The purposes of the probe is to mensurate the force per unit area distribution on the surface of a smooth cylinder placed with its axis perpendicular to the flow and to compare it with the distribution predicted for frictionless flow, and to cipher the drag coefficient of the cylinder.

In the probe being carried out, a cylinder in a closed circuit air current tunnel will be experimented upon to garner the force per unit area distribution moving on it at different velocities. When the cylinder is standing vertically to the entrance flow in a wind-tunnel, two experiments will be carried out for the same cylinder, one with smooth ( laminar ) flow and the other with disruptive flow. The experimental force per unit area distribution obtained from each experiment will be compared with the theoretical distribution predicted for frictionless flow. The retarding force coefficient for the cylinder will be calculated together with the tunnel standardization invariable for both trials.

The smooth cylinder has got 12 force per unit area tappings at angular intervals of 30° on its surface ; it is besides placed with its axis perpendicular on a turntable on the floor. These tappings are connected to multi-tube ( methylated liquors ) manometer, which is inclined at an angle of 30° to the horizontal. The multi-tube manometer has got a sum of 34 tubings, out of which the first 12 are straight connected to the force per unit area tappings on the cylinder, so that tubing 1 is connected to coerce tapping 1 and so on. Pressure tapping 1 is confronting the oncoming flow when the angular place index is set at 0° . Since force per unit area tapping 1 is connected to tube 1 in the multi-tube manometer, the caput force per unit area shown on tubing 1 will stand for the stagnancy force per unit area. Tube 34 in the multi-tube manometer is connected to the upstream portion of the wind-tunnel. The Betz manometer is used to alter the entrance flow speed at the upstream subdivision. Since both the Betz manometer and tubing 34 ( in the multi-tube manometer ) are connected to the upstream subdivision, both will demo the same tantamount reading for force per unit area but in different units.

## Background theory:

Laminar flow is defined when a fluid flows in parallel beds, with no break between the beds. In comparing to this Turbulent flow has a much more disorganised form, it is characterized by blending of the fluid by Eddies of changing size within the flow.

The Reynolds figure ( Re ) , gives the step for laminar and turbulent flows. Laminar flow takes topographic point when Reynolds figure is lower than 104, and for Turbulent flow the Re must be greater than 3A-105. Reynolds figure has got no units since it is merely a ratio. There are many diverse types of equations for deducing the Reynolds figure of an existent form.

Fig. Angstrom shows the different types of flow forms at assorted angles.

The appropriate equation for the cylinder ‘s Reynolds figure can be acquired from:

Re = [ combining weight. 1 ]

Where: vitamin D = Diameter of cylinder

Va?z = Velocity of fluid upstream

V = Kinematic viscousness of air ( 1.46A-10-5 m2s-1 )

From the equation both values of vitamin D and V stay changeless for both experiments, therefore the alteration in Reynolds figure depends straight on the upstream speed of the wind-tunnel.

From the Bernoulli ‘s equation the relationship between fluid force per unit area and speed can be established

[ eq.2 ]

Where: P = force per unit area of the fluid

Z = Height

i??air = air denseness

i?? = The denseness of the fluid

G = Gravity

V= the speed of the fluid

The tallness in remains changeless therefore the flow in the air current tunnel has an equation.

[ eq.3 ]

By spliting both sides with i?? and taking measurings from the point where the flow of speed Michigans, ( the stagnancy point where V2 = 0 ) . This is for the ground that at the stagnancy point on the surface of the tubing that is perpendicular to the flow to it, hence the dynamic force per unit area is given by:

[ combining weight. 4 ]

The force per unit area is measured utilizing the manometer, and so therefore the force per unit area at the tapping must be the same as the force per unit area caput at i??gH.

Then the stagnancy caput and inactive caput measured on the multi-tube manometer Inclined at a specific angle are given by:

[ eq.5 ] [ eq.6 ]

So when utilizing these two equations the force per unit area differences found utilizing them become.

[ eq.7 ]

The dynamic force per unit area upstream of the cylinder is gained from:

[ eq.8 ]

In the equation above K = the tunnel standardization invariable. The force per unit area alteration across the air current tunnel contraction is measured utilizing two different instruments ; the Betz manometer and the Multi-tube manometer ( tube no. 34 ) . In an ideal system where there are no losingss in energy. In processs with energy losingss, the ratio value is below 1. The relation is known as the tunnel standardization invariable ( K ) . is the force per unit area fluctuation across the contraction as displayed by the reading on the Betz micro-manometer.

