Principles and Practice of Engineering PE Mechanical Reference Handbook

533 Pages·2019·7.622 MB·English

by  National Council of Examiners for Engineering and Surveying (NCEES)

PE M e c h a n i c a l
Reference Handbook
Version 1.2
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Third post July 2020
PREFACE
About the Handbook
Beginning in April 2020, the Principles and Practice of Engineering (PE) Mechanical exam will be computer-based, and the
PE Mechanical Reference Handbook is the only resource material you can use during the exam. Reviewing it before exam
day will help you become familiar with the charts, formulas, tables, and other reference information provided. You will
not be allowed to bring your personal copy of the PE Mechanical Reference Handbook into the exam room. Instead, the
computer-based exam will include a PDF version of the handbook for your use. No printed copies of the handbook will be
allowed in the exam room.
The PDF version of the PE Mechanical Reference Handbook that you use on exam day will be very similar to this one.
However, pages not needed to solve exam questions—such as the cover and introductory material—will not be included in
the exam version. In addition, NCEES will periodically revise and update the handbook, and each PE Mechanical exam will
be administered using the version of the handbook in effect on the date the exam is given.
The PE Mechanical Reference Handbook does not contain all the information required to answer every question on the
exam. Theories, conversions, formulas, and definitions that examinees are expected to know have not been included. The
handbook is intended solely for use on the NCEES PE Mechanical exam.
Updates on Exam Content and Procedures
NCEES.org is our home on the web. Visit us there for updates on everything exam-related, including specifications,
exam-day policies, scoring, and practice tests.
Errata
To report errata in this book, send your correction using the chat feature or your account on NCEES.org. Examinees are not
penalized for any errors in the Handbook that affect an exam question.
Contents
1 BASIC ENGINEERING PRACTICE ...........................................................................................................................1
1.1 Engineering Terms and Symbols .............................................................................................................................1
1.1.1 Units ...........................................................................................................................................................2
1.2 Properties of Materials.............................................................................................................................................5
1.2.1 Properties of Air at Atmospheric Pressure .................................................................................................5
1.2.2 Critical Properties ......................................................................................................................................5
1.2.3 Properties of Water at Standard Conditions ...............................................................................................5
1.2.4 Thermal and Physical Properties of Ideal Gases (at Room Temperature) .................................................6
1.2.5 Physical Properties of Fluids .....................................................................................................................7
1.2.6 Engine Oil Viscosity Classification and Properties ...................................................................................8
1.2.7 Compressible-Flow Functions .................................................................................................................11
1.2.8 Properties of Air at Low Pressure, per Pound ..........................................................................................23
1.2.9 Properties of Water at Atmospheric Pressure ...........................................................................................26
1.2.10 Thermal Properties ...................................................................................................................................28
1.2.11 Properties of Metals .................................................................................................................................28
1.2.12 Material Properties ..................................................................................................................................31
1.3 Trigonometry .........................................................................................................................................................33
1.3.1 Basics .......................................................................................................................................................33
1.3.2 Identities ...................................................................................................................................................33
1.4 Mensuration of Areas and Volumes .......................................................................................................................35
1.4.1 Nomenclature ...........................................................................................................................................35
1.4.2 Parabola ...................................................................................................................................................35
1.4.3 Ellipse ......................................................................................................................................................35
1.4.4 Circular Segment .....................................................................................................................................35
1.4.5 Parallelogram ...........................................................................................................................................36
1.4.6 Regular Polygon With n Equal Sides ......................................................................................................36
1.4.7 Right Circular Cylinder ...........................................................................................................................36
1.4.8 Properties of Shapes .................................................................................................................................37
1.4.9 Relations of Mass and Space ...................................................................................................................43
1.5 Periodic Table ........................................................................................................................................................47
1.6 Economic Analysis ................................................................................................................................................48
1.6.1 Nomenclature and Definitions .................................................................................................................48
Contents
1.6.2 Economic Factor Tables ...........................................................................................................................50
1.6.3 Depreciation .............................................................................................................................................58
1.7 Interpretation of Technical Drawings ....................................................................................................................59
1.7.1 ANSI and ISO Orthographic Projection Styles .......................................................................................59
1.7.2 Symbols for Drawings .............................................................................................................................61
1.8 Structural Properties ..............................................................................................................................................65
1.9 Pipe and Tube Data ................................................................................................................................................77
1.10 Electrical Concepts of Motors ...............................................................................................................................80
1.10.1 Efficiency .................................................................................................................................................80
1.10.2 Power Factor ............................................................................................................................................80
1.10.3 Full-Load Current ....................................................................................................................................80
1.10.4 Torques .....................................................................................................................................................81
1.10.5 Synchronous Motor Speeds .....................................................................................................................81
1.10.6 Motor Phases ............................................................................................................................................81
1.10.7 Basic Circuits ...........................................................................................................................................82
2 MACHINE DESIGN AND MATERIALS...................................................................................................................83
2.1 Elements of Machine Design Methodologies ........................................................................................................83
