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
= µ ρ ρ Vd f d V FD 2 2 2 2 1 ---(1.0)
Note that d2 is proportional to the cross-sectional area (A = лd2/4) and therefore we could
write (Re) 2 1 3 3 2 f Vd f A V FD = = µ ρ ρ ---(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
A V F C D D 2 2 1ρ = ---(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
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
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
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 N E 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 N E T
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 (s tr ea m li n e b o d 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 (s tr ea m li n e b o d y)
Graph 4 Graph CD (streamline body) vs Re
Air density in lab RT P = ρ 5 . 297 9 . 286 105000 × = ρ 3 23 . 1 kg m = ρ
Projected area of hemisphere
4 2 d A=π 4 ) 065 . 0 ( 2 π = =3.318 ×10−3m2
CD for open end facing upstream
D = 0.065m V = 8 m/s ρ = 1.23 kg/m3 2281 . 1 ) 10 31 . 3 ( 8 23 . 1 2 1 16 . 0 2 1 3 2 2 = × × × × = = − D D D D C C A V F C ρ
CD for open end facing downstream
V = 8 m/s ρ = 1.23 kg/m3 383 . 0 ) 10 31 . 3 ( 8 23 . 1 2 1 05 . 0 2 1 3 2 2 = × × × × = = − D D D D C C A V F C ρ 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 2303 . 0 ) 10 31 . 3 ( 8 23 . 1 2 1 03 . 0 2 1 3 2 2 = × × × × = = − D D D D C C A V F C ρ Reynolds Number, Re 35912.4 Re 10 81 . 17 065 . 0 8 23 . 1 Re Re 6 = × × × = = − µ ρVD
Percentage of error of CD for open end facing upstream
CDtheory = 1.2 CDexp = 1.6307 (average)
% 4 . 26 % 100 6307 . 1 2 . 1 6307 . 1 % 100 exp exp = × − = × = − D l theoretica D D C C C
Percentage of error of CD for open end facing downstream
CDtheory = 0.4 CDexp= 0.56 (average)
Percentage of error, % % 5 . 28 % 100 56 . 0 4 . 0 56 . 0 % 100 exp exp = × − = × = − D l theoretica D D C C C
Percentage of error of CD for streamline body
CDtheory = 0.04 CDexp = 0.2760 (average)
Percentage of error, % % 50 . 85 % 100 8433 . 0 04 . 0 2760 . 0 % 100 exp exp = × − = × = − D l theoretica D D C C C 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.
µ ρVD
= Re
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
• 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.
Tabular form for velocity at 10m/s θ
Location Angle, θ (degree) Manometer Height(mm) h - h∞ (mm) P - P∞ (pa) CP = P - P∞ 1/2ρV 1 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
Sample calculation:
Location 1 at velocity 10 m/s θ = 0̊
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 (degree) Manometer Height(mm) h - h∞ (mm) p - p∞ (pa) CP = p - p∞ 1/2ρV 1 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 = 0̊
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
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