The tunnel standardization invariable can be attained straight from:

[ eq.9 ]

Differences between the force per unit area at angles from the forepart of the stagnancy point and the free steam force per unit area Pi‚µ is gained from the undermentioned equation:

[ eq.10 ]

## hi?† is a reading on tubing 1 when force per unit area tapping figure 1 is at an angle from the forepart of the stagnancy point. Therefore the force per unit area coefficient at an angle can be defined:

[ eq.11 ]

To happen the force per unit area coefficient based on frictionless flow by utilizing:

[ eq.12 ]

The equation above is applied when plotting a graph, of fluctuation of cI¦ vs. I¦ , by replacing values of angles into the equation above and so happening out the subsequent values for force per unit area coefficient ( cI¦ ) . The consequent graph drawn from the derived equation will merely match to a theoretical relationship, where the flow is believed to be frictionless.

In the illustration below, the force per unit area in the aftermath part is less than force per unit area upstream ; this causes retarding force, chiefly due to flux separation behind the organic structure. The streamline form and the force per unit area distribution are non balanced and a aftermath of slow-moving air is produced behind the cylinder.

Fig. B shows flow separation taking topographic point behind the cylinder

The retarding force force, due to the force per unit area forces on the cylinder can be derived from:

[ eq.13 ]

As the term integrates to zero, the retarding force coefficient can be simplified to:

[ eq.14 ]

Apparatus

The cylinder being experimented on is placed in the air current tunnel. The portion that will be under proving will be of size of 1.000m Ten 0.760m. The air current tunnel will hold a contraction ratio of 5.6

To link the force per unit area tappings from upstream and downstream of the tunnel contraction to a Betz micro-manometer ( mmH2O ) .

The speed of air in the trial subdivision is to be fluctuated by seting the fan velocities on a accountant.

Third a smooth round cylinder with diameter 114.3 millimeter to be placed with its axis perpendicular, on a turntable on the land of the trial subdivision country. It can be seen in the cylinder where midway along there are pressure tappings at angular intervals of 30i‚° on its surface, near to the tappings are pronounced Numberss from 1 to 12, these are connected to the upper terminals of 1 to 12 tubings on a manometer. This manometer is to be a multi-tube methylated liquors manometer.

The force per unit area upstream of the cylinder is sensed by a taping on the tunnel wall and is connected to one of the tubings. In this experiment to be tube figure 34. The staying tubes 13 to 33 are unfastened to the ambiance.

The degree of turbulency has to be changed, so in this trial subdivision it is little nevertheless to be increased by the interpolation of a grid. This grid as an array of round rods upstream of the trial subdivision.

Last as the cylinder is to be placed on the turntable that is to be rotated. The angular place of force per unit area tapping figure 1 is indicated on a digital counter in grades and in ten percents of grade.

Method:

## To be able to make this experiment the cylinder to be already oriented so that the force per unit area from tapping 1 is confronting the onset flow and the angular place index will hold to be set at 0i‚° . As we know that the force per unit area P1 tapping is the stagnancy force per unit areas and exceeds the force per unit area Infinity upstream of the cylinder by an sum.

The experiment foremost to prove laminar flow – The laminar flow of the speed of the air current tunnel will be increased bit by bit until the Betz manometer reads 15mH2O. For this speed to stay changeless accommodations are made.

From the multi-tube manometer, to take readings of unstable highs to demo a general thought of the force per unit area distribution.

The fluid tallness to be noted from the tubing which is connected to the tunnel wall upstream of the cylinder.

To mensurate the fluid tallness in tubing 1 is measured so the tabular array is to be turned in intervals of 10 grades, this is to be repeated for every 10 grades until it has to the full rotated around 360 grades.

The experiment is besides to prove in a turbulent flow – To hold a grid with an array of squares inserted in to the air current tunnel, where the air flow and the speed increases until the Betz manometer reads 35mmH2O, as the air becomes disruptive.

This whole process to be repeated.