2.2 Cylindrical Fits and Tolerances .............................................................................................................................85
2.2.1 I-P System ................................................................................................................................................85
2.2.2 SI System .................................................................................................................................................86
2.2.3 Tables of Cylindrical Fits and Tolerances ................................................................................................87
2.3 Quality Assurance/Quality Control .....................................................................................................................103
2.3.1 Dispersion, Mean, Median, and Mode Values .......................................................................................103
2.3.2 Uncertainty Analysis ..............................................................................................................................104
2.4 Statistical Quality Control ...................................................................................................................................104
2.4.1 Tests for Out of Control, for Three-Sigma Control Limits ....................................................................105
2.4.2 Nondestructive Testing ..........................................................................................................................106
2.5 Statics and Dynamics...........................................................................................................................................113
2.5.1 Force ......................................................................................................................................................113
2.5.2 Resultant (Two Dimensions) .................................................................................................................113
2.5.3 Resolution of a Force .............................................................................................................................113
2.5.4 Moments (Couples) ................................................................................................................................113
2.5.5 Systems of n Forces: ..............................................................................................................................113
2.5.6 Friction ...................................................................................................................................................114
Contents
2.6 Laws of Motion ...................................................................................................................................................114
2.6.1 Constant Acceleration ............................................................................................................................114
2.6.2 Centripetal Acceleration ........................................................................................................................115
2.6.3 Relative Motion .....................................................................................................................................115
2.6.4 Plane Circular Motion ............................................................................................................................116
2.6.5 Normal and Tangential Components .....................................................................................................116
2.6.6 Projectile Motion ...................................................................................................................................117
2.6.7 Newton's Second Law (Equations of Motion) .......................................................................................117
2.6.8 Motion of a Rigid Body .........................................................................................................................118
2.7 Principles of Work and Energy ............................................................................................................................119
2.7.1 Conservation of Energy Law .................................................................................................................119
2.7.2 Kinetic Energy .......................................................................................................................................119
2.7.3 Potential Energy .....................................................................................................................................119
2.7.4 Work .......................................................................................................................................................119
2.7.5 Power and Efficiency .............................................................................................................................120
2.7.6 Linear Momentum .................................................................................................................................120
2.7.7 Angular Momentum ...............................................................................................................................120
2.7.8 Coefficient of Restitution .......................................................................................................................120
2.8 Kinematics of Mechanisms .................................................................................................................................121
2.8.1 Instantaneous Center of Rotation (Instant Centers) ...............................................................................121
2.9 Material Properties ..............................................................................................................................................122
2.9.1 Atomic Bonding .....................................................................................................................................122
2.9.2 Corrosion ...............................................................................................................................................123
2.9.3 Electrical Properties ...............................................................................................................................125
2.9.4 Mechanical Properties ............................................................................................................................126
2.9.5 Composite Materials ..............................................................................................................................127
2.9.6 Material Hardness ..................................................................................................................................128
2.9.7 Impact Test .............................................................................................................................................128
2.9.8 Relationship Between Hardness and Tensile Strength ...........................................................................129
2.9.9 Binary Phase Diagrams ..........................................................................................................................133
2.9.10 Thermal and Mechanical Processing .....................................................................................................134
2.10 Strength of Materials ...........................................................................................................................................134
2.10.1 Strain ......................................................................................................................................................134
2.10.2 Percent Elongation .................................................................................................................................135
Contents
2.10.3 Percent Reduction in Area (RA) ............................................................................................................135
2.10.4 Shear Stress-Strain .................................................................................................................................135
2.10.5 Uniaxial Loading and Deformation .......................................................................................................135
2.10.6 Thermal Deformations ...........................................................................................................................136
2.10.7 Principal Stresses ...................................................................................................................................136
2.10.8 Mohr's Circle – Stress, 2D .....................................................................................................................137
2.10.9 Hooke's Law ..........................................................................................................................................137
2.10.10 Strain Energy .........................................................................................................................................138
2.10.11 Stress-Strain Curve for Mild Steel .........................................................................................................139
2.11 Stress Analysis .....................................................................................................................................................139
2.11.1 Torsion ...................................................................................................................................................139
