formal report 1- full report

8/3/2019 Formal Report 1- Full Report

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F3: Drag on a Cylinder

Experiment conducted 7/11/11

Report written10/12/11

Principal investigators:

Michael Golden, William Barraclough

Author: Michael Golden


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Contents

Summary 1

1- Introduction 2-3

2- Procedure 4

3- Results 5-7

4- Discussion 8

5- Conclusions 9

References 10

Appendices 11-14


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Summary

The main purpose of this experiment was to measure theprofile drag of a cylinder in a real (viscous) fluid by measuring

the distributive pressure around the surface. In this case, the

profile drag refers to the retarding force acting on a body

moving through a fluid parallel and opposite to the direction

of motion. A circular cylinder with a single hole, to which was

attached a manometer, was inserted into a wind tunnel and

progressively turned leeward against the fluid flow, all thewhile pressure was measured at regular 5 increments. The

resulting pressure readings were then plotted on to a graph in

order to determine the positive upstream, negative upstream

and negative downstream flows. The sum of these flows was

found, and from this the Reynolds number of the flow was

calculated. This number was then checked against the British

Standard value and found to be relatively accurate,accounting for expected experimental & statistical

inaccuracies.


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Introduction

The goal of this experiment was to accurately measure the profile drag of an object subjected to aconstant flow of a real (i.e. viscous to some degree) fluid within a wind tunnel, and from there

compare it to accepted values of the British Standard.

The object used was a circular cylinder of uniform diameter, which was placed in a wind tunnel and

subjected to an air flow of constant speed. The only feature on the otherwise smooth and uniform

cylinder was a small whole through which air could pass. Connected to this hole was a micro

manometer, there to measure the pressure differential between the cylinder surface pressure and a

static pressure tapping in the wall of the tunnel.

The 'drag' of a cylinder is defined as the retarding force acting on a body moving through a fluid

parallel and opposite to the direction of motion[1]

In an inviscid fluid (Inviscid, in this case, being defined as a fluid that can have no supporting

stress, and thus no energy dissipation[2]), the cumulative force of the pressure on the side of the

cylinder facing the flow would be perfectly equal to the pressure on the leeward (downstream) side

of the cylinder. This can be determined from the definition of 'Inviscid': an inviscid fluid is perfectly

frictionless, thus any molecules, upon meeting an obstruction, flow perfectly around it. As both

friction and pressure are manifestations of the same thing (namely, the force exerted on two objects

when they collide), if the fluid is frictionless, there will be no differential in pressure either.

In a real fluid, however, there is (obviously) friction (measured, in this case, by viscosity). As a

result of this, the forces in state around the cylinder do not cancel, there is a net drag force betweenthe upstream and downstream sides, and a 'wake' [3] .of flow disturbed by the object is formed. This

phenomenon can be clearly seen with any real fluid. Of particular real-world note in terms of real

world applications would be all manner of aircraft. The very principals by which the aerodynamics

of aircraft are determined are intrinsically and inextricably linked to the theory behind this

experiment. A plane that was designed without taking into account drag, pressure differentials and

airflow is a plane with an extremely short flight duration.


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p-p0

R

airflow

Figure 1. Section of a test cylinder

For the section of the cylinder shown in figure 1, p is the surface pressure obtained from the hole in

the cylinder surface and p0 is the static pressure obtained from the tapping in the tunnel wall. p-p0 is

the pressure difference measured by the micro manometer.

As drag acts against the the positive streamwise direction, so the pressure force per unit area on any

minimal patch of the cylinder surface placed at degrees to the inflow is .

The drag force of the previously defined patch is the pressure force per unit area multiplied by the

area of the patch. This would then be , where is the area acted upon

for a unit length of the cylinder.

From this equation, the total pressure drag D can be obtained via integration within the limits of =0

and =, remembering, of course, to account for both halves of the cylinder:

In order to enable easier comparison of similar shaped objects without having to account for relative

sizes, it is frequently more expedient to state dimensionless coefficients as opposed to numerical

values. This coefficient may be obtained by dividing the drag force value by a referential force,

equivalent to the force the flow exerts on a flat plate of surface area R, placed normal to the inflow.

This can be written as , where U is the air velocity in ms-1.