Fig. C shows the manometer tubing readings at a zero angle for smooth flow.

Fig. D shows the manometer tubing readings at a zero angle for turbulent flow.

The readings of the multi-tube manometer were taken earlier get downing to revolve the cylinder ( at zero angle ) . This preliminary information collected is presented visually to demo the form of the force per unit area distribution around the cylinder. Tube 33 is unfastened to air ; hence it shows the atmospheric force per unit area. And tube 34 as mentioned earlier, shows the head force per unit area of the upstream subdivision of the wind-tunnel.

Consequences

Natural Consequences:

The graduated table of the manometer used was in inch. Therefore, the consequences obtained have to be changed to meters. This is done as follows:

1 inch = 0.0254 meters

The highs of the fluids have to be multiplied by 0.0254 to alter to meters.

Smooth flow:

I± = 30A°

ha?z = 11 inch = 11 tens 0.0254

= 0.2794m

Disruptive flow:

I± = 30A°

ha?z = 10.4 inch = 10.4 tens 0.0254

= 0.26416m

The force per unit area coefficient, cI• , at an angle can be found by utilizing eq 8.

The computations to happen cI• will be the same for both laminar and turbulent flows. The lone difference would be that the value of ha?z would be different in each instance.

The value for h1 is the value obtained when the cylinder is at 0A° .

The computations to happen the force per unit area coefficient for the laminar flow at I¦ = 0A° is shown below:

= 1

Calculated Consequences

Table 1 Table 2

## Smooth Flow ( Laminar Flow )

## i?†i‚°

## H [ inch ]

## H [ metre ]

0

9.5

0.2413

10

9.7

0.24638

20

10.2

0.25908

30

10.9

0.27686

40

11.7

0.29718

50

12.4

0.31496

60

13

0.3302

70

13.2

0.33528

80

12.9

0.32766

90

12.8

0.32512

100

12.8

0.32512

110

12.8

0.32512

120

12.9

0.32766

130

13

0.3302

140

13

0.3302

150

13.1

0.33274

160

13.1

0.33274

170

13.2

0.33528

180

13.1

0.33274

190

13.2

0.33528

200

13.2

0.33528

210

13

0.3302

220

12.9

0.32766

230

12.9

0.32766

240

12.9

0.32766

250

12.8

0.32512

260

12.8

0.32512

270

12.8

0.32512

280

12.8

0.32512

290

13

0.3302

300

12.9

0.32766

310

12.4

0.31496

320

11.5

0.2921

330

10.7

0.27178

340

10.1

0.25654

350

9.6

0.24384

360

9.5

0.2413

## Turbulent Flow

## i?†i‚°

## H [ inch ]

## H [ metre ]

0

8

0.2032

10

8.4

0.21336

20

9.6

0.24384

30

11.3

0.28702

40

13.5

0.3429

50

15.7

0.39878

60

17.5

0.4445

70

18.8

0.47752

80

19

0.4826

90

17.9

0.45466

100

17.6

0.44704

110

15.2

0.38608

120

14

0.3556

130

13.8

0.35052

140

13.7

0.34798

150

13.7

0.34798

160

13.7

0.34798

170

13.6

0.34544

180

13.5

0.3429

190

13.6

0.34544

200

13.7

0.34798

210

13.7

0.34798

220

13.7

0.34798

230

13.8

0.35052

240

14.1

0.35814

250

15.9

0.40386

260

18.1

0.45974

270

18.5

0.4699

280

19.2

0.48768

290

18.6

0.47244

300

17

0.4318

310

15.2

0.38608

320

13

0.3302

330

10.9

0.27686

340

9.3

0.23622

350

8.2

0.20828

360

8

0.2032

The undermentioned information shows values, which will be used to find the force per unit area coefficient, this will be calculated utilizing combining weight. 11.

