# Lab report (Mechanics Of Materials) I have All the data, I need you to make the Lab report according to the rubric. THIS IS AN EMAIL SENT BY THE PROFESSOR

Lab report (Mechanics Of Materials) I have All the data, I need you to make the Lab report according to the rubric.

THIS IS AN EMAIL SENT BY THE PROFESSOR

>>>>

“The attached lab reports are from some of my previous courses during my undergrad years, there are a few sections that I do not have included in the lab reports but given both of them you should get an idea of what is expected with given info and the layout of the lab report that you are currently working on. As I told all the lab sections, here is the link to the youtube video of the experiment, as I stated I really like this video and think that it is very detailed in its explanation of what is going on.

https://www.youtube.com/watch?v=D8U4G5kcpcM&t=325s” Brass

Lo (in)

2

Lf (in)

Do (in)

Df (in)

Area (in )

2

2,53

0,505

0,38

0,2003

Load(lbf)

0

100

900

1000

1250

1500

1750

2000

2250

2500

2750

3000

3250

3500

3750

4000

4250

4500

4750

5000

5250

5500

5750

6000

6250

6500

6750

7000

7500

7250

7750

8000

8250

8500

8750

9000

9250

9500

9750

10000

Deflection (in)

0,0000

0,0059

0,0103

0,0108

0,0122

0,0133

0,0146

0,0162

0,0171

0,0182

0,0193

0,0206

0,0223

0,0227

0,0239

0,0250

0,0261

0,0273

0,0284

0,0294

0,0308

0,0318

0,0323

0,0345

0,0361

0,0372

0,0386

0,0396

0,0431

0,0414

0,0447

0,0463

0,0463

0,0504

0,0527

0,0560

0,0590

0,0659

0,0787

0,1000

Stress (psi)

0

499,260678

4493,3461

4992,60678

6240,75848

7488,91017

8737,06187

9985,21357

11233,3653

12481,517

13729,6687

14977,8203

16225,972

17474,1237

18722,2754

19970,4271

21218,5788

22466,7305

23714,8822

24963,0339

26211,1856

27459,3373

28707,489

29955,6407

31203,7924

32451,9441

33700,0958

34948,2475

37444,5509

36196,3992

38692,7026

39940,8543

41189,006

42437,1577

43685,3093

44933,461

46181,6127

47429,7644

48677,9161

49926,0678

Strain (in/in)

0

0,00295

0,00515

0,0054

0,0061

0,00665

0,0073

0,0081

0,00855

0,0091

0,00965

0,0103

0,01115

0,01135

0,01195

0,0125

0,01305

0,01365

0,0142

0,0147

0,0154

0,0159

0,01615

0,01725

0,01805

0,0186

0,0193

0,0198

0,02155

0,0207

0,02235

0,02315

0,02315

0,0252

0,02635

0,028

0,0295

0,03295

0,03935

0,05

10250

10500

10750

11000

11200

11000

10500

10250

0,1267

0,1678

0,2324

0,2900

0,4300

0,5500

0,6100

0,6483

51174,2195

52422,3712

53670,5229

54918,6746

55917,196

54918,6746

52422,3712

51174,2195

0,06335

0,0839

0,1162

0,145

0,215

0,275

0,305

0,32415

Aluminum

Lo (in)

2

Lf (in)

Do (in)

Df (in)

Area (in )

2,05

2,416

0,505

0,32

0,2003

Load(lbf)

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

2750

3000

3250

3500

3750

4000

4250

4500

4750

5000

5250

5500

5750

6000

6250

6500

6750

7000

7500

7250

7750

8000

8250

8500

8670

7500

7000

6400

Deflection (in)

0,0000

0,0030

0,0047

0,0063

0,0077

0,0090

0,0104

0,0117

0,0130

0,0144

0,0157

0,0170

0,0182

0,0196

0,0208

0,0221

0,0234

0,0247

0,0259

0,0272

0,0285

0,0298

0,0311

0,0323

0,0335

0,0348

0,0361

0,0374

0,0388

0,0401

0,0417

0,0447

0,0555

0,0955

0,1488

0,2550

0,3780

0,4610

0,5010

Stress (psi)

