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RULES OF THUM
FOR MECHANICAL liEH
A manual of quick, accurate solutions
to everyday mechanical engineering problems
J. Edward Pope, Editor
RULES OF THUMEI
FOR
MECHANICAL
ENGINEERS
Gulf Publishing Company
Houston, Texas
RULES OF THUMB FOR
MECHANICAL ENGINEERS
Copyright 8 1997 by Gulf Publishing Company,
Houston, Texas. All rights reserved. Printed in the
United States of America. This book, or parts thereof,
may not be reproduced in any form without permission
of the publisher.
109876543
Gulf Publishing Company
Book Division
P.O. Box 2608 0 Houston, Texas 77252-2608
Library of Congress Cataloging-in-Publication Data
Rules of thumb for mechanical engineers : a manual of
quick, accurate solutions to everyday mechanical
engineering problems / J. Edward Pope, editor ; in
collaboration with Andrew Brewington . . . [et al.].
Includes bibliographical references and index.
ISBN 0-88415-790-3 (acid-free paper)
1. Mechanical engineering-Handbooks, manuals,
etc. I. Pope, J. Edward, 1956- . 11. Brewington,
Andrew.
TJ151.R84 1996
p. cm.
62 14-20 96-35973
CIP
Printed on acid-free paper (=I.
iv
1: Fluids . 1
Fluid Properties ........................................................ Density. Specific Volume. Specific Weight.
Specific Gravity. and Pressure .................................... Surface Tension ..............................................................
Gas and Liquid Viscosity ................................................ Bulk Modulus ................................................................. Compressibility ............................................................... Units and Dimensions ..................................................... Fluid Statics .............................................................. Manometers and Pressure Measurements ....................... Hydraulic Pressure on Surfaces ...................................... Buoyancy ........................................................................ Basic Equations ........................................................ Continuity Eq~tion ........................................................ Euler’s Equation ............................................................. Bernoulli’s Equation .......................................................
Momentum Equation ...................................................... Moment-of-Momentum Equation ................................... Advanced Fluid Flow Concepts .............................. Dimensional Analysis and Similitude ............................ Nondimensional Parameters ........................................... Equivalent Diameter and Hydraulic Radius ................... Pipe Flow ...................................................................
Vapor Pressure ................................................................
Energy Equation .............................................................
2
2
2
2
3
3
3
3
4
4
4
5
5
5
5
6
6
6
6
7
7
7
8
8
Friction Factor and Darcy Equation ............................... Losses in Pipe Fittings and Valves .................................. Pipes in Series ................................................................. pipes in Parallel .............................................................. Open-Channel Flow ................................................. Frictionless Open-Channel Flow .................................... Laminar Open-Channel Flow ......................................... Turbulent Open-Channel Flow ....................................... Hydraulic Jump ............................................................... Fluid Measurements ................................................. Pressure and Velocity Measurements ............................. Flow Rate Measurement ................................................. Hot-wire and Thin-Film Anemometry ........................... Open-Channel Flow Measurements ............................... Viscosity Measurements .................................................
Unsteady Flow, Surge, and Water Hammer .................... Boundary Layer Concepts ..............................................
Oceanographic Flows .....................................................
Other Topi CS ..............................................................
Lift and Drag ...................................................................
9
10
10
10
11
11
12
12
12
13
13
14
14
15
15
16
16
16
16
17
Introduction......... ..................................................... 19
Conduction ................................................................ 19
Single Wall Conduction .................................................. 19
Composite Wall Conduction ........................................... 21
V
The Combined Heat Transfer Coefficient ....................... 22
Critical Radius of Insulation ........................................... 22
Convection ................................................................. 23
Dimensionless Numbers ................................................. 23
Correlations ..................................................................... 24
Typical Convection Coefficient Values .......................... 26
Radiation ................................................................... 26
Emissivity ....................................................................... 27
View Factors ................................................................... 27
Radiation Shields ............................................................ 29
Finite Element Analysis ........................................... 29
Boundary Conditions ...................................................... 29
2D Analysis .................................................................... 30
Evaluating Results .......................................................... 3 1
Shell-and-Tube Exchangers ............................................ 36
Shell Configurations ....................................................... 40
Miscellaneous Data ......................................................... 42
Heat Transfer ........................................................ 42
Flow Maps ...................................................................... 46
Transient Analysis .......................................................... 30
Heat Exchanger Classification ................................ 33
Types of Heat Exchangers .............................................. 33
Tube Arrangements and Baffles ..................................... 38
Flow Regimes and Pressure Drop in Two-Phase
Flow Regimes ................................................................. 42
Estimating Pressure Drop ............................................... 48
3: Thermodynamics. 51
Thermodynamic Essentials ...................................... Phases of a Pure Substance .............................................