## Smooth flow Transonic Flow

## I¦

## H [ meter ]

## cI¦

0

0.2032

1

10

0.21336

0.833333

20

0.24384

0.333333

30

0.28702

-0.375

40

0.3429

-1.29167

50

0.39878

-2.20833

60

0.4445

-2.95833

70

0.47752

-3.5

80

0.4826

-3.58333

90

0.45466

-3.125

100

0.44704

-3

110

0.38608

-2

120

0.3556

-1.5

130

0.35052

-1.41667

140

0.34798

-1.375

150

0.34798

-1.375

160

0.34798

-1.375

170

0.34544

-1.33333

180

0.3429

-1.29167

190

0.34544

-1.33333

200

0.34798

-1.375

210

0.34798

-1.375

220

0.34798

-1.375

230

0.35052

-1.41667

240

0.35814

-1.54167

250

0.40386

-2.29167

260

0.45974

-3.20833

270

0.4699

-3.375

280

0.48768

-3.66667

290

0.47244

-3.41667

300

0.4318

-2.75

310

0.38608

-2

320

0.3302

-1.08333

330

0.27686

-0.20833

340

0.23622

0.458333

350

0.20828

0.916667

360

0.2032

1

## i?†

## H [ meter ]

## ci?†

0

0.2413

1

10

0.24638

0.866667

20

0.25908

0.533333

30

0.27686

0.066667

40

0.29718

-0.46667

50

0.31496

-0.93333

60

0.3302

-1.33333

70

0.33528

-1.46667

80

0.32766

-1.26667

90

0.32512

-1.2

100

0.32512

-1.2

110

0.32512

-1.2

120

0.32766

-1.26667

130

0.3302

-1.33333

140

0.3302

-1.33333

150

0.33274

-1.4

160

0.33274

-1.4

170

0.33528

-1.46667

180

0.33274

-1.4

190

0.33528

-1.46667

200

0.33528

-1.46667

210

0.3302

-1.33333

220

0.32766

-1.26667

230

0.32766

-1.26667

240

0.32766

-1.26667

250

0.32512

-1.2

260

0.32512

-1.2

270

0.32512

-1.2

280

0.32512

-1.2

290

0.3302

-1.33333

300

0.32766

-1.26667

310

0.31496

-0.93333

320

0.2921

-0.33333

330

0.27178

0.2

340

0.25654

0.6

350

0.24384

0.933333

360

0.2413

1

Table 3 Table 4

## Frictionless flow

The values for the force per unit area coefficients will be the same for both laminar and turbulent flows since cI• merely depends on the angle I¦ .

The force per unit area coefficient for a frictionless flow is found utilizing combining weight. 12.

Table 5

## I¦A°

## cI¦

0

1

10

0.879385242

20

0.532088886

30

0

40

-0.652703645

50

-1.347296355

60

-2

70

-2.532088886

80

-2.879385242

90

-3

100

-2.879385242

110

-2.532088886

120

-2

130

-1.347296355

140

-0.652703645

150

0

160

0.532088886

170

0.879385242

180

1

190

0.879385242

200

0.532088886

210

0

220

-0.652703645

230

-1.347296355

240

-2

250

-2.532088886

260

-2.879385242

270

-3

280

-2.879385242

290

-2.532088886

300

-2

310

-1.347296355

320

-0.652703645

330

-1.77636E-15

340

0.532088886

350

0.879385242

360

1

Theoretical graph:

The graph represents in a theoretical mode in which the experimental values should be able to compare to, whereby the air fluxing in the graph, shows changeless alteration at regular angle intervals. Besides all extremums and troughs on the graph show relevant force per unit area coefficients.

The graphs illustrate the force per unit area coefficient

fluctuation with alterations in angle.

The above graph shows the fluctuation of cI¦ vs. I¦ in laminar flow.

This is so compared to the cI¦ vs. I¦ in disruptive flow.

Calculations to happen the retarding force coefficient, Cadmium:

The value for the retarding force coefficient depends on the value of cI¦ cosI¦ , this relation can besides be noticed in combining weight. 14.

