Texas instruments TI-89, TI-92 PLUS ME Pro
®
ME•Pro
Mechanical Engineeri ng
User’s Manual
A software Application
for the TI-89 and TI-92 Plus
Version 1.0 by
da V
inci Technologies Group Inc
ME••••Pro®
A software Application
For TI-89 and TI-92 Plus
User’s Guide
August 2000
© da Vinci Technologies Group, Inc.
Rev. 1.0
da Vinci Technologies Group, Inc.
1600 S.W. Western Blvd
Suite 250
Corvallis, OR 97333
www.dvtg.com
2
Notice
This manual and the examples contained herein are provided “as is” as a supplement to ME•
Pro
application software available from Texas Instruments for TI-89, and TI-92 Plus platforms. da Vinci
Te chnologies Gro up, Inc. (“da V inci”) makes no warranty of any kind with r egard t o this manual
or the accompanying software, including, but not limited to, the implied warranties of
merchantability and fitness for a particular purpose. da Vinci shall not be lia ble for any errors or f or
incidenta l or consequ ent ial dama ges in connec tion with the furnishing, per f ormance, or use of this
manual , or the examp l es her ei n .
Copyr ight da Vinci Technologies Gr oup, Inc. 2000. All rights reserved.
PocketProfessional and ME•Pro are registered trademarks of da Vinci Technologies Group, Inc.
TI-GRAPH LINK is a trademark of Texas Instruments Incorporated, and Acrobat is a registered
trademark of Adobe Systems Incorporated.
We welcome your comments on the software and the manual. Forward your comments, preferably by
e-mail, to da Vinci at support@dvtg.com.
Acknowledgements
The ME•Pro software was developed by Chris Bunsen, Dave Conklin, Michael Conway, Curtis Gammel, and
Megh a Shyam with the gene r ou s support of TI’ s developmen t te a m . The user ’ s gu ide wa s developed by Mi cha e l
Conway, Curtis Gammel, Melinda Shaffer, and Megha Shyam. Many helpful comments from the testers at
Texas Instrume nts and other locations during β testing phase is gratefully acknowledged.
3
Table of Contents
TABLE OF CONTENTS4
HAPTER
C
NTRODUCTION TO
1: I
1.1 Key Featur es of ME•Pro....................................................................................................12
1.2 Purchasing, Downloading and Installing ME•Pro...............................................................13
1.3 Ordering a Manual.............................................................................................................13
1.4 Memory Requirements......................................................................................................13
1.5 Differences between TI-89 and TI-92 plus.......................................................................... 13
1.6 Starting ME•Pro................................................................................................................13
1.7 How to use this Manual......................................................................................................14
1.8 Manual Disclaimer............................................................................................................. 14
1.9 Summary.................................................................................................................... ....... 15
PART I: ANALYSIS……………………………………………………………………………………...16
HAPTER
C
NTRODUCTION TO ANALYSIS
2: I
2.1 Introduction.......................................................................................................................17
2.2 Features of Analysis...........................................................................................................18
2.3 Finding Analysis................................................................................................................18
2.4 Solving a Problem in Analysis ...........................................................................................18
2.5 Tips for Analysis ...............................................................................................................20
2.6 Function keys ....................................................................................................................20
2.7 Session Folders, Variable Names.......................................................................................22
2.8 Overwriting of variable values in graphing......................................................................... 22
2.9 Reserved Variables............................................................................................................22
HAPTER
C
TEAM TABLES
3: S
3.1 Saturated Steam Properties................................................................................................. 23
3.2 Superheated Steam Properties............................................................................................23
3.3 Air Properties ....................................................................................................................23
3.4 Using Steam Tables ...........................................................................................................24
3.5 Validity Range for Temperature and Pressure..................................................................... 25
HAPTER
C
HERMOCOUPLES
4: T
4.1 Introduction.......................................................................................................................26
4.2 Using the Thermocouples Function ....................................................................................26
4.3 Basis for Temperature/Voltage Conversions.......................................................................27
HAPTER
C
APITAL BUDGETING
5: C
5.1 Using Capital Budgeting.................................................................................................... 28
HAPTER
C
FOR MECHANICAL ENGINEERS
6: EE
6.1 Impedance Calculations..................................................................................................... 32
6.2 Circuit Performance...........................................................................................................33
6.3 Wye ↔ ∆ Conversion........................................................................................................ 34
HAPTER
C
7: E
FFLUX
..........................................................................................................................36
7.1 Constant Liquid Level........................................................................................................36
7.2 Varying Liquid Level......................................................................................................... 36
7.3 Conical Vessel................................................................................................................... 37
7.4 Horizontal Cylinder ........................................................................................................... 38
7.5 Large Rectangular Orifice.................................................................................................. 38
7.6 ASME Weirs......................................................................................................................... 39
7.6.1 Rectangular Notch .......................................................................................................... 39
7.6.2 Triangular Weir ..............................................................................................................39
7.6.3 Suppressed Weir .............................................................................................................40
7.6.4 Cipolletti Weir................................................................................................................40
HAPTER
C
ECTION PROPERTIES
8: S
8.1 Rectangle........................................................................................................................... 42
••••
RO
P
ME
............................................................................................12
..........................................................................................17
................................................................................................................23
............................................................................................................26
.......................................................................................................28
...................................................................................32
.....................................................................................................42
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4
8.2 Hollow Rectangle.............................................................................................................. 43
8.3 Circle.................................................................................................................................43
8.4 Circular Ring.....................................................................................................................44
8.5 Hollow Circle....................................................................................................................45
8.6 1 Section - Uneven.............................................................................................................45
8.7 I Section - Even ................................................................................................................. 46
8.8 C Section........................................................................................................................... 47
8.9 T Section ...........................................................................................................................48
8.10 Trapezoid.........................................................................................................................48
8.11 Polygon ........................................................................................................................... 49
8.12 Hollow Polygon............................................................................................................... 50
HAPTER
C
ARDNESS NUMBER
9: H
.......................................................................................................52
9.1 Compute Hardness Number ...............................................................................................52
PART II: EQUATIONS………………………………………………………………………………… ...54
HAPTER
C
NTRODUCTION TO EQUATIONS
10: I
.....................................................................................55
10.1 Solving a Set of Equations ...............................................................................................55
10.2 Viewing an Equation or Result in Pretty Print ..................................................................56
10.3 Viewing a Result in different units ...................................................................................56
10.4 Viewing Multiple Solutions..............................................................................................57
10.5 when (…) - conditional constraints when solving equations .............................................. 58
10.5 Arbitrary Integers for periodic solutions to trigonometric functions................................... 58
10.7 Partial Solutions...............................................................................................................59
10.8 Copy/Paste.......................................................................................................................59
10.9 Graphing a Function.........................................................................................................59
10.10 St oring a nd re c alling variabl e value s in M E•Pro-creation of session folders.................... 61
10.11 solve, nsolve, and csolve and user-defined functions (UDF)........................................ 61
10.12 Entering a guessed value for the unknown using nsolve ..................................................61
10.13 Why can't I compute a solution?.....................................................................................62
10.14 Care in choosing a consistent set of equations.................................................................62
10.15 Not e s for the adva nced user in troubleshooting calculations ............................................ 62
HAPTER
C
EAMS AND COLUMNS
11: B
..................................................................................................64
11.1 Simple Beams......................................................................................................................64
11.1.1 Uniform Load...............................................................................................................64
11.1.2 Point Load ....................................................................................................................66
11.1.3 Moment Load ............................................................................................................... 68
11.2 Cantilever Beams.................................................................................................................70
11.2.1 Uniform Load...............................................................................................................70
11.2.2 Point Load ....................................................................................................................71
11.2.3 Moment Load ............................................................................................................... 73
11.3. Columns............................................................................................................................. 75
11.3.1 Buckling.......................................................................................................................75
11.3.2 Eccentricity, Axial Load................................................................................................ 76
11.3.3 Secant Formula ............................................................................................................. 77
11.3.4 Imperfections in Columns .............................................................................................79
11.3.5 Inelastic Buckling .........................................................................................................81
HAPTER
C
12: EE
FOR MES
................................................................................................................83
12.1 Basic Electricity...................................................................................................................83