0

1248

2496

3744

4993

6241

7489

8737

9985

11233

12482

13730

14978

16226

17474

18722

19970

21219

22467

23715

24963

26211

27459

28707

29956

31204

32452

33700

34948

37445

36196

38693

39941

41189

42437

43286

37445

34948

31953

Strain (in/in)

0,0000

0,0015

0,0023

0,0031

0,0038

0,0044

0,0051

0,0057

0,0063

0,0070

0,0077

0,0083

0,0089

0,0096

0,0101

0,0108

0,0114

0,0120

0,0126

0,0133

0,0139

0,0145

0,0152

0,0158

0,0163

0,0170

0,0176

0,0182

0,0189

0,0196

0,0203

0,0218

0,0271

0,0466

0,0726

0,1244

0,1844

0,2249

0,2444

Steel

Lo (in)

Lf (in)

Do (in)

Df (in)

Area (in )

2,00

2,76

0,505

0,295

0,2003

Load(lbf)

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

2750

3000

3250

3500

3750

4000

4250

4500

4750

5000

5250

5500

5750

6000

6250

6500

6750

7000

7500

7250

7750

8000

8250

8500

8750

9000

9250

9500

9800

Deflection (in)

0,0000

0,0021

0,0037

0,0051

0,0062

0,0072

0,0081

0,0091

0,0100

0,0109

0,0118

0,0127

0,0136

0,0145

0,0154

0,0163

0,0171

0,0180

0,0188

0,0197

0,0206

0,0215

0,0223

0,0231

0,0239

0,0247

0,0256

0,0264

0,0272

0,0280

0,0288

0,0296

0,0305

0,0313

0,0321

0,0329

0,0337

0,0345

0,0415

0,0450

Stress (psi)

0

1248

2496

3744

4993

6241

7489

8737

9985

11233

12482

13730

14978

16226

17474

18722

19970

21219

22467

23715

24963

26211

27459

28707

29956

31204

32452

33700

34948

37445

36196

38693

39941

41189

42437

43685

44933

46182

47430

48928

Strain (in/in)