## Laminar flow

Table 6

## I¦ A°

## Pressure coefficient, cI¦

## cI¦cosI¦

0

1

1

10

0.866667

0.8535

20

0.533333

0.501169

30

0.066667

0.057735

40

-0.46667

-0.35749

50

-0.93333

-0.59994

60

-1.33333

-0.66667

70

-1.46667

-0.50163

80

-1.26667

-0.21995

90

-1.2

-7.4E-17

100

-1.2

0.208378

110

-1.2

0.410424

120

-1.26667

0.633333

130

-1.33333

0.85705

140

-1.33333

1.021393

150

-1.4

1.212436

160

-1.4

1.31557

170

-1.46667

1.444385

180

-1.4

1.4

190

-1.46667

1.444385

200

-1.46667

1.378216

210

-1.33333

1.154701

220

-1.26667

0.970323

230

-1.26667

0.814198

240

-1.26667

0.633333

250

-1.2

0.410424

260

-1.2

0.208378

270

-1.2

2.21E-16

280

-1.2

-0.20838

290

-1.33333

-0.45603

300

-1.26667

-0.63333

310

-0.93333

-0.59994

320

-0.33333

-0.25535

330

0.2

0.173205

340

0.6

0.563816

350

0.933333

0.919154

360

1

1

Using Simpson ‘s regulation, the country under the graph can be found. This in bend will be used to cipher the retarding force coefficient.

Simpson ‘s regulation:

Where ; R = amount of the staying odd-numbered ordinates

F + L = amount of the first and last ordinates

s = breadth of the strip ( taken as Iˆ/18 ) .

E = amount of the even-numbered ordinates

e5

e44

e3

e2

e1

Area under single extremums:

e1 = 1/3 A- Iˆ/18 A- [ ( 1 + 0.057735 ) + 4 ( 0.8535 ) + 2 ( 0.501169 ) = ( + ) 0.3185

e2 = 1/3 A- Iˆ/18 A- [ ( 0.057735-7.4E-17 ) +4 ( -0.59994 – 0.50163 ) +2 ( -0.35749 – 0.66667

– 0.21995 ) ]

## = ( – ) 0.3976

e3 = 1/3 A- Iˆ/18 A- [ ( -7.4E-17 + 2.21E-16 ) + 4 ( 0.410424 + 0.85705 + 1.212436 + 1.444385

+ 1.444385 + 1.154701 + 0.814198 + 0.410424 ) + 2 ( 0.208378

+ 0.633333 + 1.021393 + 1.31557 + 1.4 + 1.378216 + 0.970323

+ 0.633333 + 0.208378 ) ]

## = ( + ) 2.7069

A4 = 1/3 x Iˆ/18 x [ ( 2.21E-16 + 0.173205 ) + 4 ( -0.45603 – 0.59994 ) + 2 ( -0.20838 – 0.63333 –

0.25535 ) ]

= ( – ) 0.3633

Area of A5:

A5 = 1/3 x Iˆ/18 x [ ( 0.173205 + 1 ) + 4 ( 0.919154 ) + 2 ( 0.563816 ) ]

= ( + ) 0.3478

Entire country A = ( 0.3185 – 0.3976 + 2.7069 – 0.3633 + 0.3478 )

= 2.6123

The retarding force coefficient for the laminar flow = A? x A

= A? x 2.6123

= 1.30615

## Turbulent flow

Table 7

## I¦ A°

## Pressure coefficient, cI¦

## cI¦cosI¦

0

1

1

10

0.833333

0.820673

20

0.333333

0.313231

30

-0.375

-0.32476

40

-1.29167

-0.98947

50

-2.20833

-1.41949

60

-2.95833

-1.47917

70

-3.5

-1.19707

80

-3.58333

-0.62224

90

-3.125

-1.9E-16

100

-3

0.520945

110

-2

0.68404

120

-1.5

0.75

130

-1.41667

0.910616

140

-1.375

1.053311

150

-1.375

1.190785

160

-1.375

1.292077

170

-1.33333

1.313077

180

-1.29167

1.291667

190

-1.33333

1.313077

200

-1.375

1.292077

210

-1.375

1.190785

220

-1.375

1.053311

230

-1.41667

0.910616

240

-1.54167

0.770833

250

-2.29167

0.783796

260

-3.20833

0.557121

270

-3.375

6.2E-16

280

-3.66667

-0.63671

290

-3.41667

-1.16857

300

-2.75

-1.375

310

-2

-1.28558

320

-1.08333

-0.82988

330

-0.20833

-0.18042

340

0.458333

0.430692

350

0.916667

0.90274

360

1

1

s3

s5

s4

s2

s1

Area of A1:

A1 = 1/3 x Iˆ/18 x [ ( 1 – 0.32476 ) + 4 ( 0.820673 ) + 2 ( 0.313231 ) ]