12.1.1 Resistance Formulas......................................................................................................83
12.1.2 Ohm’s Law and Power..................................................................................................84
12.1.3 Temperature Effect ....................................................................................................... 85
12.2 DC Motors...........................................................................................................................86
12.2.1 DC Series Motor ...........................................................................................................86
12.2.2 DC Shunt Motor............................................................................................................88
12.3 DC Generators..................................................................................................................... 90
12.3.1 DC Series Generator ..................................................................................................... 90
12.3.2 DC Shunt Generator......................................................................................................91
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Table of Contents
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12.4 AC Motors...........................................................................................................................92
12.4.1 Three φ Induction Motor I............................................................................................. 92
12.4.2 Three φ Induction Motor II............................................................................................ 94
12.4.3 1 Induction Motor......................................................................................................... 96
HAPTER
C
13: G
AS LAWS
.....................................................................................................................98
13.1 Ideal Gas Laws....................................................................................................................98
13.1.1 Ideal Gas Law...............................................................................................................98
13.1.2 Constant Pressure.......................................................................................................... 99
13.1.3 Constant Volume........................................................................................................ 101
13.1.4 Constant Temperature.................................................................................................103
13.1.5 Internal Energy/Enthalpy............................................................................................. 104
13.2 Kinetic Gas Theory........................................................................................................ 106
13.3 Real Gas Laws................................................................................................................... 108
13.3.1 van der Waals: Specific Volume..................................................................................108
13.3.2 van der Waals: Molar form.......................................................................................... 109
13.3.3 Redlich-Kwong: Sp.Vol.............................................................................................. 110
13.3.4 Redlich-Kwong: Molar................................................................................................112
13.4 Reverse Adiabatic.......................................................................................................... 113
13.5 Polytropic Process.......................................................................................................... 115
HAPTER
C
14: H
EAT TRANSFER
.........................................................................................................118
14.1 Basic Transfer Mechanisms ............................................................................................... 118
14.1.1 Conduction ................................................................................................................. 118
14.1.2 Convection..................................................................................................................120
14.1.3 Radiation .................................................................................................................... 121
14.2 1 1D Heat Transfer ................................................................................................................ 122
14.2.1 Conduction..................................................................................................................... 122
14.2.1.1 Plane Wall ............................................................................................................... 122
14.2.1.2 Convective Source ................................................................................................... 123
14.2.1.3 Radiative Source......................................................................................................125
14.2.1.4 Plate and Two Fluids................................................................................................127
14.2.2 Electrical Analogy .......................................................................................................... 128
14.2.2.1 Two Conductors in Series......................................................................................... 129
14.2.2.2 Two Conductors in Parallel ...................................................................................... 131
14.2.2.3 Parallel-Series.......................................................................................................... 132
14.2.3 Radial Systems ...............................................................................................................135
14.2.3.1 Hollow Cylinder....................................................................................................... 135
14.2.3.2 Hollow Sphere ......................................................................................................... 136
14.2.3.3 Cylinder with Insulation Wrap.................................................................................. 137
14.2.3.4 Cylinder - Critical radius..........................................................................................139
14.2.3.5 Sphere - Critical radius.............................................................................................141
14.3 Semi-Infinite Solid.............................................................................................................142
14.3.1 Step Change Surface Temperature............................................................................... 142
14.3.2 Constant Surface Heat Flux......................................................................................... 143
14.3.3 Surface Convection..................................................................................................... 145
14.4 Radiation........................................................................................................................... 146
14.4.1 Blackbody Radiation................................................................................................... 146
14.4.2 Non-Blackbody radiation ............................................................................................148
14.4.3 Thermal Radiation Shield............................................................................................ 149
HAPTER
C
HERMODYNAMICS
15: T
.....................................................................................................152
15.1 Fundamentals................................................................................................................. 152
15.2 System Properties .............................................................................................................. 153
15.2.1 Energy Equations........................................................................................................ 153
15.2.2 Maxwell Relations ...................................................................................................... 155
15.3 Vapor and Gas Mixture...................................................................................................... 157
15.3.1 Saturated Liquid/Vapor ............................................................................................... 157
15.3.2 Compressed Liquid-Sub cooled ...................................................................................159
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15.4 Ideal Gas Properties........................................................................................................... 160
15.4.1 Specific Heat...............................................................................................................160
15.4.2 Quasi-Equilibrium Compression..................................................................................162
15.5 First Law...............................................................................................................................163
15.5.1 Total System Energy...................................................................................................163
15.5.2 Closed System: Ideal Gas...............................................................................................167
15.5.2.1 Constant Pressure.....................................................................................................167
15.5.2.2 Binary Mixture......................................................................................................... 169
15.6 Second Law........................................................................................................................... 171
15.6.1 Heat Engine Cycle .......................................................................................................... 171
15.6.1.1 Carnot Engine..........................................................................................................171
15.6.1.2 Diesel Cycle............................................................................................................. 173
15.6.1.3 Dual Cycle............................................................................................................... 177
15.6.1.4 Otto Cycle................................................................................................................180
15.6.1.5 Brayton Cycle .......................................................................................................... 184
15.6.2 Clapeyron Equation.....................................................................................................186
HAPTER
C
ACHINE DESIGN
16: M
.......................................................................................................188
16.1 Stress: Machine Elements .................................................................................................. 188
16.1.1 Cylinders .................................................................................................................... 188
16.1.2 Rotating Rings............................................................................................................ 189
16.1.3 Pressure and Shrink Fits.............................................................................................. 190
16.1.4 Crane Hook................................................................................................................. 192
16.2 Hertzian Stresses................................................................................................................193
16.2.1 Two Spheres...............................................................................................................193
16.2.2 Two Cylinders............................................................................................................ 195
16.3.1 Bearing Life................................................................................................................ 197
16.3.2 Petroff's law................................................................................................................ 198
16.3.3 Pressure Fed Bearings................................................................................................. 199
16.3.4 Lewis Formula............................................................................................................200
16.3.5 AGMA Stresses.......................................................................................................... 201
16.3.6 Shafts..........................................................................................................................203
16.3.7 Clutches and Brakes ........................................................................................................... 204
16.3.7.1 Clutches....................................................................................................................... 204
16.3.7.1.1 Clutches ................................................................................................................ 204
16.3.7.2 Uniform Wear - Cone Brake.....................................................................................206
16.3.7.3 Uniform Pressure - Cone Brake................................................................................ 207
16.4 Spring Design........................................................................................................................208
16.4.1 Bending.......................................................................................................................... 208
16.4.1.1 Rectangular Plate.....................................................................................................208
16.4.1.2 Triangular Plate........................................................................................................ 209
16.4.1.3 Semi-Elliptical......................................................................................................... 210
16.4.2 Coiled Springs................................................................................................................ 212
16.4.2.1 Cylindrical Helical - Circular wire............................................................................ 212
16.4.2.2 Rectangular Spiral.................................................................................................... 213