2.11.2 Torsional Strain ......................................................................................................................................139
2.11.3 Interference-Fit Stresses ........................................................................................................................140
2.11.4 Rotating Rings .......................................................................................................................................141
2.11.5 Hollow, Thin-Walled Shafts ...................................................................................................................141
2.11.6 Beams .....................................................................................................................................................142
2.12 Intermediate- and Long-Length-Column Determination ....................................................................................149
2.12.1 Intermediate Columns ............................................................................................................................149
2.12.2 Long Columns ........................................................................................................................................150
2.13 Failure Theories ...................................................................................................................................................150
2.13.1 Brittle Materials .....................................................................................................................................150
2.13.2 Ductile Materials ....................................................................................................................................151
2.14 Variable Loading Failure Theories ......................................................................................................................151
2.15 Vibration/Dynamic Analysis................................................................................................................................155
2.15.1 Free Vibration ........................................................................................................................................155
2.15.2 Torsional Vibration ................................................................................................................................156
2.15.3 Vibration Transmissibility, Base Motion ...............................................................................................157
2.15.4 Vibration – Rotating Unbalance ............................................................................................................158
2.15.5 Vibration Absorber .................................................................................................................................158
2.15.6 Dunkerley's Equation .............................................................................................................................159
2.15.7 Viscous Damping ...................................................................................................................................159
2.15.8 Equivalent Masses, Springs, and Dampers ............................................................................................160
2.15.9 Pendulum Motion ..................................................................................................................................162
Contents
2.16 Mechanical Components .....................................................................................................................................162
2.16.1 Springs ...................................................................................................................................................162
2.16.2 Bearings .................................................................................................................................................164
2.16.3 Power Screws .........................................................................................................................................166
2.16.4 Power Transmission ...............................................................................................................................167
2.16.5 Gears ......................................................................................................................................................168
2.16.6 Belts, Pulleys, and Chain Drives ...........................................................................................................177
2.16.7 Clutches and Brakes ...............................................................................................................................185
2.17 Welding ................................................................................................................................................................186
2.18 Joints and Fasteners ............................................................................................................................................190
2.18.1 Bolts .......................................................................................................................................................190
2.18.2 Tension Connections—The External Load ............................................................................................193
2.18.3 Adhesives and Bonding .........................................................................................................................202
2.19 Pressure Vessels ...................................................................................................................................................204
2.19.1 Cylindrical Pressure Vessel ....................................................................................................................204
2.19.2 Definitions ..............................................................................................................................................205
3 HYDRAULICS, FLUIDS, AND PIPE FLOW ..........................................................................................................206
3.1 Definitions ...........................................................................................................................................................206
3.1.1 Density, Specific Weight, and Specific Gravity .....................................................................................206
3.1.2 Stress, Pressure, and Viscosity ...............................................................................................................207
3.2 Characteristics of a Static Liquid.........................................................................................................................207
3.2.1 Pressure Field in a Static Liquid ............................................................................................................207
3.2.2 Forces on Submerged Surfaces and the Center of Pressure ...................................................................208
3.2.3 Archimedes' Principle and Buoyancy ....................................................................................................208
3.3 Principles of One-Dimensional Fluid Flow .........................................................................................................208
3.3.1 The Continuity Equation .......................................................................................................................208
3.3.2 The Bernoulli Equation ..........................................................................................................................209
3.4 Fluid Flow............................................................................................................................................................209
3.4.1 Reynolds Number ..................................................................................................................................209
3.4.2 Head Loss Due to Flow .........................................................................................................................210
3.4.3 Water Hammer .......................................................................................................................................227
3.5 Pipe Bends, Enlargements, and Contractions ......................................................................................................228
3.5.1 The Impulse-Momentum Principle ........................................................................................................228
3.5.2 Jet Propulsion .........................................................................................................................................229
Contents
3.5.3 Deflectors and Blades ............................................................................................................................229
3.6 Compressible Flow ..............................................................................................................................................230
3.6.1 Mach Number ........................................................................................................................................230
3.6.2 Isentropic Flow Relationships ...............................................................................................................231
3.6.3 Normal Shock Relationships .................................................................................................................232
3.6.4 Adiabatic Frictional Flow in Constant Area Ducts ................................................................................232