Determining Properties ................................................... Types of Systems ............................................................ Types of Processes ..........................................................
Thermodynamic Properties .............................................
The Zeroth Law of Thermodynamics ............................. First Law of Thermodynamics ................................ Work ................................................................................ Heat ................................................................................. First Law of Thermodynamics for Closed Systems ....... First Law of Thermodynamics for Open Systems .......... Second Law of Thermodynamics ............................ Reversible Processes and Cycles ....................................
Useful Expressions ......................................................... Thermodynamic Temperature Scale ...............................
Thermodynamic Cycles ........................................... Basic Systems and Systems Integration ......................... Carnot Cycle ...................................................................
Reversed Rankine Cycle: A Vapor Refrigeration Cycle . Brayton Cycle: A Gas Turbine Cycle ............................. Otto Cycle: A Power Cycle ............................................
Rankine Cycle: A Vapor Power Cycle ............................
52
52
53
55
56
56
57
58
58
58
58
58
59
59
59
59
60
60
60
61
61
62
63
Diesel Cycle: Another Power Cycle ............................... Gas Power Cycles with Regeneration ............................. 63
64
4: Mechanical Seals. 66
Basic Mechanical Seal Components ....................... Sealing Points ............................................................ Mechanical Seal Classifications .............................. Basic Seal Designs ..................................................... Basic Seal Arrangements ......................................... Basic Design Principles ............................................ Materials of Construction ........................................ Desirable Design Features ....................................... Equipment Considerations ...................................... Calculating Seal Chamber Pressure .......................
Integral Pumping Features ...................................... Seal System Heat Balance ........................................
Seal Flush Plans ........................................................
Flow Rate Calculation .............................................. References .................................................................
5: Pumps and Compressors. 92
67
67
68
68
72
74
77
79
80
81
82
85
87
89
91
~~ ~
Pump Fundamentals and Design ............................ Pump and Head Terminology ......................................... 93
93
Pump Design Parameters and Formulas ......................... 93
Types of Pumps ............................................................... 94
Centrifugal Pumps .......................................................... 95
Net Positive Suction Head (NPSH) and Cavitation ........ 96
Pumping Hydrocarbons and Other Fluids ...................... 96
Recirculation ................................................................... 97
Pumping Power and Efficiency ...................................... 97
Specific Speed of Pumps ................................................ 97
Pump Similitude ............................................................. 98
Performance Curves ........................................................ 98
Series and Parallel Pumping ........................................... 99
Design Guidelines ........................................................... 100
Reciprocating Pumps ...................................................... 103
Compressors ............................................................. 110
Definitions ...................................................................... 110
Compressors ............................................................... 111
Compressors ............................................................... 114
Compression Horsepower Determination ....................... 117
Centrifugal Compressor Performance Calculations ....... 120
Estimate HP Required to Compress Natural Gas ........... 123
Estimate Engine Cooling Water Requirements .............. 124
Performance Calculations for Reciprocating
Estimating Suction and Discharge Volume Bottle
Sizes for Pulsation Control for Reciprocating
Generalized Compressibility Factor ............................... 119
vi
Estimate Fuel Requirements for Internal Combustion
Engines ....................................................................... 124
References ........... ............... " ........... ... .... .. .... 12A
6: Drivers. 125
Motors: Efficiency .................................................... 126
Motors: Starter Sizes ............................................... 127
Motors: Service Factor ............................................ 127
Motors: Useful Equations ........................................ 128
Motors: Relative Costs ............................................. 128
Motors: Overloading ................................................ 129
Steam Wbines: Steam Rate ................................... 129
Steam mrbines: Efficiency ...................................... 129
Gas Wbines: Fuel Rates ......................................... 130
Gas Engines: Fuel Rates .......................................... 132
Gas Expanders: Available Energy ............. 132
7: liearsJ33 .