16.4.3 Torsional Spring............................................................................................................. 215
16.4.3.1 Circular Straight Bar ................................................................................................215
16.4.3.2 Rectangular Straight Bar...........................................................................................216
16.4.4 Axial Loaded.................................................................................................................. 217
16.4.4.1 Conical Circular Section........................................................................................... 217
16.4.4.2 Cylindrical - Helical..................................................................................................... 219
16.4.4.2.1 Rectangular Cross Section .....................................................................................219
16.4.4.2.2 Circular Cross Section ........................................................................................... 220
HAPTER
C
UMPS AND HYDRAULICS
17: P
............................................................................................222
17.1 Basic Definitions ...........................................................................................................222
17.2 Pump Power .................................................................................................................. 223
17.3 Centrifugal Pumps.............................................................................................................225
ME⋅Pro for TI-89, TI-92 Plus
Table of Contents
7
17.3.1 Affinity Law-Variable Speed.......................................................................................225
17.3.2 Affinity Law-Constant Speed......................................................................................226
17.3.3 Pump Similarity.......................................................................................................... 227
17.3.4 Centrifugal Compressor............................................................................................... 228
17.3.5 Specific Speed ............................................................................................................229
HAPTER
C
AVES AND OSCILLATION
18: W
...........................................................................................231
18.1 Simple Harmonic Motion...................................................................................................231
18.1.1 Linear Harmonic Oscillation........................................................................................231
18.1.2 Angular Harmonic Oscillation..................................................................................... 232
18.2 Pendulums.........................................................................................................................233
18.2.1 Simple Pendulum........................................................................................................233
18.2.2 Physical Pendulum...................................................................................................... 235
18.2.3 Torsional Pendulum....................................................................................................236
18.3 Natural and Forced Vibrations.............................................................................................. 236
18.3.1 Natural Vibrations...........................................................................................................236
18.3.1.1 Free Vibration..........................................................................................................236
18.3.1.2 Overdamped Case (ξ>1)........................................................................................... 238
18.3.1.3 Critical Damping (ξ=1) ............................................................................................ 239
18.3.1.4 Underdamped Case (ξ<1)......................................................................................... 241
18.3.2 Forced Vibrations ........................................................................................................... 244
18.3.2.1 Undamped Forced Vibration.....................................................................................244
18.3.2.2 Damped Forced Vibration ........................................................................................ 245
18.3.3 Natural Frequencies...........................................................................................................247
18.3.3.1 Stretched String........................................................................................................ 247
18.3.3.2 Vibration Isolation ................................................................................................... 248
18.3.3.3 Uniform Beams............................................................................................................249
18.3.3.3.1 Simply Supported..................................................................................................250
18.3.3.3.2 Both Ends Fixed.................................................................................................... 251
18.3.3.3.3 1 Fixed End / 1 Free End....................................................................................... 252
18.3.3.3.4 Both Ends Free...................................................................................................... 254
18.3.3.4 Flat Plates.................................................................................................................... 255
18.3.3.4.1 Circular Flat Plate.................................................................................................. 255
18.3.3.4.2 Rectangular Flat Plate............................................................................................257
HAPTER
C
EFRIGERATION AND AIR CONDITIONING
19: R
...................................................................259
19.1 Heating Load.................................................................................................................259
19.2 Refrigeration......................................................................................................................261
19.2.1 General Cycle .............................................................................................................261
19.2.2 Reverse Carnot............................................................................................................ 262
19.2.3 Reverse Brayton.......................................................................................................... 263
19.2.4 Compression Cycle.....................................................................................................264
HAPTER
C
TRENGTH MATERIALS
20: S
...............................................................................................267
20.1 Stress and Strain Basics ..................................................................................................... 267
20.1.1 Normal Stress and Strain.............................................................................................267
20.1.2 Volume Dilation.........................................................................................................268
20.1.3 Shear Stress and Modulus............................................................................................ 269
20.2 Load Problems...................................................................................................................270
20.2.1 Axial Load.................................................................................................................. 270
20.2.2 Temperature Effects....................................................................................................271
20.2.3 Dynamic Load ............................................................................................................272
20.3 Stress Analysis ..................................................................................................................274
20.3.1 Stress on an Inclined Section ....................................................................................... 274
20.3.2 Pure Shear...................................................................................................................275
20.3.3 Principal Stresses........................................................................................................276
20.3.4 Maximum Shear Stress................................................................................................277
20.3.5 Plane Stress - Hooke's Law..........................................................................................278
20.4 Mohr’s Circle Stress..........................................................................................................280
ME⋅Pro for TI-89, TI-92 Plus
Table of Contents
8
20.4 Mohr’s Circle Stress.......................................................................................................280
20.5 Torsion.............................................................................................................................. 281
20.5.1 Pure Torsion............................................................................................................... 281
20.5.2 Pure Shear...................................................................................................................283
20.5.3 Circular Shafts............................................................................................................ 284
20.5.4 Torsional Member.......................................................................................................285
HAPTER
C
LUID MECHANICS
21: F
.....................................................................................................288
21.1 Fluid Properties .......................................................................................................... ....... 288
21.1.1 Elasticity..................................................................................................................... 288
21.1.2 Capillary Rise............................................................................................................. 289
21.2 Fluid Statics............................................................................................................. ............. 291
21.2 1 Pressure Variation........................................................................................................... 291
21.2.1.1 Uniform Fluid.......................................................................................................... 291
21.2.1.2 Compressible Fluid..................................................................................................292
21.2.1 Pressure Variation........................................................................................................... 292
21.2.1.3 Troposphere.............................................................................................................292
21.2.1.4 Stratosphere............................................................................................................. 293
21.2.2.1 Floating Bodies........................................................................................................294
21.2.2.2 Inclined Plane/Surface.............................................................................................. 296
21.3 Fluid Dynamics.................................................................................................................297
21.3.1 Bernoulli Equation...................................................................................................... 297
21.3.2 Reynolds Number ....................................................................................................... 299
21.3.3 Equivalent Diameter....................................................................................................300
21.3.4 Fluid Mass Acceleration.................................................................................................. 302
21.3.4.1 Linear Acceleration .................................................................................................. 302
21.3.4.2 Rotational Acceleration ............................................................................................303
21.4 Surface Resistance............................................................................................................. 304
21.4.1 Laminar Flow – Flat Plate ........................................................................................... 304
21.4.2 Turbulent Flow – Flat Plate.........................................................................................306
21.4.3 Laminar Flow on an Inclined Plane..............................................................................309
21.5 Flow in Conduits ................................................................................................................... 311
21.5.1 Lamina r F l ow: Smooth Pipe....................................................................................... 311
21.5.2 Turbulent Flow: Smooth Pi pe..................................................................................... 313
21.5.3 Turbulent Flow: Rough Pipe....................................................................................... 316
21.5.4 Flow pipe Inlet............................................................................................................ 319
21.5.5 Series Pipe System...................................................................................................... 321
21.5.6 Parallel Pipe System .................................................................................................... 322
21.5.7 Venturi Meter.................................................................................................................324
21.5.7.1 Incompressible Flow ................................................................................................ 324
21.5.7.2 Compressible Flow...................................................................................................327
21.6 Impulse/Momentum............................................................................................................... 330
21.6.1 Jet Propulsion ............................................................................................................. 330
21.6.2 Open Jet..........................................................................................................................331