0,0000

0,0011

0,0019

0,0026

0,0031

0,0036

0,0041

0,0046

0,0050

0,0055

0,0059

0,0064

0,0068

0,0073

0,0077

0,0082

0,0086

0,0090

0,0094

0,0099

0,0103

0,0108

0,0112

0,0116

0,0120

0,0124

0,0128

0,0132

0,0136

0,0140

0,0144

0,0148

0,0153

0,0157

0,0161

0,0165

0,0169

0,0173

0,0208

0,0225

2

10000

10250

10500

10750

11000

11250

11500

11750

12000

12250

12500

12750

13000

13250

13500

13750

14000

14250

14325

12500

11000

0,0907

0,0956

0,1018

0,1090

0,1175

0,1265

0,1365

0,1478

0,1604

0,1735

0,1879

0,2032

0,2258

0,2490

0,2758

0,3130

0,3780

0,5580

0,571

0,6300

0,6500

49926

51174

52422

53671

54919

56167

57415

58663

59911

61159

62408

63656

64904

66152

67400

68648

69896

71145

71519

62408

54919

0,0454

0,0478

0,0509

0,0545

0,0588

0,0633

0,0683

0,0739

0,0802

0,0868

0,0940

0,1016

0,1129

0,1245

0,1379

0,1565

0,1890

0,2790

0,2855

0,3150

0,3250

ENGR 350 A-001: Tentative Lab Schedule

Description

Assign Date

Tension Lab

1/22/2019

Compression Lab

2/12/2019

Buckling Lab

2/26/2019

Torsion Lab

3/19/2019

Shear and Moment Lab

4/2/2019

Lab Final

4/16/2019

Due Date

2/12/2019

2/26/2019

3/19/2019

4/2/2019

4/16/2019

4/16/2019

ENGR 350 A/B-002: Tentative Lab Schedule

Description

Assign Date

Tension Lab

1/22/2019

Compression Lab

2/12/2019

Buckling Lab

2/26/2019

Torsion Lab

3/19/2019

Shear and Moment Lab

4/2/2019

Lab Final

4/16/2019

Due Date

2/12/2019

2/26/2019

3/19/2019

4/2/2019

4/16/2019

4/16/2019

ENGR 350 A/B-003: Tentative Lab Schedule

Description

Assign Date

Tension Lab

1/23/2019

Compression Lab

2/13/2019

Buckling Lab

2/26/2019

Torsion Lab

3/19/2019

Shear and Moment Lab

4/3/2019

Lab Final

4/17/2019

Due Date

2/13/2019

2/26/2019

3/19/2019

4/3/2019

4/17/2019

4/17/2019

ENGR 350 A/B-004: Tentative Lab Schedule

Description

Assign Date

Tension Lab

1/24/2019

Compression Lab

2/14/2019

Buckling Lab

2/27/2019

Torsion Lab

3/20/2019

Shear and Moment Lab

4/4/2019

Lab Final

4/18/2019

Due Date

2/14/2019

2/27/2019

3/20/2019

4/4/2019

4/18/2019

4/18/2019

Rectilinear Dynamic System Control

ME 407

Measurements & Controls

Lab 8

Lab Conducted By:

Sulaiman Alareefi

David McKavanagh

Cameron Bowes

Maxwell Hopkins

Lab Report Written By:

David McKavanagh

Due By:

12/2/2016

1|Page

Table of Contents

Section

Page

Title Page

1

Table of Contents

2

Procedure

3

Results

3

❖

❖

❖

❖

❖

❖

❖

❖

❖

❖

❖

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Figure 11

Analysis

3

4

4

5

5

6

6

7

7

8

8

9

Conclusions

2|Page

Procedure

First the system must be set up properly, with the four 500g masses on the first

carriage, no springs or dampers connected to it, and the other carriages secured out of range of

the first carriage’s path. Set Ts at 0.00442, the step size of 0, duration set to 3000 ms, and

repetition of 1. Once these amounts have been entered the PID controller needs to be set up

with the value found, and then execute the program, when the program is finished the data is

exported for use later. The process is repeated with the derivative gain, critically damped,

overdamped, and the integral gain.

Results

Figure 1: Proportional Gain

3|Page

Figure 2: Doubled Proportional Gain

Figure 3: Derivative Gain

4|Page

Figure 4: Five Times Derivative Gain

Figure 5: Underdamped

5|Page

Figure 6: Critically Damped

Figure 7: Overdamped

6|Page

Figure 8: Integral Gain

Figure 9: Integral Gain Doubled

7|Page

Figure 10: Integral Gain Halved

Figure 11: Integral Adjusted

8|Page

Analysis

Through this experiment the carts mass and the mass upon it is unchanged. It was

possible to find out the natural frequency for each of the trial with the data that was graphed. From the

four figures above it was possible to find To, Xo, Tn, Xn, and n for each of the segments of the lab. τd=(τnτo)/n, then uses τd for ωd=(2π)/τd then δ=(1/n)ln(Xo/Xn), from there the value d would be used to find ζ

which is ζ=(1/(1+(2π/δ)2)1/2), with ζ we can find the ωn which is ωn=(ωd/(1-ζ2)1/2). The values that were

obtained from Figure 1, Proportional Gain To=0.522, Xo=2071, Tn=1.372, Xn=396, and n being 1. Using

the formals Wn = 7.64. Also calculating the derivational gain, kd=50 N/(m/s)/khw, giving us a kd of 0.0043,

ki=750 N/(m/s)/khw, giving us a ki value of 0.0645. These values are the derivative gain and the integral

gain respectively.

Conclusion

Though this experiment was interesting, the values for the integral gain seem to have

been calculated wrong, as the values needed to be changed to 0.02 to get the correct graph as

seen in the adjusted integral gain graph. Though there also seemed to be a small point in the

cart where it would get hung up and stall as it was moving. These two problems seem to have

kept us from achieving the correct outcome of this experiment.

9|Page

Southern Illinois University Carbondale

Department of Engineering

Bernoulli’s Equation

Lab # 2

Fluid Mechanics

ENGR 370A

Written By: David McKavanagh

Submitted to: Ganesh Ghimire

Completed on:

Wednesday July 8th 2015

Submitted on:

Thursday July 9th 2015

1|Page

Table of Contents

A.