Ratios and Nomenclature ........................................ 134
Spur and Helical Gear Design ................................. 134
Bevel Gear Design .................................................... 139
Cylindrical Worm Gear Design .............................. 141
Materials ................................................................... 142
Buying Gears and Gear Drives ............................... 144
References ................................................................. 144
sw of Gear Qpes .......................................... 143
8: Bearings. 145
Qpes of Bearings ..................................................... 146
Ball Bearings .................................................................. 146
Roller Bearings ............................................................... 147
Standardization ............................................................... 149
Materials ......................................................................... 151
ABMA Definitions ......................................................... 152
Fatigue Life ..................................................................... 153
Life Adjustment Factors ................................................. 154
Load and Speed Analysis ......................................... 156
Equivalent Loads ............................................................ 156
Contact Stresses .............................................................. 157
Preloading ....................................................................... 157
Special Loads .................................................................. 158
Effects of Speed .............................................................. 159
Lubrication ............................................................... 160
General ............................................................................ 160
Oils .................................................................................. 161
Greases ............................................................................ 161
Rating and Life ......................................................... 152
Lubricant Selection ......................................................... 162
Lubricating Methods ....................................................... 163
Relubncahon ................................................................... 164
Cleaning. Preservation. and Storage ............................... 165
Mounting ................................................................... 166
Shafting ........................................................................... 166
Housings ......................................................................... 169
Bearing Clearance ........................................................... 172
Seals ................................................................................ 174
Sleeve Bearings ......................................................... 175
References ................................................................. 177
..
9 Pipina and Pressure Vessels. 178
Process Plant Pipe .................................................... 179
Definitions and Sizing .................................................... 179
Pipe Specifications .......................................................... 187
Storing Pipe .................................................................... 188
Calculations to Use ......................................................... 189
Transportation Pipe Lines ....................................... 190
Steel Pipe Design ............................................................ 190
Gas Pipe Lines ............................................................ 190
Liquid pipe Lines ........................................................ 192
Pipe Line Condition Monitoring ............................. 195
Pig-based Monitoring Systems ....................................... 195
Coupons .......................................................................... 196
Manual Investigation ...................................................... 196
Cathodic Protection ........................................................ 197
Pressure Vessels ........................................................ 206
Stress Analysis ................................................................ 206
Failures in Pressure Vessels ............................................ 207
Loadings ......................................................................... 208
stress ............................................................................... 209
procedure 1 : General Vessel Formulas ........................... 213
Procedure 2: Stresses in Heads Due to Internal
Pressure ....................................................................... 215
Joint Efficiencies (ASME Code) .................................... 217
Properties of Heads ......................................................... 218
Volumes and Surface Areas of Vessel Sections .............. 220
Maximum Length of Unstiffened Shells ........................ 221
Useful Formulas for Vessels ........................................... 222
Material Selection Guide ................................................ 224
References ....................................................................... 225
10: Tribology. 226
Introduction .............................................................. 227
Contact Mechanics ................................................... 227
Two-dimensional (Line) Hertz Contact of Cylinders ..... 227
Three-dimensional (Point) Hertz Contact ....................... 229
Effect of Friction on Contact Stress ................................ 232
vii
Yield and Shakedown Criteria for Contacts ................... 232
Topography of Engineering Surfaces ........... 233
Contact of Rough Surfaces ............................................. 234
Life Factors ..................................................................... 234
Friction ...................................................................... 235
Wear ........................................................................... 235
Lubrication ............................................................... 236
References ................................................................. 237
Definition of Surface Roughness .................................... 233
11: Vibration. 238
Mechanical Testing ................................................... 284
Tensile Testing ................................................................ 284
Fatigue Testing ................................................................ 285