21.6.2.1 Vertical Plate ........................................................................................................... 331
21.6.2.2 Horizontal Plate ....................................................................................................... 332
21.6.2.3 Stationary Blade.......................................................................................................333
21.6.2.4 Moving Blade..........................................................................................................335
HAPTER
C
YNAMICS AND STATICS
22: D
.............................................................................................338
22.1 Laws of Motion ............................................................................................................. 338
22.2 Constant A ccelerat ion........................................................................................................ 340
22.2.1 Linear Motion............................................................................................................. 340
22.2.2 Free Fall .....................................................................................................................341
22.2.3 Circular Motion........................................................................................................... 342
22.3 Angular Motion................................................................................................................. 343
22.3.1 Rolling/Rotation.......................................................................................................... 343
22.3.2 Forces in Angular Motion............................................................................................ 345
ME⋅Pro for TI-89, TI-92 Plus
Table of Contents
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22.3.3 Gyroscope Motion.......................................................................................................346
22.4 Projectile Motion ........................................................................................................... 347
22.5 Collisions..............................................................................................................................349
22.5.1 Elastic Collisions ............................................................................................................ 349
22.5.1.1 1D Collision............................................................................................................. 349
22.5.1.2 2D Collisions........................................................................................................... 350
22.5.2 Inelastic Collisions.......................................................................................................... 351
22.5.2.1 1D Collisions........................................................................................................... 351
22.5.2.2 Oblique Collisions.................................................................................................... 352
22.6 Gravitational Effects.......................................................................................................... 354
22.6.1 Law of Gravitation...................................................................................................... 354
22.6.2 Kepler's Laws ............................................................................................................. 356
22.6.3 Satellite Orbit..............................................................................................................358
22.7 Friction..............................................................................................................................360
22.7.1 Frictional Force........................................................................................................... 360
22.7.2 Wedge........................................................................................................................ 362
22.7.3 Rotating Cylinder........................................................................................................363
22.8 Statics................................................................................................................................364
22.8.1 Parabolic cable............................................................................................................ 364
22.8.2 Catenary cable............................................................................................................365
PART III: REFERENCE ……………………………………………………………………….368
HAPTER
C
NTRODUCTION TO REFERENCE
23: I
...................................................................................369
23.1 Introduction................................................................................................................... 369
23.2 Finding Reference.......................................................................................................... 369
23.3 Reference Screens.......................................................................................................... 370
23.4 Using Reference Tables .................................................................................................370
HAPTER
C
NGINEERING CONSTANTS
24: E
..........................................................................................372
24.1 Using Constants............................................................................................................. 372
HAPTER
C
25: T
RANSFORMS
..............................................................................................................374
25.1 Using Transforms ..........................................................................................................374
HAPTER
C
ALVES AND FITTING LOSS
26: V
.........................................................................................376
26.1 Valves and Fitting Loss Screens.....................................................................................376
HAPTER
C
RICTION COEFFICIENTS
27: F
............................................................................................377
27.1 Friction Coefficients Screens..........................................................................................377
HAPTER
C
ELATIVE ROUGHNESS OF PIPES
28: R
................................................................................378
28.1 Relative Roughness Screens ........................................................................................... 378
HAPTER
C
ATER-PHYSICAL PROPERTIES
29: W
...................................................................................379
29.1 Water-Physical Properties Screens..................................................................................379
HAPTER
C
ASES AND VAPORS
30: G
.....................................................................................................380
30.1 Gases and Vapors S creens.............................................................................................. 381
HAPTER
C
HERMAL PROPERTIES
31: T
................................................................................................382
31.1 Thermal Properties Screens............................................................................................ 382
HAPTER
C
UELS AND COMBUSTION
32: F
............................................................................................383
32.1 Fuels and Combustion Screens.......................................................................................383
HAPTER
C
33: R
EFRIGERANTS
...........................................................................................................385
33.1 Refrigerants Screens ...................................................................................................... 386
HAPTER
C
34: SI P
REFIXES
...............................................................................................................387
34.1 Using SI Prefixes........................................................................................................... 387
HAPTER
C
REEK ALPHABET
35: G
......................................................................................................388
PART IV: APPENDIX AND INDEX…………………………………………………………….…….389
PPENDIX
A
REQUENTLY ASKED QUESTIONS
A F
.................................................................................390
A.1 Questions and Answers...................................................................................................390
A.2 General Questions........................................................................................................... 390
A.3 Analysis Questions.......................................................................................................... 392
A.4 Equations Questions........................................................................................................ 392
A.5 Graphing.........................................................................................................................395
ME⋅Pro for TI-89, TI-92 Plus
Table of Contents
10
A.6 Reference........................................................................................................................ 396
PPENDIX
A
B W
ARRANTY
ECHNICAL SUPPORT
, T
................................................................................397
B.1 da Vinci License Agreement............................................................................................397
B.2 How to Contact Customer Support................................................................................... 398
PPENDIX
A
C: TI-89 & TI-92 P
LUS
EYSTROKE AND DISPLAY DIFFERENCES
- K
...................................399
C.1 Display Property Differences between the TI-89 and TI-92 Plus......................................399
C.2 Keyboard Differences Between TI-89 and TI-92 Plus ..................................................... 400
PPENDIX
A
RROR MESSAGES
D E
.......................................................................................................404
D.1 General Error Messages..................................................................................................404
D.2 Analysis Error Messages................................................................................................. 405
D.3 Equation Messages.......................................................................................................... 405
D.4 Reference Error Messages...............................................................................................406
PPENDIX E: SYSTEM VARIABLES AND RESERVED NAMES
A
.............................................................407
INDEX ……………………………………………………………………………………………………408
ME⋅Pro for TI-89, TI-92 Plus
Table of Contents
11
Chapter 1: Introduction to ME••••Pro
Thank you for purchasing the ME•Pro, a m ember of the PocketProfessiona l® Pro software series designed
by da Vin ci Technologies Group, Inc., t o meet the porta ble computing needs of student s an d p rofessionals
in mechanical engineering. The software is organized in a hierarchical manner so t hat the topics easy to
find. We hope that you will find the ME•Pro to be a valuable companion in your career as a student and a
professional of m echanical engi neering.
Topics in this chapter include:
Key Features of ME•Pro
Purchasing, Download and Installing ME•Pro
Ordering a Manual
Memory Requirements
Differences between the TI-89 and TI-92 Plus
Starting the ME•Pro
How to use this Manual
Manual Disclaimer
Summary
1.1 Key Features of ME••••Pro
The manual is organized into t hree sections representing the main menu headings of ME•Pro.
Analysis Equations Reference
Steam Tables Beams and Columns Engineering Constants
Thermocouples EE For MEs Transforms
Capital Budgeting Gas Laws Valves/Fitting Loss
EE For MEs Heat Transfer Friction Coefficients
Efflux Thermodynamics Roughness of Pipes
Section Properties Machine Design Water Physical Properties
Hardness Number Pumps and Hydraulic Machines Gases and Vapors
Waves and Oscillation Thermal Properties
Refrigeration and Air Conditioning Fuels and Combustion
Strength Materials Refrigerants
Fluid Mechanics SI Prefixes
Dynamics and Statics Greek Alphabet
Thes e main topi c headings a re further divi d ed int o sub- topics. A brief descri ption of the main sections of
the software is listed below:
Analysis: Chapt er s 2-9
Analysis is organized into 7 topics and 25 sub-topics. The software tools available in this section
incorporate a va riety of an alysis methods used by mech anical en g ineers. Examples include Steam
Tables, Thermocouple Calculations, EE for MEs; Efflux, Section Properties, Hardness Number
Computations and Capital Budgeting. Wh er e appropriate, dat a en t er ed supports commonly used units.
Equations: Chapters 10-22
This section contains over 1000 equations organized under 12 major subjects in over 150 sub -topics. The
equations in each sub-topic have been selected to provide maximum coverage of the subject material. In
ME⋅Pro for TI-89, TI-92 Plus
Chapter 1 - Introduction to ME-Pro
12
addition, the math engine is able to compute multiple or partial solutions to the equation sets. The
computed values are filtered to identify results that h ave engineering merit. A powerful built-in unit
management feature permits inputs in SI or other customary measurement systems. Over 80 diagrams
help clar ify the essentia l na ture of th e problems covered by the equations. Topics covered include, Beams
and Columns; EE for MEs; Gas Laws; Heat Transfer; Thermodynamics; Machine Design; Pumps
and Hydraulic Machines; Waves and Oscillation; Strength of Materials; Fluid Mechanics; and,
Dynamics and Statics.
Reference: Chapters 23-25
The Reference section contains tables of information commonly needed by mechanical engineers. Topics
include, values for Constants used by mechanical engineers; Laplace and Fourier Transform tables;
Valves and Fitting Loss; Friction Coefficient; Roughness of Pipes; Water Physical Properties;
Gases and Vapors; Thermal Properties; Fuels and Combustion; Refrigerants; SI prefixes; and the
Greek Alphabet.
1.2 Purchasing, Downloading and Installing ME••••Pro
The ME•Pro software can on ly be purch ased on- lin e from the Tex a s Instruments I nc. Online Stor e at
http://www.ti.com/calc/docs/store.htm. Th e software can be installed directly from your computer to your
calculator using TI-GRAPH LINK
downloading and installing ME•Pro software are available from TI’s website.
