = 226 mm

h∞ = 223 mm

H = h – h∞

= 226 – 223

= 3 mm

= 3x10-3 m

P1 = P∞ + ρgH

Given ρ = 0.784 kg/m2

g = 9.81 m/s2

H = 3x10-3

P1 - P∞ = ρgH

= 0.784x9.81x3x10-3

= 0.023 Pa

CP = P1 - P∞

1/2ρV = 0.023 (0.5)(0.784)(10)

= 5.867x10-3

Tabular form for velocity at 20m/s

Location Angle, θ Manometer h - h∞ p - p∞ CP = p - p∞

(degree) Height(mm) (mm) (pa) 1/2ρV1 0 216 6 0.046 2.93x10-4

2 0 220 10 0.077 4.91x10-4

3 0 230 20 0.154 9.82x10-4

4 0 244 34 0.261 1.665x10-3

5 0 262 52 0.400 2.55x10-3

6 0 279 69 0.531 3.387x10-3

7 0 292 82 0.631 4.024x10-3

8 0 298 88 0.677 4.32x10-3

9 0 292 82 0.631 4.02x10-3

10 0 290 80 0.615 3.92x10-3

11 0 284 74 0.569 3.62x10-3

12 0 290 80 0.615 3.92x10-3

13 0 292 82 0.631 4.024x10-3

14 0 292 82 0.631 4.024x10-3

15 0 293 83 0.638 4.069x10-3

16 0 294 84 0.646 4.12x10-3

17 0 294 84 0.646 4.12x10-3

18 0 294 84 0.646 4.12x10-3

19 0 294 84 0.646 4.12x10-3

Sample calculation:

Location 1 at velocity 20 m/s

θ = 0N

h = 216 mm

h∞ = 210 mm

H = h – h∞

= 216 – 210

= 6 mm

= 6x10-3 m

P1 = P∞ + ρgH

Given ρ = 0.784 kg/m2

g = 9.81 m/s2

H = 6x10-3

P1 - P∞ = ρgH

= 0.784x9.81x6x10-3

= 0.046 Pa

CP = P1 - P∞

1/2ρV = 0.046 (0.5)(0.784)(20)

= 2.93x10-3

Discussion:

1. According to the graph coefficient of pressure against location, there are two type of graph refer to velocity 10 m/s and 20 m/s. The gradient for the graph at velocity 20 m/s and 10 m/s is mostly same. At the beginning the value of coefficient pressure is increased until point 4.3x10-3. Then the value decreased at location 11 and next it increased at location 12. After location 12, the graph is constant until end of location.

2. The influence of velocity between 10 m/s and 20 m/s are very small. It not affects the experiment result. We can assume the neglected.

Conclusion:1. The coefficient pressure increase due to locations but at the certain point it

down and become constant at the end.2. The velocity does not give big effects to the value of coefficient pressure.

References:

1. Fluids Mechanics

Volume 2

J.F Doughlas & R.D Matthews

Third Edition

2. Fluids Power with applications

Sixth Edition

Anthony Esposito

3. Fluids Mechanics

Fundamentals And Applications

Yunus A.Cengal, John M. Cimbala

Mc Graw Hill