Hardness Testing ............................................................. 286
Creep and Stress Rupture Testing ................................... 287
Forming ..................................................................... 288
Casting ....................................................................... 289
Case Studies .............................................................. 290
Failure Analysis .............................................................. 290
Corrosion ........................................................................ 291
References ................................................................. 292
Vibration Definitions. Terminology. and
Solving the One Degree of Freedom System .......... 243
Solving Multiple Degree of Freedom Systems ....... 245
Vibration Measurements and Instrumentation ..... 246
Table A: Spring Stiffness ......................................... 250
Table B: Natural Frequencies of Simple Systems .. 251
Table C: Longitudinal and Torsional Vibration of
Uniform Beams ..................................................... 252
Table D: Bending (Transverse) Vibration of
Uniform Beams ..................................................... 253
Table E: Natural Frequencies of Multiple DOF
Systems .................................................................. 254
Table F: Planetary Gear Mesh Frequencies .......... 255
Table G: Rolling Element Bearing Frequencies
and Bearing Defect Frequencies ............. 256
Table H: General Vibration Diagnostic
Frequencies ........................................................... 257
References ................................................................. 258
Symbols ................................................................. 239
12: Materials. 259
Classes of Maferials .................................................. 260
Defrrutons ................................................................. 260
Metals ........................................................................ 262
Steels ............................................................................... 262
Tool Steels ...................................................................... 264
Cast Iron .......................................................................... 265
Stainless Steels ................................................................ 266
Superalloys ..................................................................... 268
Aluminum Alloys ........................................................... 269
Joining ............................................................................. 270
Coatings .......................................................................... 273
Corrosion ........................................................................ 276
Powder Metallurgy ......................................................... 279
PolJTme rs .................................................................... 281
cera^^................. ................................................... 284
..
13: Stress and Strain. 294 ~ ~~ ~~ ~~
Fundamentals of Stress and Strain ............. 295
Introduction ..................................................................... 295
Definitions4tress and Strain ....................................... 295
Equilibrium ..................................................................... 297
Compatibility .................................................................. 297
Saint-Venant’s Principle .................................................. 297
Superposition .................................................................. 298
Plane Stress/Plane Strain ................................................ 298
Thermal Stresses ............................................................. 298
Stress Concentrations ............................................... 299
Determination of Stress Concentration Factors .............. 300
Design Criteria for Structural Analysis ................. 305
General Guidelines for Effective Criteria ....................... 305
Strength Design Factors .................................................. 305
Beam Analysis ........................................................... 306
Limitations of General Beam Bending Equations .......... 307
Short Beams .................................................................... 307
Plastic Bending ............................................................... 307
Torsion ............................................................................ 308
Pressure Vessels ........................................................ 309
Thin-walled Cylinders .................................................... 309
Thick-walled Cylinders .................................................. 309
Press Fits Between Cylinders .................................. 310
Rotating Equipment ................................................. 310
Rotating Disks ................................................................ 310
Rotating Shafts ................................................................ 313
Flange Analysis ......................................................... 315
Flush Flanges .................................................................. 315
Undercut Flanges ............................................................ 316
Mechanical Fasteners ............................................... 316
Threaded Fasteners ......................................................... 317
Pins ................................................................................. 318
Rivets .............................................................................. 318
Welded and Brazed Joints ....................................... 319
Finite Element Analysis ........................................... 320
Creep Rupture .......................................................... 320
viii
Overview ......................................................................... 321
The Elements .................................................................. 321
Modeling Techniques ...................................................... 322
Advantages and Limitations of FEM .............................. 323
Centroids and Moments of Inertia for Common
Shapes .................................................................... 324
Beams: Shear. Moment, and &flection Formulas
for Common End Conditions .............................. 325
References ................................................................. 328
Strain Measurement ................................................. 362
The Electrical Resistance Strain Gauge .......................... 363