TM
hardware and software (sold separ at ely). Directions for purchasing,
1.3 Ordering a Manual
Chapters and Appe ndices of the Manual for ME•Pro can be downloa ded through TI’ s Web Store an d
viewed using the free Adobe Acrobat Reader
Printed manuals can be purchased separately from da Vinci Technologies Group, Inc. by visiting the
website http://www.dvtg.com/ticalcs/docs
TM
that can be downloaded from http://www.adobe.com.
or calling (541) 754-2860, Extension 100.
1.4 Memory Requirements
The ME•Pro program is installed in the system memory portion of the Flash ROM that is separate from the
RAM available to the user. ME•Pro uses RAM to store some of its session information, including values
entered and computed by the user. The exact amount of mem ory requi red depe n d s on the number of userstored variables and the number of session folders designated by the user. To view the available memory in
your TI calculator, use the function
. It is recommended that at least 10K of free RAM be
available for installation and use of ME•Pro.
1.5 Differences between TI-89 and TI-92 plus
ME•Pro is designed for two models of graphing calculators from Texas Instruments, the TI-92 Plus and the
TI-89. For consistency, keystrokes and symbols used in the manual are consistent with th e TI-89.
Equivalent key strokes for the TI-92 Plus are listed in Appendix D.
1.6 Starting ME••••Pro
To begin ME•Pro, start by pressing t he
move t he cu rsor bar to
press the
key to get to the home screen of ME•Pro. Alternatively, press
ME•Pro and press the
FlashApps...
key to get to the home screen of ME•Pro.
/
key. This accesses a pull down menu. Use the $ key to
. an d press
. Then move the highlight bar to ME•Pro and
/
; then, scroll to
ME⋅Pro for TI-89, TI-92 Plus
Chapter 1 - Introduction to ME-Pro
13
Pull down Menu for
/
(FlashApps...option is at the top of the list)
Pull down Menu on for FlashApps...
(ME•Pro will be in the list)
The ME•Pro home screen is displayed to the right. The tool bar at the
top of the screen lists the titles of the main sections of ME•Pro which
can be activated by pressing the function keys.
b
: Tools: Editing features, information about ME•Pro in A: About.
c
: Analysis: Accesses the Analysis section of the software.
d
: Equations: Accesses the Equations section of the software.
e
: Reference: Accesses the Reference section of the software.
f
: Info: Helpful hints on ME•Pro.
To select a topic, use the $ ke y to mov e the highl i ght bar to the d e s ired top ic and pr e s s
, or
alternatively type the number next to the item. The Analysis, Equation and Reference menus are
organized in a menu tree of topics and sub-topics. The user can r eturn to a previous level of ME•Pro by
pressing . You can exi t ME•Pro at any time by pressing the
key. When ME•Pro is restarted ,
the software returns to its previous location in th e program.
1.7 How to use this Manual
The manual section, chapter heading and page number appear at the bottom of each page. The first chapter
in ea ch of the Analysis, Equations and Reference sections gives an overview of succeeding chapters and
introduces the navigation and computation features common to each of the main sections. For example,
Chapter 2 explains the basic layout of the Analysis section menu and the navigation principles, giving
examples of fe atu re s common to all topi cs in Analysis. Each topic in Analysis has a chapter dedicated to
describing its functionality in detail. The titles of these chapters correspond to the topic headings in the
software menus . They contain example problems and scr een di s p lays of the compu ted solut ions. Troubl eshooting information, commonly as ked questions , and a bibliograp hy use d to develop the sof tware a re
provided in appendixes.
1.8 Manual Disclaimer
The calculator screen displays in the manual were obtained during the testing stages of the software. Some
screen displays may appear slightly different due to final chan ges made in the software while the Manual
was being comple ted.
ME⋅Pro for TI-89, TI-92 Plus
Chapter 1 - Introduction to ME-Pro
14
1.9 Summary
The designers of ME•Pro invite your comments by logging on to our website at http://www.dvtg.com or
by e-mail to improvements@dvtg.com
easy with the software by providing the following features:
• Easy-to-use, menu-based interface .
• Computational efficiency for speed and performance.
• Helpful-hints and context-sensitive information provided in the status line.
• Advanced ME analysis routines, equations, and reference tables.
• Comprehensive manual documentation for examples and quick reference.
. We hope that you agree we have made complex computations
ME⋅Pro for TI-89, TI-92 Plus
Chapter 1 - Introduction to ME-Pro
15
Part I: Analysis
ME⋅Pro for TI-89, TI-92 Plus
Analysis -
16
Chapter 2: Introduction to Analysis
2.1 Introduction
The analysis section contains subroutines and tools designed to perform specific calculations. Computations
include estimating thermodynamic properties of water at different temperature and pressure, in Steam
∆
Tables, computing fluid flow rates through different shaped orifices in Efflux, performing Wye to
conversions of AC circuits in EE for MEs, and evalueating cash flow for different projects in Capital
Budgeting. The computations are strictly top-down (i.e. the inputs and outputs are generally the same) and
the interface for each section guides the user through the solving process. A brief description of some of the
diff erent sections in Analys is appear below:
Steam Tables (3 sections): Saturated Steam, Superheated Steam, Air Properties computes the
thermodynamic parameters of steam including saturated pressure, enthalpy, entropy, internal energy, and
specific volume of the liquid and vapor forms of water given entri es of temperature and/or pressure. This
final topic covered computes the thermodynamic properties of dry air at different temperature s.
Thermocouples: This tool converts a specified tempe rature to an emf output in millivolts (mV) or from emf
output millivolts (mV) to a specified temperature. The software supports T, E, J, K, S, R and B type
thermocouples. These computation algor i t hms result from the IPTS -68 sta ndards adopted in 1968 and
modified in 1985.
circuit
Capital Budgeting: This section performs analysis of capital expenditure for a project and compares
projects against one another. Four measures of capital budgeting are included in thi s section: Payback
period (Payback); Net Present Value (NPV); Internal Rate of Return (IRR); and Profitability Index (PI).
This module provides the capability of entering, storing and editing capital expenditures for nine different
project s. Project s can be graph ed on NPV vs. k scale.
EE for Mechanical Engineers (3 sections): Performs e valuations on three types of circ u its: Impedance
↔∆
calculations; Circuit Performance; Wye
impedance admittance of a circuit consisting of a resistor, capacitor and inductor connected in Series or
Parallel. Performance parameters section computes load voltage and current, complex power delivered,
power factor, m axim u m power a va ilabl e to the l oad, a nd the load i mpedance req u ired t o receive the
maximum power from a single power source. The final segment of the software converts configurations
expressed as a Wye to its ∆∆∆∆ equivalent. It also performs the reverse computation.
Efflux (6 sections): Constant Liquid level; Varying liquid level; Conical Vessel; Horizontal Cylinder;
Large Rectangular Orifice; ASME Weirs (Rectangular notch; Triangular Weir; Suppres s ed Weir; Cipolletti
Weir) This section contai ns methods to compute fluid flow via cross sections of different shapes.
Section Properties (1 2 s ect ions): Rectangle; Hollow Rectangle; Circle; Circular Ring (Annulus); Uneven
I-section; Even I-section; C section; T section; Trapezoid; Polygon (n-s ided); Hollow P olygon (n-sided, side
thickness) Computes are a moment and location of center of mass for diff erent shaped cross sections.
Computed parameters inc lude the cross section area, the pol ar moment o f inertia, the area moment of inertia
and radius of gyration on x and y axes.
Hardness Number: A dimensionless number is a measure of the yield of a material from impact. Brinell
and Vicker developed two popular methods of measuring the Hardness number. These tests consist of
dropping a 10 mm ball of steel with a specified load such as 500 lbf and 3000 lbf. This steel ball results in
an indentation in the material. The diameter of indentation indicate s o f the hardness numbe r using e ither the
Brinell's or Vicker's formulation.