= ( + ) 0.2667

Area of A2:

A2 = 1/3 x Iˆ/18 x [ ( -0.32476 – 1.9E-16 ) + 4 ( -1.41949 – 1.19707 ) + 2 ( -0.98947 – 1.47917 –

0.62224 ) ]

= ( – ) 0.9874

Area of A3:

A3 = 1/3 x Iˆ/18 x [ ( -1.9E-16 + 6.2E-16 ) + 4 ( 0.68404 + 0.910616 + 1.190785 + 1.313077 +

1.313077 + 1.190785 + 0.910616 + 0.783796 ) + 2 ( 0.520945 + 0.75 + 1.053311 +

1.292077 + 1.291667 + 1.292077 + 1.053311 + 0.770833 + 0.557121 ) ]

= ( + ) 2.9292

Area of A4:

A4 = 1/3 x Iˆ/18 x [ ( 6.2E-16 – 0.18042 ) + 4 ( -1.16857 – 1.28558 ) + 2 ( -0.63671 – 1.375 –

0.82988 ) ]

= ( – ) 0.9122

Area of A5:

A5 = 1/3 x Iˆ/18 x [ ( -0.18042 + 1 ) + 4 ( 0.90274 ) + 2 ( 0.430692 ) ]

= ( + ) 0.3079

Entire country A = ( 0.2667 – 0.9874 + 2.9292 – 0.9122 + 0.3079 )

= 1.6042

The retarding force coefficient for the turbulent flow = A? x A

= A? x 1.6042

= 0.8021

Calculations to happen the tunnel standardization invariable, K:

Using eq 9, the tunnel standardization invariable, K, can be found.

where, I?ms = 809 kg/m3 ;

I?w = 1000 kg/m3

Laminar Flow

The unit for a?†hc is in mmH2O and this needs to be changed to mH2O

a?†hc = 15 mmH2O

= 0.015 mH2O

Using eq 5, the tunnel standardization invariable can hence be found.

= 1.02743

Turbulent Flow

The same stairss are used to happen the tunnel standardization invariable in a turbulent flow.

a?†hc = 35 mmH2O

= 0.035 mH2O

= 0.7045

Discussion:

## Throughout this experiment several factors were found out these include:

The force per unit area distribution in the system

Drag of the cylinder

Drag coefficient

Reynolds figure

Mistakes in the experiment which may hold caused anomalousnesss

1. Looking at the graphs it can be seen that the force per unit area distribution in the system as in both lamina and turbulent flow besides in parts off the graph it shows steady correlativity, between angles 900 and 3100 in laminar flow. Angles 1300 and 2300 in disruptive flow.

2. The retarding force on the cylinder in turbulent and lamina conditions show through the consequences and graphs shown. As there is more drag when there is disruptive flow than lamina, nevertheless this easy to understand as, in lamina flow the Eddies produced have a little aftermath so hence it does non hold a big force per unit area so do non increase retarding force. From the graphs it can be seen that the force per unit area coefficient in lamina flow at 90i‚° is greater than the force per unit area coefficient at disruptive flow. However in the turbulent flow the gesture cut down the force per unit area and so increases the retarding force.

The drag coefficient can be found by looking at the consequences and graphs, which both show that it is less in disruptive flow as the separation point occurs after 90i‚° ensuing in less Eddies so less aftermath and therefore a high force per unit area with a terminal of low drag coefficient. Whereas in lamina flow it is greater than in turbulent. This may be due to the fact that the separation point occurs before 90i‚° , this has a ensuing consequence of more Eddies which induce aftermaths and low force per unit area, the terminal consequence of this is a high retarding force coefficient.

Separation point is where the angle flows become steady. The separation point occurs when the speed of the fluid is cut downing, in which the force per unit area flows bring on a positive force per unit area gradient.

Then one time the separation has passed the boundary beds bend over and flux in the opposite way.

The force per unit area remains changeless after the separation point because Eddies are transferred to another energy.

The separation point at lamina flow is at 90i‚° than for turbulent which is after 90i‚° as the force per unit area gradient is greater in laminar flow, which means that the greater the force per unit area gradient the earlier the separation.