Electrical Resistance Strain Gauge Data Acquisition ..... 364
Liquid Level and Fluid Flow Measurement .......... 366
Liquid Level Measurement ............................................. 366
Fluid Flow Measurement ................................................ 368
References ................................................................. 370
16: Engineering Economics. 372
14: Fatigue. 329
Introduction .............................................................. 330
Design Approaches to Fatigue ................................. 331
Crack Initiation Analysis ......................................... 331
Residual Stresses ............................................................ 332
Notches ........................................................................... 332
Real World Loadings ...................................................... 335
Temperature Interpolation .............................................. 337
Material Scatter ............................................................... 338
Time Value of Money: Concepts and Formulas .... 373
Simple Interest vs . Compound Interest ........................... 373
Nominal Interest Rate vs . Effective Annual
Stages of Fatigue ....................................................... 330
Estimating Fatigue Properties ......................................... 338
Crack Propagation Analysis .................................... 338
Crack Propagation Calculations ..................................... 342
K-The Stress Intensity Factor ...................................... 339
Creep Crack Growth ....................................................... 344
Inspection Techniques .............................................. 345
Fluorescent Penetrant Inspection (PI) .......................... 345
Magnetic Particle Inspection (MPI) ................................ 345
Radiography .................................................................... 345
Ultrasonic Inspection ...................................................... 346
Eddy-current Inspection .................................................. 347
Evaluation of Failed Parts ............................................... 347
Nonmetallic Materials .............................................. 348
Fatigue T~~g .......................................................... 349
Liabrllty Issues .......................................................... 350
References ................................................................. 350
..
Inkrest Rate ................................................................ 374
in the Future ................................................................ 374
Future Value of a Single Investment ............................... 375
The Importance of Cash Flow Diagrams ........................ 375
Multiple or Irregular Cash Flows ............................... 375
Perpetuities ..................................................................... 376
Annuities, Loans, and Leases ......................................... 377
Growth Rates) ............................................................. 378
Cash Flow Problems ................................................... 379
Present Value of a Single Cash Flow To Be Received
Analyzing and Valuing InvestmenBRrojects with
Future Value of a Periodic Series of Investments ........... 377
Gradients (PayoutsPayments with Constant
Analyzing Complex Investments and
Decision and Evaluation Criteria for Investments
and Financial Projects .......................................... 380
Payback Method ............................................................. 380
Accounting Rate of Return (ROR) Method .................... 381
Internal Rate of Return (IRR) Method ............................ 382
Net Present Value (NPV) Method ................................... 383
Sensitivity Analysis ................................................... 384
Accounting Fundamentals ....................................... 389
References and Recommended Reading ................ 393
Decision 'he Analysis of Investments and
Financial Projects ................................................. 385
15: Instrumentation. 352 Appendix. 394
Introduction .............................................................. 353
Temperature Measurement ..................................... 354 Conversion Factors .................................................. 395
Fluid Temperature Measurement 354 SysternS of Basic Units 399
Surface Temperature Measurement ................................ 358 Decimal Multiples and Fractions of SI units ......... 399
Pressure Measurement ............................................. 359
Total Pressure Measurement 360
.................................... ..............................................
Common Temperature Sensors ....................................... 358
StaticKavity Pressure Measurement .............................. 361
Temperature Conversion Equations ............ 399
Index, 400 ...........................................
ix
Bhabani P . Mohanty. Ph.D., Development Engineer. Allison Engine Company
Fluid Prope ............................................................ Density. Specific Volume. Specific Weight.
Specific Gravity. and Pressure ...................................... Surface Tension ................................................................ Vapor Pressure .................................................................. Gas and Liquid Viscosity ................................................. Bulk Modulus ................................................................... Compressibility ................................................................ Units and Dimensions ......................................................
Fluid StSlti. ................................................................ Manometers and Pressure Measurements ........................ Hydraulic Pressure on Surfaces ........................................ Buoyancy ..........................................................................
Basic Equations .......................................................... Continuity Equation ......................................................... Euler’s Equation ...............................................................
Energy Equation ............................................................... Momentum Equation ........................................................ Moment-of-Momentum Equation ....................................
Bernoulli’s Equation .........................................................
Advanced Fluid Flow Concepts ................................ Dimensional Analysis and Similitude ..............................