Circuit conversion
Impedance Calcula tions,
computes the
ME⋅Pro for TI -89, TI-92 Plus
Chapter 2- Introduction to Analysis
17
2.2 Features of Analysis
Unit Management: Appropriate unit menus for appending units to variable entries or converting computed
results are accessible in most sections.
Numeric Computation – Variable entries must consist of real numbers (unless specified). Algebraic
expressions must consis t of defined variables so a numeri c val u e can be condensed upon entry.
2.3 Finding Analysis
The following panels illustrate how to start ME•Pro and locate the
Analysis
section.
1. Press the
HOME screen to list the
applications stored in your
calculator.
There are seven sections under
desired heading and pressing
/
key in the
Analysis
2. Press 1:FlashApps and
press
to display the
applications stored in the
Flash section of memory.
1
3. HOME screen of ME
Analysis is listed as c on the
top function key row.
Pro.
•
. To sel ect a topic, use t he $ ke y to mov e the highl i ght bar to the
, or alternatively type the number next to the item to select. If a topic
contains several sections (Steam Tables, EE for MEs, Efflux, Section properties, an ellipsis (…) will appear
next to the title (see below).
From t he home screen of
ME•Pro
Press c
to display
Press for topics in
Tables
…
Steam
…or, press Z for topics in
Efflux.
the Analysis menu…
2.4 Solving a Problem in Analysis
The following example presents some of the navigational features in Analysis. This example is drawn from
Chapter 6: EE for MEs.
Problem - Calculate the performance parameters of a circuit consisting of a current source (10 - 5*i) with a
source admittance of .0025 - .0012*I, a load of .0012 + .0034*i. Display the real result of power in
kilowatts.
1
Steps 1 and 2 can be combined by pressing and
ME⋅Pro for TI -89, TI-92 Plus
Chapter 2- Introduction to Analysis
/
.
18
1. From the home screen of
Pro, Press c to display
ME
•
the menu of Analysis.
4. While the cursor is
highlighting Load Type,
press the right arrow key,
or g to display the menu for
Load Type.
7. Variable descriptions
beginning with ‘Enter’ require
numeric entries.
2. Move the cursor to EE for
MEs and press
press Y).
5. In the menu for Load
Type move the cursor to
Admittance and press
.
(or
3. Select Circuit
Performance from the
submenu in EE for Mes.
6. Admittance is now
selected for Load Type and
the appropriate variables are
displayed.
8. Variable descriptions
beginning with the word
‘Resu lt’ are computed fields.
9. When entering a value,
press a function key to add
the appropriate units (c-h).
10. Following entry of all
input fields, pres s c: Solve to
compute the results.
13. To display a result in
different unit s , highlight the
variable and press f:Opts
move the cursor to 4
:Conv.
ME⋅Pro for TI -89, TI-92 Plus
Chapter 2- Introduction to Analysis
11. Results: Upper Half 12. Results: Lower Half
14. The unit menu for the
variable appears in the top
bar. Press t he func tion key
,
15. The computed value for
Real Power, P, is now displaye d
in kilowatts (kW).
corresponding to the desired
units.
19
There are two types of interfaces in
Type 1: Input/Output/Choose Fields (Steam Tables, Thermocouples, EE for MEs, Efflux, Section
Properties, and Hardness Number). This input form lists the variables for which a numeric entry is required
and prompts the user to choose a calculation setting if applicable before computing the results. The entries
and results are always displayed in the same screen.
Type 2: Multiple Forms/Graphing (Capital Budgeting) This interface includes most of the features of
Type 1 with the additional screens used for entering cash flow for individual projects. The graphing
feat ures of t he calculator are enabled i n t his section for v i sualizing the rate of return (Net Present Value vs.
discount rate). An example of this interface is described briefly in this chapter, but in mor e detail in Chapter
5: Capital Budgeting.
Capital Budgeting
relevant data such as
displays below illustrate the basic user interface.
Input Screen for Capital
Budgeting
display Cash Flow for Project
1.
. Press e to
allows the user to compare relative financial performance of several projects with
Interest rate or discount rate (k), IRR, NPV, or Payback period. The screen
Analysis
A separate screen displays
the Cash Flow for ‘Project 1’.
Press c: Solve to r evert to
the previous screen.
:
Press d: Graph. Select ing
‘Multiple Graphs’
overlap of plots for different
projects (Projec t 1, Project 2,
etc.)
allows the
2.5 Tips for Analysis
The following instructions are useful in the Analysis section:
1. If an ellipsis (…) appears at the end of a menu title, a menu of subtopics exists i n this se ct i on .
2. An arrow ‘→→→→’ to the right of a heading, as in Load T ype, indicates an additional menu.
3. Variables ending with an underscore ‘_’, such as Vs_, Zs_, and IL_, allow complex values.
4. Descriptions for variables generally appear in the status line when the variable is highlighted.
5. Variables for which an entr y is required will have a description prefaced by the word ‘Enter’.
Computed variables begin with the word, ‘Result’.
To convert values from one unit to another, press
6.
th e variable at t h e top of the screen. Press the functio n key co rresponding to the appropriate units.
7. To return to the previous level of ME•Pro, press ..
8. To exit ME•Pro, press b: Tools and N: Clear.
9. To return to ME•Pro, p ress
10. To toggle between a graph and ME•Pro in split-screen mode, press
11. To remove the split screen in ME•Pro. 1) Press
Full Screen, 5)
: Save.
/
.
f:Opts, and 4:Conv to dis play the unit menu for
/
.
, 2) c: Page 2, 3) ": Split Screen App., 4) :
2.6 Function keys
Analysis
When
are s p ecific to the cont ex t of the section. Th ey are listed in Table 2-1:
functions are selected, the function keys in the tool bar access or activate features, which
ME⋅Pro for TI -89, TI-92 Plus
Chapter 2- Introduction to Analysis
20
Table 2-1 Description of Analysis Function keys
Function Key Description
and
Tools
Solve
Graph
/
b
c
d
e
Labeled "
screen level. Th ese fu nctions are:
1: Open – This opens an existing folder to store or recall variables used in an
ME•Pro session.
2: (save as) – Not active in Analysis.
3: New – Creates a new folder for storing variable values used in an ME•Pro
session.
4: Cut - Removes entered values into the clipboard. Enabled for variables for
which t he user ca n enter va l u es.
5: Copy – Copies a highlighted value into the clipboard.
6: Paste – Pastes clipboard contents at cursor location.
7: Delete – Deletes highlighted values.
8: Clear – Return s to the HOME screen of ME•Pro.
9: (format)-Not active in Analysis.
A: About - Displays product name and version number.
Labeled "
selected problem and display any resulting output to the user.
Labeled "
be represent ed in graphical form. A gr aph can be viewed i n the full s creen or a
split screen mode. This can be performed by pressing
Normally labeled as "
cursor to be displayed using the entire screen in Pretty Print format.
In some cases @ is labeled as "Pict", "Cash".
"Pict" is available in the Section Properties or Hardness Number sections
and when selected displays a diagram to facilitate better understanding of the
problem.
"Cash" is used in Capital Budgeting section of the software.
Labeled "Opts" - Thi s key displays a po p up me nu l i s ting the options:
1: View - allows the highlighted item to be viewed using Pretty Print.
2: (type) - Not active
3: Units – This activates, or deactivates the unit management feature.
4: Conv – Displays the unit menu for the highlighted variable and allows the
conversion of an entry or result into different units.
5: Icons - Presents a dialog box identifying certain Icons used by the software to
display content and context of the information. These icon systems are only used
in equ a t ions.
6: (know)- Not active
7: Want - Not active
“Edit” - Brings in a data entry line for the highlighted parameter.
“Choose” in Capital Budg et ing enables th e user to select from one of n ine
project s.
“√ Check” requesting the user to press this k ey to select a highlighted parameter for
use in an Analysis computation.