3.7 Fluid Flow Machinery .........................................................................................................................................233
3.7.1 Hydraulic Pneumatic Cylinder Forces ...................................................................................................233
3.7.2 Force and Pressure to Extend Cylinder ..................................................................................................234
3.7.3 Force and Pressure to Retract Cylinder .................................................................................................234
3.7.4 Centrifugal Pump Characteristics ..........................................................................................................234
3.7.5 Pump Power Equation ...........................................................................................................................237
3.7.6 Pump Affinity Laws ...............................................................................................................................238
3.8 Fluid Flow Measurement .....................................................................................................................................238
3.8.1 The Pitot Tube ........................................................................................................................................238
3.8.2 Pitot-Static Tubes ...................................................................................................................................239
3.8.3 Manometers ...........................................................................................................................................239
3.8.4 Venturi Meters ........................................................................................................................................240
3.8.5 Orifices ...................................................................................................................................................240
3.8.6 Submerged Orifice Operating under Steady-flow Conditions: ..............................................................241
3.8.7 Orifice Discharging Freely into Atmosphere .........................................................................................242
3.8.8 Open Channel Flow ...............................................................................................................................242
3.9 Properties of Glycol/Water Solutions ..................................................................................................................243
3.9.1 Pressure Drop for Glycol Solutions .......................................................................................................243
3.9.2 Properties of Aqueous Solutions of Ethylene Glycol ............................................................................244
3.9.3 Properties of Aqueous Solutions of Propylene Glycol ..........................................................................248
4 THERMODYNAMICS ...............................................................................................................................................252
4.1 Properties of Single-Component Systems ...........................................................................................................252
4.1.1 Definitions ..............................................................................................................................................252
4.1.2 Properties for Two-Phase (Vapor-Liquid) Systems ...............................................................................253
4.2 PVT Behavior for Gases ......................................................................................................................................254
4.2.1 Ideal Gas ................................................................................................................................................254
4.2.2 Ideal Gas Mixtures .................................................................................................................................255
4.2.3 Compressibility Factor and Charts ........................................................................................................256
4.2.4 Equations of State (EOS) .......................................................................................................................258
Contents
4.3 First Law of Thermodynamics ............................................................................................................................259
4.3.1 Closed Thermodynamic Systems ...........................................................................................................259
4.3.2 Open Thermodynamic Systems .............................................................................................................260
4.3.3 Steady-Flow Systems .............................................................................................................................261
4.4 Second Law of Thermodynamics ........................................................................................................................262
4.4.1 Kelvin-Planck Statement of the Second Law ........................................................................................262
4.4.2 Clausius' Statement of the Second Law .................................................................................................262
4.4.3 Entropy ...................................................................................................................................................262
4.4.4 Vapor-Liquid Equilibrium (VLE) ..........................................................................................................263
4.4.5 Phase Relations ......................................................................................................................................264
4.5 Thermodynamic Cycles .......................................................................................................................................264
4.5.1 Basic Cycles ...........................................................................................................................................264
4.5.2 Common Thermodynamic Cycles .........................................................................................................265
4.5.3 Compressors ...........................................................................................................................................268
4.5.4 Turbines .................................................................................................................................................269
5 HEAT TRANSFER ......................................................................................................................................................276
5.1 Conduction...........................................................................................................................................................276
5.1.1 Fourier's Law of Conduction .................................................................................................................276
5.1.2 Thermal Diffusivity ................................................................................................................................276
5.1.3 Conduction Through a Uniform Material ..............................................................................................277
5.1.4 Conduction Through a Cylindrical Wall (Heat Loss Through a Pipe) ...................................................277
5.2 Thermal Resistance (R) .......................................................................................................................................277
5.2.1 Composite Plane Wall ............................................................................................................................278
5.2.2 Transient Conduction Using the Lumped Capacitance Model ..............................................................279
5.2.3 Constant Fluid Temperature ...................................................................................................................279
5.2.4 Fins.........................................................................................................................................................280
5.3 Convection ...........................................................................................................................................................281
5.3.1 Terms .....................................................................................................................................................281
5.3.2 Newton's Law of Cooling ......................................................................................................................281
5.3.3 Grashof Number ....................................................................................................................................281
5.3.4 External Flow .........................................................................................................................................281
5.3.5 External Flow: Cylinder of Diameter D in Cross Flow .........................................................................282
5.3.6 External Flow Over a Sphere of Diameter D .........................................................................................282
5.3.7 Internal Flow ..........................................................................................................................................282
5.3.8 Laminar Flow in Circular Tubes ............................................................................................................282