2
2
2
2
3
3
3
3
4
4
4
5
5
5
5
6
6
6
6
7
7
Nondimensional Parameters ............................................. 7
Equivalent Diameter and Hydraulic Radius ..................... 8
9
Pipe Flow .................................................................... 8
Friction Factor and Darcy Equation ................................. Losses in Pipe Fittings and Valves ................................... 10
Pipes in Series .................................................................. 10
Open-Channel Flow ................................................... 11
Frictionless Open-Channel Flow ...................................... 11
Laminar Open-Channel Flow ........................................... 12
Turbulent Open-Channel Flow ......................................... 12
Hydraulic Jump ................................................................ 12
Fluid Measurements .................................................. 13
Pressure and Velocity Measurements ............................... 13
Flow Rate Measurement ................................................... 14
Hot-wire and Thin-Film Anemometry ............................ 14
Open-Channel Flow Measurements ................................. 15
Viscosity Measurements ................................................... 15
Other Topi ................................................................ 16
Unsteady Flow. Surge. and Water Hammer ..................... 16
Boundary Layer Concepts ................................................ 16
Lift and Drag .................................................................... 16
Oceanographic Flows ....................................................... 17
Pipes in Parallel ................................................................ 10
1
2 Rules of Thumb for Mechanical Engineers
FLUID PROPERTIES
Afluid is defined as a “substance that deforms continuously when subjected to a shear stress” and is divided into
two categories: ideal and real. A fluid that has zero viscosity, is incompressible, and has uniform velocity distribution is called an idealfluid. Realfluids are called either
Newtonian or non-Newtonian. A Newtonian fluid has a linear relationship between the applied shear stress and the
resulting rate of deformation; but in a non-Newtonian
fluid, the relationship is nonlinear. Gases and thin liquids
are Newtonian, whereas thick, long-chained hydrocarbons are non-Newtonian.
Density, Specific Volume, Specific Weight, Specific Gravity, and Pressure
The density p is defined as mass per unit volume. In inconsistent systems it is defined as lbdcft, and in consistent systems it is defined as slugs/cft. The density of a gas
can be found from the ideul gas law:
The specific gravity s of a liquid is the ratio of its
weight to the weight of an equal volume of water at standard temperature and pressure. The s of petroleum
products can be found from hydrometer readings using
MI (American Petroleum Institute) scale.
p = p/RT (1)
where p is the absolute pressure, R is the gas constant, and The fluid pressure at a point is the ratio of normal
T is the absolute temperature.
The density of a liquid is usually given as follows:
force to area as the area approaches a small value. Its
unit is usually lbs/sq. in. (psi). It is also often measured
as the equivalent height h of a fluid column, through
the relation:
The specific volume v, is the reciprocal of density:
The specific weight y is the weight per unit volume:
v, = l/p
Y= Pg
P=Yh
Surface Tension
Vapor Pressure
Molecules that escape a liquid surface cause the evaporation process. The pressure exerted at the surface by these
free molecules is called the vaporpressure. Because this is
caused by the molecular activity which is a function of the
temperature, the vapor pressure of a liquid also is a function
of the temperature and increases with it. Boiling occurs
when the pressure above the liquid surface equals (or is less
than) the vapor pressure of the liquid. This phenomenon,
which may sometimes occur in a fluid system network,
causing the fluid to locally vaporize, is called cavitation.
Fluids 3
Gas and liquid Viscosity
Viscosi~ is the property of a fluid that measures its re
sistance to flow. Cohesion is the main cause of this resistance. Because cohesion drops with temperature, so does
viscosity. The coefficient of viscosity is the proportionality constant in Newton’s law of viscosity that states that the
shear stress z in the fluid is directly proportional to the velocity gradient, as represented below:
z=pdY
The p above is often called the absolute or dynamic
viscosity. There is another form of the viscosity coefficient
called the kinematic viscosity v, that is, the ratio of viscosity
to mass density:
V = cl/p
Remember that in U.S. customary units, unit of mass dendu (2) sity p is slugs per cubic foot.