The ground why Reynolds figure is greater in turbulent flow than lamina, as the chief ground for this is that less force per unit area and drag coffeicnet and more retarding force is moving on to the cylinder.

## Decision:

In this experiment a cylinder was used to happen laminal and disruptive flow around it, the chief aim was to see if the retarding force and flow increased or decreased, this was achieved and so this was shown that they increased in disruptive conditions and decreased in laminal conditions. Besides in a disruptive status the separation will increase to 90 grades and the Reynolds figure besides increases.

## Discussion

Figure G & A ; H shows the caput force per unit area distribution around the cylinder. As it can be seen from the laminal caput force per unit area distribution ( figure G ) , the force per unit area between tubes 3-11 ( i.e. angle 90° up to 330° ) is about the same. This shows that the force per unit area is more or less the same around the cylinder ( seen from top position ) , except from its forepart point confronting the onset flow, where the force per unit area is equal to the stagnancy force per unit area.

In the instance of turbulent flow ( figure H ) , the caput force per unit area distribution form is slightly different. The head force per unit area values bead between tubing no. 5 to 9, which is the rear portion of the cylinder. This cogent evidence that a “ low-pressure ” part exists at the rear of the cylinder in disruptive flow. This part of “ low-pressure ” is mentioning to the aftermath part. The force per unit area distribution is besides clearly symmetrical about tubes 6 and 7, which proofs that the force per unit area distribution on one ( horizontal ) side of the cylinder is the similar to the 1 on the opposite side of the cylinder.

The per centum mistake for the coefficient of retarding force ( Cadmium ) value in experiment 1 was calculated to be about 2.5 % . This is a comparative little per centum mistake, which shows that the experimental mistakes involved in experiment 1 were non important. However, the per centum mistake for the Cadmium value in experiment 2 was a monolithic 56 % , which clearly shows that the experimental mistakes involved in experiment 2 did play a important function.

The mistake due to parallax is one of those mistakes. The parallax mistake is human reading mistake, where the oculus needs to be precisely in line with the reading to be measured.

In both experiments, the multi-tube manometer was at an inconvenient place ( on the floor ) . And furthermore the whole manometer system was slanting at an angle of 30° to the horizontal. Both of these factors made it hard to acquire the oculus degree precisely in line with the reading to be measured from the multi-tube manometer. This might hold caused inaccuracy in the readings.

The trapezium regulation was used to find the country under the graph of cI¦cosI¦ , which was used to cipher the coefficient of retarding force. Since the graph had parts of both “ negative ” and “ positive ” countries, the trapezium regulation had to be applied individually for each subdivision of the graph. The whole graph was divided into strips, each with a breadth of Iˆ/18 ( 10 grades in radians ) .

When the graph of cI¦cosI¦ goes from a positive part into a negative one, the experimental information in some instances does non make precisely zero before the information “ switches marks ” . This consequences in some minor countries of the graph being neglected. This would non significantly affect the entire country found from the trapezium regulation, since the countries neglected are comparatively little. But since some countries of the graph are ignored, the entire country found would non be the exact country under the graph. This will ensue in an mistake in the concluding values of the coefficient retarding force.

The tunnel standardization invariable for laminar flow ( k1 ) was found to be 1.0959. Clearly this value can non be accurate because the ratio of the two force per unit areas must be equal to 1 or below, since both are stand foring the force per unit area across the same points. The unexpected high value for k1 must hold been a consequence of experimental mistake. Since most footings are changeless in the equation used to happen K, the lone factors that could hold contributed to the mistake must hold been the values of ha?z & A ; h1, which were obtained from the multi-tube manometer.

While taking the readings from the multi-tube manometer, the fluid ( methylated spirit ) in the tubing was fluctuating. Some of the fluctuations were every bit big as +/- 0.5 inch. For this ground, many of the readings obtained might hold been greatly inaccurate, which finally could hold lead to a important mistake in the concluding values for the coefficient of retarding force in both experiments, every bit good as the value of K for laminar flow.

The tunnel standardization invariable for turbulent flow ( K2 ) was found to be 0.7632. This value clearly indicates that energy losingss did take topographic point since the value is good below 1. Energy losingss may hold occurred in 2 chief signifiers ; as heat and sound energy produced by clash and hits of air molecules with particularly the grid system at the upstream.