Finally, dividing the former equation for total pressure drag by , and remembering that

can be written as and thus replacing the relevant values

with that, we end up with:

where Cd = Coefficient of Drag

p = Surface pressure

p0 = Static pressureU = Air velocity

= Angle of incidence Equations on this page taken from data book[3]


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Procedure

As described in the introduction, the experiment was conducted using a small wind tunnel

containing a circular cylinder; this cylinder had a small hole drilled into it, to which was attached a

micro manometer measuring the pressure on the wall of the cylinder against the static pressure at apoint on the wall of the tunnel. The cylinder was allowed to rotate my means of a small wire

extending out of the top of the wind tunnel with a protractor inset to allow for easy referral when

changing the angle of incidence of the hole.

The experiment was begun by bringing the wind tunnel up to a suitable speed (in this case the exact

speed itself was not relevant, so long as it remained constant for the entire duration of testing). The

first point measured was with the area containing the pressure sensor upstream, directly facing

against the direction of the flow; from now on this point shall be known as 0.

At this point the pressure was taken from the readout of the micro manometer three times, in order

to acceptably account for the inevitable variations in pressure due to an inherently unstable flow.This instability was not born of any specific failures in the enactment of the experiment itself, but

rather an expected product of chaos theory- the flow of fluid in a three dimensional space being an

emergent phenomenon, thus being naturally chaotic & impossible to predict on a small level whilst

still demonstrating a relatively consistent pattern on a macro level. The average & standard

deviation was thence taken from the three results in order to provide a relatively trustworthy

indicator of the overall pattern within the data.

Having collected the data from the 0 position, the dial was then adjusted, rotating the focus area of

the cylinder to 5 from the air flow. Once again, three measurements were then taken from this

position and an average determined.

This procedure was then repeated at 5 increments all the way to 180 (focus point directly facing

away from flow, minimum exposure to oncoming fluid). The result of this was a set of results &

averages for pressure ranging from 0 to 180.

Some significant difficulties encountered during the undertaking of the experiment included:

-Problems with the delicacy of the apparatus rotating the cylinder, potentially resulting in

rotational increments of slightly more or slightly less than 5. In order to alleviate this, in

future it would be advisable to utilise more robust apparatus.

-Issues of extreme variability of results due to an unstable flow. There are two principal

issues here that, if addressed, would likely negate much of the resultant difficulty:

-The wind tunnel was not a closed system, and was in fact based within a

large, open room, with potential for significant variability in terms of

pressure & temperature; this would naturally have had a significant

effect on the air flow. A solution to this would involve placing the wind

tunnel within a sealed area, allowing for greater control over ambient

environmental conditions.

-Despite attempts to account for the unstable pressure variance by taking

multiple readings, it still likely had a statistically significant effect on

the results. Thus, in the event this experiment is repeated, it would be

advisable to take a much larger sample base from which to determine

the averages- ten sets of results would likely be sufficient.


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Results

As described in the Procedure, three results were taken for each position in 5 increments, from

which the average and the standard deviation were calculated. The raw results (including multiple

results per iteration & standard deviation values) are posited in the Appendices

[a]

. The data shownbelow in Figure 2. is the average pressure (Pa) for each increment, the sine of each angle (to 2 d.p),

and the coefficient of pressure for each result.

Figure 2. Flow measurement in Pipes Measured Data with respect to flow rate (kg/s) in column 1

Pressure (Pa) Sin (angle) Cp

0.00 112.00 0.00 1.00

5.00 100.00 0.09 0.89

10.00 88.00 0.17 0.79

15.00 69.30 0.26 0.62

20.00 37.30 0.34 0.33

25.00 20.00 0.42 0.18

30.00 -0.30 0.50 0.00

35.00 -31.00 0.57 -0.28

40.00 -59.00 0.64 -0.53

45.00 -74.67 0.71 -0.67

50.00 -88.30 0.77 -0.79

55.00 -97.00 0.82 -0.87

60.00 -95.00 0.87 -0.85

65.00 -87.67 0.91 -0.78

70.00 -85.00 0.94 -0.76

75.00 -82.00 0.97 -0.73

80.00 -78.00 0.98 -0.70

85.00 -75.00 1.00 -0.67

90.00 -74.00 1.00 -0.66

95.00 -72.00 1.00 -0.64

100.00 -70.00 0.98 -0.62

105.00 -70.00 0.97 -0.62

110.00 -71.33 0.94 -0.64

115.00 -69.00 0.91 -0.62

120.00 -72.00 0.87 -0.64

125.00 -70.67 0.82 -0.63

130.00 -70.67 0.77 -0.63

135.00 -73.33 0.71 -0.65

140.00 -74.33 0.64 -0.66

145.00 -72.67 0.57 -0.65

150.00 -73.33 0.50 -0.65

155.00 -74.00 0.42 -0.66

160.00 -72.00 0.34 -0.64

165.00 -71.67 0.26 -0.64

170.00 -74.00 0.17 -0.66

175.00 -74.00 0.09 -0.66

180.00 -71.67 0.00 -0.64


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Figure 3. Graph of Pressure difference -v- angle