Bulk Modulus
A liquid‘s compressibility is measured in terms of its bulk
modulus of elasticity. Compressibility is the percentage
change in unit volume per unit change in pressure:
The bulk modulus of elasticity K is its reciprocal:
K= 1/C
6VlV C=- K is expressed in units of pressure.
sp
Compressibility
Compressibility of liquids is defined above. However, for
a gas, the application of pressure can have a much greater
effect on the gas volume. The general relationship is governed by the pe$ect gas law:
pv, = RT
Where P is the d~olute Pressure, V, is the Specific Volume,
R is the gas constant, and T is the absolute temperature.
Units and Dimensions
One must always use a consistent set of units. Primary
units are mass, length, time, and temperature. A unit system
is called consistent when unit force causes a unit mass to
achieve unit acceleration. In the U.S. system, this system is
represented by the (pound) force, the (slug) mass, the (foot)
length, and the (second) time. The slug mass is defined as
the mass that accelerates to one ft/& when subjected to one
pound force (lbf). Newton’s second law, F = ma, establishes this consistency between force and mass units. If the
mass is ever referred to as being in lbm (inconsistent system), one must first convert it to slugs by dividing it by
32.174 before using it in any consistent equation.
Because of the confusion between weight (lbf) and mass
(lbm) units in the U.S. inconsistent system, there is also a
similar confusion between density and specific weight
units. It is, therefore, always better to resort to a consistent
system for engineering calculations.
4 Rules of Thumb for Mechanical Engineers
FLUID STATICS
Fluid statics is the branch of fluid mechanics that deals
with cases in which there is no relative motion between fluid
elements. In other words, the fluid may either be in rest or
at constant velocity, but certainly not accelerating. Since
there is no relative motion between fluid layers, there are
no shear stresses in the fluid under static equilibrium.
Hence, all bodies in fluid statics have only normal forces
on their surfaces.
Manometers and Pressure Measurements
Pressure is the same in all directions at a point in a static fluid. However, if the fluid is in motion, pressure is defined as the average of three mutually perpendicular normal compressive stresses at a point:
P = (Px + Py + PJ3
Pressure is measured either from the zero absolute pressure or from standard atmospheric pressure. If the reference
point is absolute pressure. the pressure is called the absohte
pressure, whereas if the reference point is standard atmospheric (14.7 psi), it is called the gage pressure. A barometer is used to get the absolute pressure. One can make a
simple barometer by filling a tube with mercury and inverting it into an open container filled with mercury. The
mercury column in the tube will now be supported only by
the atmospheric pressure applied to the exposed mercury
surface in the container. The equilibrium equation may be
written as:
pa = 0.491(144)h
where h is the height of mercury column in inches, and 0.491
is the density of mercury in pounds per cubic inch. In the
above expression, we neglected the vapor pressure for
mercury. But if we use any other fluid instead of mercury,
the vapor pressure may be signifcant. The equilibrium
equation may then be:
Pa = [(O-O361)(s)(h) + pvl(144)
where 0.0361 is the water density in pounds per cubic
inch, and s is the specific gravity of the fluid. The consistent equation for variation of pressure is
P=Yh
where p is in lb/ft2, y is the specific weight of the fluid in
lb/ft3, and h is infeet. The above equation is the same as p
= ywsh, where yw is the specific weight of water (62.4
lb/ft3) and s is the specific gravity of the fluid.
Manometers are devices used to determine differential
pressure. A simple U-tube manometer (with fluid of specific weight y) connected to two pressure points will have
a differential column of height h. The differential pressure
will then be Ap = (p2 - pl) = 'yh. Corrections must be
made if high-density fluids are present above the manometer fluid.
Hydraulic Pressure on Surfaces
(3)
For a horizontal area subjected to static fluid pressure,
the resultant force passes through the centroid of the area.
1
2 pavg =-(h, +h,)sine
If the Plane is hAkd at an angle 0, then the local Pressure
Will VW linearly with the depth- The average Pressure
occurs at the average depth:
However, the center of pressure will not be at average depth
but at the centroid of the triangular or trapezoidal pressure
distribution, which is also known as the pressure prism.