Heat energy ( and some sound energy ) is besides produced due to clash of the interior wall of the air current tunnel. The fluxing air must make work to get the better of this clash, and hence some kinetic energy of the fluxing air is lost as heat. To acquire disruptive flow, the flow rate was increased and a grid system was introduced.

With the debut of a grid system at the upstream in experiment 2, more hits of air molecules took topographic point, hence ensuing in increased “ loudness ” of flow. This addition in volume ( due to the addition in hits and clash ) resulted in some kinetic energy of the flow being converted into heat and more perceptibly sound energy, and hence some of the initial kinetic energy of the flow was “ lost ” .

Energy in signifier of heat is besides lost due to formation of disruptive Eddies. The formation of Eddies takes topographic point in turbulent flow. All these energy loss factors mentioned earlier might explicate why the k-value for turbulent flow was less than the k-value of laminar flow.

In figure I, three graphs were plotted for the fluctuation of force per unit area coefficient with angle. Each of the graphs was stand foring informations for a alone status. In the instance of the theoretical informations graph ( green coloured ) , which represents the status of frictionless flow, shows that at zero angle the force per unit area is a maximal ( stagnation force per unit area ) . Furthermore at an angle of 180° ( rear of cylinder ) , the force per unit area one time once more reaches a maximal value. This relationship clearly indicates that the force per unit area distribution form would hold been precisely symmetrical around a perpendicular axis at the Centre of the cylinder.

However, in the instance of both laminar and turbulent flow the lines if symmetricalness is non perpendicular but horizontal about the Centre of the cylinder. By looking at the graphs, all graphs show a maximal force per unit area coefficient at an angle of nothing ( tantamount to 360° ) , which shows that whatever flow status is imposed a maximal force per unit area will still stay at the stagnancy point, which is the point where the fluid is brought to a halt.

For laminar flow, the force per unit area coefficient remains more or less changeless after an angle of about 75° . This point is referred as the angle of separation, where the flow starts to “ divide ” from the cylinder ‘s surface. This value of 75° is really near to the value of 82° given for angle of separation for laminar flow in figure E.

In the instance for turbulent flow, the force per unit area coefficient stays more or less changeless after an angle of about 130° ( i.e. angle of separation ) . Once once more, even this value for angle of separation is really similar to the value of 120° given for turbulent flow in figure E.

One of the chief grounds why there is a difference in form between the theoretical graph and the experimental graphs for force per unit area coefficient is due to the fact that the premise of air being a frictionless flow is invalid, since air is a syrupy fluid. Overall the features of the force per unit area coefficient graphs can be said to be an accurate presentation of existent informations, since the three force per unit area coefficient graphs ( between angle 0 to 180° ) are extremely indistinguishable in footings of both the form and graduated table of the force per unit area coefficient graphs shown in figure E.

## Decision

The value of tunnel standardization invariable ( K ) for experiment 1 was found to be inaccurate ( due to experimental mistakes ) since the value is non expected to transcend 1. However, the value of K for experiment 1 shows that really negligible energy losingss take topographic point across the contraction of the air current tunnel under laminar flow. The value of K was significantly lower for experiment 2 ; this clearly shows that the energy losingss that take topographic point across the contraction of the air current tunnel are important. The chief ground for important sum of energy losingss is due to the debut of a grid system at the upstream in experiment 2. The grid system dramatically increases the effects of clash to the oncoming flow. For this ground, some of the initial kinetic energy of the air flow is “ lost ” as heat and sound energy.

The obtained graphs for fluctuation of force per unit area coefficient with angle around the cylinder margin can be said to be reasonably accurate, since both the form and graduated table of them is highly indistinguishable to the graphs stand foring the same information in figure D.

For experiment 1 the coefficient of retarding force value had a per centum mistake of merely 2.5 % , which shows that the experimental mistakes did non hold a important impact on the concluding consequence. However, in the instance of experiment 2, the per centum mistake for the coefficient of retarding force was a monolithic 56 % , clearly the experimental mistake did significantly impact the concluding consequence in experiment 2.

In future betterments, the per centum mistake of the Cadmium value in experiment 2 could be farther decreased by cut downing experimental mistakes mentioned in the treatment subdivision.