Having calculated the coefficient Cp for each pressure reading and the sine of the angle, the next

step was to plot this to the graph, Figure 4, shown below.

Figure 4. Graph of Cp -v- Sine(angle)


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From here the graph was numerically integrated by calculating the area under each portion of the

graph (positive upstream, negative upstream and negative downstream), and the sum of these areas,

Cd, was determined.

Positive Cp upstream:

Total area = 0.283

Negative Cp upstream

Total area = 0.2859

Negative Cp downstream

Total area = 0.643

Sum of areas, Cd = 1.2119 Complete calculations can be found in Appendices[b]

With the total coefficient Cd calculated, it was possible from here to determine the Reynold's

Number of the flow. The Reynold's number is a dimensionless number that expressed the ratio of

forces of inertia to viscosity.[4] The full method of how this was calculated can be seen in the

appendices[c]

Re = 12702 (5 s.f)

Finally, the coefficient of drag Cd as measured in the experiment was compared with the officially

accepted calculated value as determined from a chart showing accepted differences in coefficients

according to shape[e]

Calculated Cd = 1.2

Measured Cd = 1.2119

This difference is small enough to be accounted for in statistical and practical error analysis and assuch can be accepted as a reasonably successful result.


10/15

Discussion

At the conclusion of the section of this report detailing the results of the experiment, it was shown

that the measured Cd, 1.2119, matched the expected calculated Cd of 1.2 rather well, with a

divergence of just 0.99%.

[d]

Considering the latent instability in the environment within which theexperiment was conducted, this may be considered a successful result.

As stated previously, the experimental factor that initially caused the most concern whilst

conducting the experiment was that of the environment. The primary piece of apparatus in the

experiment was the wind tunnel, and much of the calculation was based upon an assumption of a

steady air flow. As the wind tunnel did not take its air flow from a closed system, it was understood

that atmospheric conditions would play a significant factor in the flow itself and thus they were of

large concern.

Unfortunately, the area the experiment was conducted in was a large, open lab, with multiple

entrances & exits, and large numbers of people passing through frequently. The effects of suchunaccounted variables would be to introduce instabilities into the fluid flow, and potentially have a

significant effect on the results. Fortunately, it would seem that these unknown factors did not have

as disastrous an effect on the experiment as feared; it would be reasonable to assume, however, that

they are the largest factor in the small difference between the calculated coefficient and the

observed coefficient.

In order to understand why such an experiment is necessary at all however, one must first

understand the difference between a real and an inviscid fluid. Put simply, an 'inviscid' or 'perfect'

fluid is one that has zero viscosity; viscosity in this context being defined as a fluid property that

related the magnitude of fluid shear stresses to the fluid strain rate, or more simply, to the spatial

rate of change in the fluid velocity field[3].. Thus a circular cylinder of the same kind in theexperiment subjected to a flow of an inviscid fluid would experience no drag. All fluids (barring

some exceptional so-called 'super-fluids') are subject to internal resistance and shear force. In a

perfectly steady one-dimensional flow, this would not be an issue; however when a viscous fluid is

forced to move around an object within a three-dimensional flow (in this case the circular cylinder),

its internal friction prevents it from steadily and perfectly moving- the change of direction of some

of the flow causes a change in velocity relative to the rest of the flow. In a fluid not subject to

internal resistance or shear force this would not be a problem, but in a real fluid this relative

dichotomy of velocities causes turbulence and drag.

The study of turbulence and drag around an object, whatever the shape, is a fundamental aspect of

engineering design, particularly in nautical and aeronautical engineering. Although a simpleexample, the application of experiments such as this is fundamental to all successful design

projects involving vehicles moving in a fluid, whether that fluid be air or water.