"Add” Adds a cash flow entr y for a project in Ca pital Budget ing section.
(Not active)
" - displays all the functions available on the TI-89 at the Home
" - Pressing this key enables the software to begin solving a
" - This feature is available in input scree ns where the solution can
followed by c. Use
to toggle between the data entry screen and graph window.
View
" - This enables the information highlighted b y the
ME⋅Pro for TI -89, TI-92 Plus
Chapter 2- Introduction to Analysis
21
2.7 Session Folders, Variable Names
ME•Pro automatically stores its variables in the current folder specified by the user in
screen. The cur rent folder name is displayed in th e lower left corner of th e s creen (default is “Main”). To
create a new folder to store values for a particular session of ME•Pro, press :/TOOLS, :/NEW and
type t he nam e of the new folder (see Gu idebook for the com plete det ail s of crea ting and m anaging fol ders;
Chapter 5 for the TI-89 and Chapter 10 for the TI-92 Plus).
There are several ways to display or recall a value:
• The conten ts of variables in any folder can be d ispla yed using
variable name and pressing to display the contents of a particular variable.
• Variables in a current folder can be recalled in the HOME screen by typing the variable name.
• All inputs and calculated results from the Analysis and Equations section are saved as variable
names. Previously cal culat ed , or enter ed values for va ria bl es in a fold er are rep laced wh en
equatio ns are solved using new values for inputs.
or the HOME
, moving the cursor to the
2.8 O verwriting of variable values in graphing
When an equation or analysis function is graphed, ME•Pro creates a function for the TI grapher, which
expresses the dependent variable in terms of the independent variable. This function is stored under the
variable name pro (x). When ME•Pro’s equation grapher is execute d , v alu es are inserted into the
independent variable for pro (x) an d va lues for the dependen t value ar e calcul ated. Whatever val u es
previously existed in either of the dependent and independent variables in the current folder are cleared. To
preserve data under variable names, which may conflict with ME•Pro’s variables, run ME•Pro in a separate
folder.
2.9 Reserved Variables
A list of reserved variable names used by the TI operating system, which cannot be used as user variable
names or entries are listed in Appendix F.
ME⋅Pro
for TI -89, TI-92 Plus
Chapter 2- Introduction to Analysis
22
F2: Analysis/1: Steam Tables
Chapter 3: Steam Tables
Steam properties are a complex function of temperature, pressure, volume, critical temperature, critical
pressure, and molecular weight of water. Our software takes into account the ranges of temperature and
pressure that results in good fits to data gathered over a long periods in many parts of the world.
Steam Tables offer a collectio n of programs organized as a powerful computational engine to calculate
thermodynamic properties of steam in a user-friendly environment. Calculations of thermodynamic
properties are based on standards and conventions adopted by the International Conventi ons covering
properties of saturated and superheated steam.
3.1 Saturated Steam Properties
This section computes the properties of saturated steam at a single temperature or pressure.
Variable Description Units
Ps Saturation pressure MPa
Ts Saturation temperature K
Vf Specific volume – liquid m3/kg
Vg Specific volume – vapor m3/kg
Hf Enthalpy – liquid kJ/kg
Hfg Latent heat of vaporization kJ/kg
Hg Enthalpy – vapor kJ/kg
Sf Entropy – liquid
Sfg S (g) - S (f)
Sg Entropy – vapor
UF Internal energy – liquid
UG Internal energy – vapor
kJ/(kg⋅K)
kJ/(kg⋅K)
kJ/(kg⋅K)
kJ/(kg⋅K)
kJ/(kg⋅K)
3.2 Superheated Steam Properties
The properties of superheated steam require two inputs: temperature and pressure. From the data suppli ed ,
the program will compute saturated temperature, specific volume, enth alpy and entropy. The data is
displayed in a tabular form.
Variable Description Units
Temp Given temperature K
Sat Pressure Given pressure MPa
Sat Temperature Corresponding temperature K
Specific Volume Specific volume m3/kg
Enthalpy Enthalpy kJ/kg
Entropy Entropy
kJ/(kg⋅K)
3.3 Air Properties
The properties of dry air are computed using the ideal gas law model as the basis. Using temperature as a n
input, the softwa re computes a var iety of parameters including specific heats, enthalpy, entrop y, and
velocity of sound.
Variable Description Units
Temp Given temperature K
CP Specific heat at constant pressure
J/(kg⋅K)
ME⋅Pro for TI -89, TI-92 Plus
Chapter 3 - Analysis – Steam Tables
23
F2: Analysis/1: Steam Tables
Variable Description Units
CV Specific heat at constant volume
H Enthalpy J/kg
U Internal energy J/kg
E Entropy function
IPR Isentropic pressure function unitless
IVR Isentropic volume function unitless
G Specific heat ratio unitless
A Speed of sound m/s
J/(kg⋅K)
J/(kg⋅K)
3.4 Using Steam T ables
Once you have selected STEAM TABLES at the main menu, the first screen displays three subtopics Saturated steam, Superheated steam and Air properties. Selecting “saturated steam properties”, allows
properti es t o be calcula ted from u ser- entered value of t emperature or pressure. However, p roperties for
“superheated steam” req uire v a lues for both tempe ra t ure and pressure. Thermodyna mic properties of air are
calculated for dry air conditions only.
Example 3.1:
Calculate the properties of saturated steam at 130 °C.
Solution - Select the Saturated S team section. The input screen calls for defining known parameter
(temperature o r pressure) . The default condition is temperature. Move the pointer to the next line and start
entering the temperature. The function keys assume unit assignments for the data about to be entered. For
our example, enter 130 an d press ? key thereby attaching °C to the value just entered. Press > to solve
for the thermodynamic parameters.
Upper Display Lower Display
All the calculated parameters are displayed on the screen w ith SI units attached as shown. If you desire to
see the value of saturated pressure parameter Ps, use the ke y to mov e the highl i gh t bar to capture Ps.
Press A to display a pull down menu of items to select. Select 4 (Conv). This allows other units for Ps
such as Pa, kPa, atm, psi, torr attached to ?, @, A, B, and C respect ively. Pres sing B converts the
value of Ps into the new units of psi. The display is refreshed immediately in the units just selected.
Example 3.2:
Calculate the properties of superheated steam at 125 °C and 20 psi.
Solution - Select the Supe rhea ted Steam se ction. The input screen calls for e ntering temperat ure and
pressure. Move the pointer to enter the 125 °C and 20 psi for temperature and pressure. Make sure that the
appropriate units are attached to the data using the function keys. Press > to solve for the thermodynamic
parameters.
ME⋅Pro for TI -89, TI-92 Plus
Chapter 3 - Analysis – Steam Tables
24
F2: Analysis/1: Steam Tables
Upper Display Lower Display
All the calculated parameters are displayed on the screen with units attached as shown. The displayed
results could be converted to other un its as described in the first example described earlier.
Example 3.3:
Calculate the properties of dry air to be -20 °C.
Select the Air Properties section. The input screen calls for defining the temperature. Enter a temperature
of – 20 °C. When ent erin g -20 °C, be sure to u se the unary operat or key followed by 20 °C. If you
use\ key fo r a negative value this will result in an input error.
Press > to solve for the thermodynamic properties of air.
Input Screen Result screen
All the calculated parameters are displayed on the screen with SI units attached as shown. The parameters
computed can be viewed in other units as described in the examples shown here.
3.5 Validity Range for Temperature and Pressure
The computed results are valid only for the following finite ranges of temperature and pressure:
Saturated Superheated
Temperature: 273.16 - 647.3 K Saturated temperature
Pressure: 0.006113 - 22.08 MPa Pressure: 0.006113 - 22.08 MPa
References:
1. Lester Haar, John S. Gallagher and George S. Kell, NBS/NRC Steam Tables, Thermodynamic and
Transport Properties for Vapor and Liquid States of Water, Hemisphere Publishing Corporation,
Washington, DC.