List of Figures

2

B.

Objectives

3

C.

Theory

3

D.

Apparatus

5

E.

Procedure

5

F.

Results

6

G.

Conclusion

8

H.

Appendix

10

I.

Figure 1: Venturi Nozzle

5

II.

Table 1

6

III.

Table 2

6

IV.

Table 3

7

V.

Table 4

7

2|Page

Objectives

It is to show the validity of the Bernoulli equation by gathering data from different points

along a horizontal duct. Gathering the pressure heads and the velocity heads along said duct.

Theory

This experiment focuses on gathering data from points along a horizontal duct called a

Venturi Nozzle. There are multiple forces acting on the flow of fluids through the horizontal

duct. Those forces are: Static Pressure Head, Stagnation Pressure Head, the Velocity Head,

and the Total Energy Head.

The Summation of Forces

∑ =

Where the ∑F is the summation of the forces acting on the fluid traveling through the Bernoulli

Apparatus.

The Bernoulli Equation

1 12

+

+ 1 = =

2

Where p is the pressure, ᵞ is the specific weight of the fluid, V is the velocity, g is the force of

gravity, and z is the elevation of the fluid.

This equation is frequently expressed as:

1

12 2

22

+ 1 +

= + 2 +

2

2

Since there is no elevation component

3|Page

1 12 2 22

+

= +

2

2

To find the Flow Rate

=

∀

Where Q is the volumetric flow rate of the fluid, ∀ is the volume in cubic meters, and t is the time

measured in seconds

Finding the cross section of the flow area,

=

2

4

Where A is the area, and D is the diameter of the Venturi Nozzle. These are the important

equations that are used to find the figures needed in the Bernoulli Equation.

4|Page

Apparatus:

Venturi Nozzle

At least six manometers

Bernoulli Apparatus

At least twelve liters of fluid

Figure 1: Venturi Nozzle

Procedure:

The measurements of the diameter, the distance from a fixed point (called point

A), and the Volume target that must be reached for time where given by the instructor.

Firstly activate the entire system and begin running water through the system to clear

the air out of all of the manometers. Once all of the air is removed from the system start

your timer, adjust the device until there is a steady flow and record the amount of fluid

within the manometers. After ten liters of fluid has flowed through the venturi nozzle

stop the timer and record the amount of time that has elapsed. After recording the

figures for the static pressure heads and the stagnation pressure head (which would be

5|Page

the last of the manometers on the device, adjust the flow rate of the fluid to the second

rate that is to be used in the experiment. Once that flow rate is achieved start the timer

once again, and record the static pressure heads and the stagnation pressure head on

the manometers. Stop the timer once the ten liter amount is reached.

Results

Table 1: First Flow Rate

Volume, L

1.00E+01

Test

Section

Time, t (s)

Volume m^3

3.57E+02

Diameter, d,

(mm)

Flow rate, Q (m^3/s)

1.00E-02

Distance from Test

Section A (mm)

2.80E-05

Static Pressure Head Stagnation Pressure

(mm)

Head (mm)

A

2.50E+01

0.00E+00

9.50E+01

9.60E+01

B

1.39E+01

6.03E+01

9.40E+01

9.60E+01

C

1.18E+01

6.87E+01

9.00E+01

9.60E+01

D

1.07E+01

7.26E+01

8.90E+01

9.60E+01

E

1.00E+01

8.11E+01

8.60E+01

9.60E+01

Cross

Section of

Flow Area, A Velocity, V Velocity

(m^2)

(m/s)

Head (m)

Total

Energy

Head (m)

Table 2: Calculations for First Flow Rate

Distance from Static

Diameter, Test Section Pressure

d (m)

A (m)

Head (m)

Stagnation

Pressure

Head (m)

2.50E-02

0.00E+00

9.50E-02

9.60E-02

4.91E-04

0.00E+00

0.00E+00 9.69E-06

1.39E-02

6.03E-02

9.40E-02

9.60E-02

1.52E-04

1.69E-04

1.45E-09 9.59E-06

1.18E-02

6.87E-02

9.00E-02

9.60E-02

1.09E-04

5.94E-05 1.798E-10 9.18E-06

1.07E-02

7.26E-02

8.90E-02

9.60E-02

8.99E-05

5.32E-05

1.44E-10 9.08E-06

1.00E-02

8.11E-02

9.60E-02

9.60E-02

7.85E-05

4.26E-05

9.25E-11 8.78E-06

6|Page

Table 3: Second Flow Rate

Volume, L

1.00E+01

Test

Section

Time, t (s)