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Conclusion

This experiment, although initially subject to some potential unreliability due to environmental

conditions, has been shown to be in line with results calculated from the approved standard to

within a statistically acceptable margin (0.9916..%).

Whilst not breaking new ground in and of itself, the experiment comfortably demonstrates, all

inaccuracies accounted for, the reliability of using the standard coefficients of drag (table shown in

appendices[e]). On this basis, it would be reasonable to call the experiment a success, as the results

observed were in line with the predicted results, and an important demonstration of the difference

between the theoretical action of an inviscid flow and the actual action of a fluid flow subject to

normal viscosity.

Whilst some fluids of negligible viscosity may well exist within laboratory conditions, one cannotexpect to encounter them within the every day applications of fluid mechanics; as such turbulence

and drag are an unfortunate but unavoidable part of most vehicle design, whatever the type. Thus

the results obtained in this experiment, and all others like it, are of paramount importance in all

successful engineering design involving objects moving within a fluid. Whilst simple, the idea

behind this experiment demonstrates the fundamental mechanics necessary to all good design.


12/15

References

[1] Merriam Webster definition- Drag

http://www.merriam-webster.com/dictionary/drag

Accessed 10/11/11

[2] Clancy, L.J. (1975), Aerodynamics, Pitman Publishing Limited, London.

[3] Efunda, Engineering Reference- Viscosity

http://www.efunda.com/formulae/fluids/glossary.cfm

[4] Department of Engineering Lab Handbook, F3-2,3

[5] Glen Research Centre, Nasa- Reynolds Number

http://www.grc.nasa.gov/WWW/BGH/reynolds.html


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Appendices

[a] Table of raw results taken from micro manometer; table shows three measurements of

pressure and the mean derived from them for every 5 increment.

Degrees

0 112 120 104 112

5 100 104 96 100

10 88 94 80 88

15 68 76 60 69.33

20 32 37 43 37.33

25 15 20 25 20

30 -9 0 8 -0.33

35 -26 -30 -37 -31

40 -65 -59 -53 -5945 -79 -75 -70 -74.67

50 -94 -88 -83 -88.3

55 -104 -97 -90 -97

60 -105 -95 -90 -95

65 -95 -88 -90 -87.67

70 -70 -86 -90 -85

75 -77 -84 -88 -82

80 -75 -77 -86 -78

85 -72 -75 -81 -75

90 -70 -75 -80 -74

95 -65 -71 -78 -72

100 -64 -70 -77 -70

105 -74 -70 -66 -70

110 -76 -71 -67 -71.33

115 -73 -69 -65 -69

120 -78 -72 -66 -72

125 -75 -70 -67 -70.67

130 -75 -71 -66 -73.33

135 -80 -72 -68 -73.33

140 -80 -74 -69 -74.33

145 -77 -70 -68 -72.67

150 -78 -73 -68 -73

155 -81 -74 -68 -74

160 -74 -72 -68 -72

165 -78 -73 -64 -71.67

170 -78 -74 -70 -74

175 -81 -73 -68 -74

180 -77 -72 -66 -71.67

P1 P2 P3 Pm


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[b] Full calculations for numerical integration of drag coefficients

Positive Cp upstream:

(0.9 x 0.085) + (0.8 x 0.085) + (0.6 x 0.085) + (0.35 x 0.085) + (0.2 x 0.08) = 0.24125

(8 + 18 + 23 + 10 + 17) x 0.0005 = 0.04175

Total area= 0.283

Negative Cp upstream

(0.3 x 0.07) =+ (0.55 x 0.06) + (0.45 + 0.05) + (0.74 x 0.18) + (0.7 x 0.04) = 0.2494

(19.5 + 12 + 6 + 7 +23.5 + 3 + 2) x 0.0005 = 0.0345

Total area= 0.2859

Negative Cp downstream

0.65 x 0.76 = 0.494

0.24 x 0.6 = 0.144

10 x 0.0005= 0.643

Total area= 0.643

Total area= 1.2119, thus Cd =1.2119


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[c] Full calculations for determining Reynolds Number

Where Vo = Velocity = 13.59

d = Diameter = 1.43 x 10-4

V = Viscosity = 1.53 x 10-5

(5 sf)

Calculated Cd = 1.2

Measured Cd = 1.2119

[d] Calculation of percentage difference between Calculated coefficient and Measured

Coefficients

=

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