2. Steam Tables, 1967; Thermodynamic properties of Water a nd Steam, The Electric Research Association,
Edward Arnold Limited, London England, 1967
3. Th omas F. Levine, Jr., and Peter E. Liley, Steam and Gas Tables with Computer Equations, Academic
Press, New York, NY, 1984
ME⋅Pro for TI -89, TI-92 Plus
Chapter 3 - Analysis – Steam Tables
25
F2: Analysis/ 2: Thermocouples
Chapter 4: Thermocouples
This chapter describes using the software in the Thermocouples menu. Thermocouple parameters are
calculated for the class of thermocoupl es in comm on usa g e.
4.1 Introduction
This tool c onverts a specified temperature to an emf output, millivolts (mV), and from an emf output,
millivolts (mV), to a specified temperatur e. The software supports Type T, E, J, K , S, R and B
thermocouples. The underlying assumption is a reference t emperature of 0 °C. These computation algorithms
result from the IPTS-68 standards adopted in 1968 and modified in 1985.
4.2 Using the Thermocouples Function
Select the Thermocouples function from the Analysis menu by highlightin g Thermocouples an d pressing
¸
. This action brings out the main use r inte rf ace scre en. Press B to view the choices availabl e. Seven
types of T hermocou ples a re a vail able for com putations. For example, to sele c t a Pt-10%Rh-Pt thermocoup l e
referr ed to as S Type ther mocouple, move the hi g h th e highlight bar to Type S and press
At this point, the software presents the primary user interface awaiting data entry. At the same time, the
mat erial of the ther mocouple a nd the vali d ran g e are displa yed for reference.
¸
or press z.
Thermocouple computations involve computing emf available from a known temperature or computing a
temperature from an emf. The latter case is by its very nature not as accurate as the first type of computation.
Screen 1 (for temperature) Screen 2 (for emf)
Example 4.2:
Find the emf for an S type thermocouple at 400 °F. From the value of emf computed, compute t he
temperature.
Solution 4.2:
Select Type S thermocouple for t his problem. For temperature, enter 400, t hen press …. The computed emf
is 1.4777mV. Now return t o Kn own line and select emf for input. Ent er 1.4777 mV for emf to get 403.989 °F
for temperature.
Notes: Th e ther mocouple em f ca lcula tion can be ex p anded t o cover the em f produced by th e thermocouple if
the reference temp erat ure was di fferent from 0 °C. For example, if t he reference t emperature was 30 °C
instead of 0 °C, you compute the resulting emf in two steps; first find the emf (emf 1) for the temperature
desired, say 300 °C, and the emf (emf 0) for the reference temperature. The resulting emf for the new
refer ence temperature of 30 °C is the difference between the two emf’ s, i.e., "em f 1 - emf 0".
ME⋅Pro for TI-89, TI-92Plus
Chapter 4 - Analysis - Thermocouples
26
F2: Analysis/ 2: Thermocouples
4.3 Basis for Temperature/Voltage Conversions
The temperature-to-voltage conversion is based on either a polynomial approximation or a combination of a
polynomial coupled with a special sequence. This ensures precise calculations within some prescribed error
range. These rages a re displayed on each inpu t screen.
References:
1. Robert L. Powell, William J. Hall, Clyde H. Hyink, Larry L. Sparks, George W. Burns, Margaret Scoger
and Harmon H. Plumb, Thermocouple Reference Tables based on IPTS-68, NBS Monograph 125, Omega
Press, 1975
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Chapter 4 - Analysis - Thermocouples
27
F2: Analysis/3: Capital Budgeting
Chapter 5: Capital Budgeting
This chapter covers the four basic measures of capital budgeting:
♦ Payback Period ♦ Internal Rate of Return
♦ Net Present Value ♦ Profitability Index
5.1 Using Capital Budgeting
This section performs analysis of capital expenditure for a project and compares projects against one another.
Four measures of capital budgeting are included in this section: Payback period (Payback); Net Present Value
(NPV); Internal Rate of Return (IRR); and Profitability Index (PI). This module provides the capability of
entering, storing and editing capital expenditures for nine different projects. The following equations are used
in calculations:
n
CF
()1
t
−
CF
t
=
t
+
k
0
Eq. 1
NPV
=
∑
t
=
1
n
CF
+
n
∑
t
=
t
IRR
()1
1
∑
t
=
PI
()1
1
=
CF
CFt: Cash Flow at time t.
Payback: The number of time periods it take s a fir m to re cover its original invest ment.
NPV: The present values of all future cash flows, discounted at the selected rate, minus the cost of the
investment.
IRR: The discount rate that equates the present value of expected cash flows to the initial co st of the proj ect.
PI: The present va lue of the future cash flows, discounted at the selected rate, over the initial cash outlay.
CF
−=
t
=
0
t
CF
+
t
=
t
t
k
0
0
Eq. 2
Eq. 3
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Chapter 5 - Analysis - Capital Budgeting
28
F2: Analysis/3: Capital Budgeting
Field Descripti ons - Input Screen
Project:
k:
Payback:
npv:
IRR:
PI:
Multiple
Graphs
Full
Screen
Graph
NAME:
t0:
t1:
tn:
(Project)
Press
to select one of nine unique
projects or edit the current name of the project
by pressing e for Cash option.
(Discount Rate per Period in %) Enter a real number.
(Payback Period) Returns a real number.
(Net Present Value) Returns a real number.
(Internal Rate of Return) Returns a real number (%).
(Profitability Index) Returns a real number.
(Graph multiple projects
simultaneously)
(Graph on full or split screen?) Press
Activation of this feature enables the overlay
of each success i ve gr a p h (pr oject s) on t he
Press
same axis.
to activate.
to activate.
Field Descriptions - Project Edi t Screen
(Project Name) Enter the name of the project.
(Investment at t=0) Enter a real number.
(Cash flow at t=1) Enter a positive or negative real number.
(Cash flow at t=n) Enter a positive or negative real number.
Example 5.1:
The following projects have been proposed by ACME Consolidated Inc. What are t he Payback period, Net
Present Value, Internal Rate of Return, and Profitability Index of each project? Which is the more viable
project?
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Chapter 5 - Analysis - Capital Budgeting
29
Table 5-1 Cash Flow for two projects
Name of Project: Plant 1 Plant 2
Investment Outlay:
$75,000 (at t=0) $75,000 (at t =0)
Cost of Capital: 12% 12%
Year Net Cash Flow ($) Net Cash Flow ($)
0 -75,000 -75,000
1 40,000 10,000
2 30,000 20,000
3 20,000 30,000
4 10,000 40,000
F2: Analysis/3: Capital Budgeting
Cash Flow Input: plant1 Cash Flow Input: plant2
Output Scr een: plant1
Output Scr een: plant2
1. With the highlight bar on the Project field, press
not been used. Note: this example uses projects 1 and 2. Press
to select a project to edit. Select a project that has
to return to the Capital Budgeting
screen.
2. Press e to select Cash option; enter the project edit screen; and, edit the cash flows.
3. Enter “plant1” in the Name field. Note: Cash flo w data for this proj ect will be sto r ed in a variable of thi s
name. Therefore the entered name must begin with a letter; be no more than 8 characters in length; and,
contain no embedded spaces.
4. Press h 5 times to add 5 time points and enter the cash flows at each time point from the table on the
pr e vious page. W hen finished, your s c reen shoul d look like the projec t edi t screen above. Be s ure to en ter
75,000 as a negative number for t0. Press . to save your changes and return to the Capital Budgeting
screen.
5. Enter 12 for k.
6. Press c to calculate Payback, NPV, IRR, and PI.
7. Move the highlight bar to Multiple Graphs and press
to en able overlayin g of succes s ive grap hs of
each p roject.
8. Press d to graph the curvilinear relationshi p between the Net Present Value and the Discount Rate.
9. Press followed by
/
to enable the graph editing toolbar.
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Chapter 5 - Analysis - Capital Budgeting
30
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