Volume m^3

1.12E+02

Diameter, d,

(mm)

Flow rate, Q (m^3/s)

1.00E-02

8.90E-05

Distance from Test

Section A (mm)

Static Pressure Head Stagnation Pressure

(mm)

Head (mm)

A

2.50E+01

0.00E+00

2.70E+02

2.73E+02

B

1.39E+01

6.03E+01

2.50E+02

2.73E+02

C

1.18E+01

6.87E+01

2.34E+02

2.73E+02

D

1.07E+01

7.26E+01

2.30E+02

2.73E+02

E

1.00E+01

8.11E+01

1.85E+02

2.73E+02

Cross

Section of

Flow Area, A Velocity, V Velocity

(m^2)

(m/s)

Head (m)

Total

Energy

Head (m)

Table 4: Calculations for the Second Flow Rate

Distance from Static

Diameter, Test Section Pressure

d (m)

A (m)

Head (m)

Stagnation

Pressure

Head (m)

2.50E-02

0.00E+00

2.70E-01

2.73E-01

4.91E-04

0.00E+00

0.00E+00 2.76E-05

1.39E-02

6.03E-02

2.50E-01

2.73E-01

1.52E-04

2.46E-04

3.08E-09 2.55E-05

1.18E-02

6.87E-02

2.34E-01

2.73E-01

1.09E-04

1.89E-04

1.82E-09 2.39E-05

1.07E-02

7.26E-02

2.30E-01

2.73E-01

8.99E-05

1.70E-04

1.47E-09 2.35E-05

1.00E-02

8.11E-02

1.85E-01

2.73E-01

7.85E-05

1.36E-04

9.43E-10 1.89E-05

The values presented in tables 1 and 3 were partially given by the instructor, those

being the diameter, the volume, and the distance from test section A. The values

entered into the table, being static pressure head, stagnation pressure head, and time

where found during the experiment. The values in tables 2 and 4 where calculated

using the formula given in the Theory section.

7|Page

Discussion

Accuracy and Precision:

The topic of accuracy and precision is probably the most important aspect of

experimentation, this is true, especially within this experiment. Within the general

populous the terms are interchangeable, while with in the scientific community they

couldn’t be farther from one another. Accuracy refers to the ability to record a

measured variable close to the known value of a substance. Precision refers to the

ability to record two or more measurements close to each other. To ensure a proper

experiment, accuracy and precision is what is needed.

The first results that need to be checked for accuracy and precision would be

calculations from millimeters to meter for the first four columns in the second and fourth

tables. Those would be diameter, distance from test section A, the Static Pressure

Head and the Stagnation Pressure Head.

The second result that needs to be checked would be to ensure that the correct

equations are used to calculate the flow rate, the cross section of flow area, velocity,

velocity head and the total energy head for both flow rate tables.

Probable Sources of Error

The main source of error that would present its self in these experiments would be

human error, if not all of the air was removed from the manometers, or that if the person

recording the numbers from the manometers, watching the time, or watching for the

mark of the volume.

8|Page

Conclusion

The initial objective was met, the experiment definitely show the validity of Bernoulli

Equation. The students gained the knowledge of how to read a Bernoulli Apparatus

correctly and with the proper procedures. A recommendation for a future of the

experiment would be to have a better timer, or a bigger Bernoulli Apparatus that would

be easier to read, to negate the human error. Ensuring that all equations needed for the

experiment would also be a step to reduce the error.

9|Page

Appendix

References Cited

Nicklow, John, PHD. “Engineering Fluid Mechanics -Laboratory Manual.” Fluids. Southern

Illinoi University, # Nov. 2010. Web. 24 June 2014.

10 | P a g e

outs

62%ys

OE

E

Non-Linear

Deformation

0.002

EE

Figure 6

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