Fluid Mechanics: Fundamentals and Applications 4th Ed in SI 4th Edition Yunus A. Çengel
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Fluid Mechanics: Fundamentals and Applications 4th Ed in SI 4th Edition Yunus A. Çengel
Fluid Mechanics: Fundamentals and Applications 4th Ed in SI 4th Edition Yunus A. Çengel
Fluid Mechanics: Fundamentals and Applications 4th Ed in SI 4th Edition Yunus A. Çengel
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a
FLUID. MECHANICS
FLUID. MECHANICS
FLUID MECHANICS
FUNDAMENTALS AND APPLICATIONS
FOURTH EDITION IN SI UNITS
FUNDAMENTALS AND APPLICATIONS
FOURTH EDITION IN SI UNITS
ABOUT THE AUTHORS
Yunus A. Gengel is Professor Emeriws of Mechanical Engineering atthe
University of Neva, Reno He recived his B.S in mechanical engineering from
Istanbul Technical University and his M.S and PhD. in mechanical engineering
from North Carolina State Universi. His reach ares are renewable ents)
‘destination exergy analysis hea an fr enhancement radiation eat ans, and
{energy conservation. He served asthe director ofthe Inusual Asessment Center
(IAG) atthe University of Nevada, Reno, from 1996 to 2000. He ha ld teams
‘of engineering students to numerous manufacturing facies in Northern Nevada
“nd Califia to do industrial assessments and has prepared cneray conservation,
‘ste minimization, and productivity enhancement repart rthem.
Dr Cengelisthe coator ofthe widely adopted textbook Thermodhramis; An Eng
neering Approach Stein (2015) published McGrail cn. He slo
Ah coa ofthe textbook Het and Mass Transfer: Fundamentals & Applications
Sih Edition (2015) and the coutshor of th texbook Fundamental of Thermal lad
Sciences, Shion 2017, bh published by MeGraw- Hil Education, Some of his
textooks have bee translate to Chinese, Japanese, Korean, Spanish, Tsk, ala,
and Grek,
Dr. Cenge isthe recipient of several outstanding teacher award, and he has
received the ASEE Merlam Wiley Distinguished Author Award fr excellence in
“authors in 1992 and again in 2000.
Dr. Gengel ia registered Professional Engineer in the State of Nevada, and is
member a the American Society of Mechanical Engineers (ASME) andthe Ame
an Society for Engineering Education (ASE)
John M. Cimbala is Professor of Mechanical Engineering at The Pennsyl
‘ania State Universi, University Park He received his B.S. in Aerospace Eng
Peering from Penn Slate and his MLS, in Aeronautics from the Califor Insitute
‘of Technology (CalTech). He received his PAD. in Aeronautics from CalTech in
1984 under he supervision of Profesor Anatol Rosiko to whom he will be forever
gratful. His esearch areas include experimental and computational Fluid mechan
des and heat transfer. turbulence, turbulence modeling, tubomachinery indoor sit
‘quality, and ar pollution control, Professor Cimbala completed sabbatical leaves
at NASA Langley Research Center (1993-04), where he advanced his knowledge
of computational id dynamics (CFD), and at Weir American Hydo (2010-11),
where he performed CFD analyses to asis in the design of hydroturbines.
Dr. Cimbala isthe coauthor of three other textbooks: Indoor Air Quality Engi
neering: Environmental Health and Control of Indoor Pollutants (2003). pub
lished by Marcel-Dekker, Ine: Essentials of Fluid Mechanics: Fundamentals and
Applications (2008); and Fundamentals of Thermal-Fluid Sciences, th edition
(2017, both published by McGraw-Hill Education. He has ls contibuted1 pans
‘of other books, and isthe author or coauthor of dozens of journal and conference
Papers. He has also recently ventured ino writing novels, More information can be
Found at www mc pau cducimbala
Professor Cimbal is the recipient of several oustanding teaching awards and
views his book writing as an extension of his love of teaching, He i member of
the American Society of Mechanical Engineers (ASME), the American Society for
Engineering Education (ASE), and the American Physical Society (APS).
Yunus A. Gengel is Professor Emeriws of Mechanical Engineering atthe
University of Neva, Reno He recived his B.S in mechanical engineering from
Istanbul Technical University and his M.S and PhD. in mechanical engineering
from North Carolina State Universi. His reach ares are renewable ents)
‘destination exergy analysis hea an fr enhancement radiation eat ans, and
{energy conservation. He served asthe director ofthe Inusual Asessment Center
(IAG) atthe University of Nevada, Reno, from 1996 to 2000. He ha ld teams
‘of engineering students to numerous manufacturing facies in Northern Nevada
“nd Califia to do industrial assessments and has prepared cneray conservation,
‘ste minimization, and productivity enhancement repart rthem.
Dr Cengelisthe coator ofthe widely adopted textbook Thermodhramis; An Eng
neering Approach Stein (2015) published McGrail cn. He slo
Ah coa ofthe textbook Het and Mass Transfer: Fundamentals & Applications
Sih Edition (2015) and the coutshor of th texbook Fundamental of Thermal lad
Sciences, Shion 2017, bh published by MeGraw- Hil Education, Some of his
textooks have bee translate to Chinese, Japanese, Korean, Spanish, Tsk, ala,
and Grek,
Dr. Cenge isthe recipient of several outstanding teacher award, and he has
received the ASEE Merlam Wiley Distinguished Author Award fr excellence in
“authors in 1992 and again in 2000.
Dr. Gengel ia registered Professional Engineer in the State of Nevada, and is
member a the American Society of Mechanical Engineers (ASME) andthe Ame
an Society for Engineering Education (ASE)
John M. Cimbala is Professor of Mechanical Engineering at The Pennsyl
‘ania State Universi, University Park He received his B.S. in Aerospace Eng
Peering from Penn Slate and his MLS, in Aeronautics from the Califor Insitute
‘of Technology (CalTech). He received his PAD. in Aeronautics from CalTech in
1984 under he supervision of Profesor Anatol Rosiko to whom he will be forever
gratful. His esearch areas include experimental and computational Fluid mechan
des and heat transfer. turbulence, turbulence modeling, tubomachinery indoor sit
‘quality, and ar pollution control, Professor Cimbala completed sabbatical leaves
at NASA Langley Research Center (1993-04), where he advanced his knowledge
of computational id dynamics (CFD), and at Weir American Hydo (2010-11),
where he performed CFD analyses to asis in the design of hydroturbines.
Dr. Cimbala isthe coauthor of three other textbooks: Indoor Air Quality Engi
neering: Environmental Health and Control of Indoor Pollutants (2003). pub
lished by Marcel-Dekker, Ine: Essentials of Fluid Mechanics: Fundamentals and
Applications (2008); and Fundamentals of Thermal-Fluid Sciences, th edition
(2017, both published by McGraw-Hill Education. He has ls contibuted1 pans
‘of other books, and isthe author or coauthor of dozens of journal and conference
Papers. He has also recently ventured ino writing novels, More information can be
Found at www mc pau cducimbala
Professor Cimbal is the recipient of several oustanding teaching awards and
views his book writing as an extension of his love of teaching, He i member of
the American Society of Mechanical Engineers (ASME), the American Society for
Engineering Education (ASE), and the American Physical Society (APS).
FLUID MECHANICS
FUNDAMENTALS AND APPLICATIONS
FOURTH EDITION IN SI UNITS
Adopted by
MEHMET KANOGLU
University of Gaziantep
YUNUS A.
GENGEL
JOHN M.
CIMBALA
FUNDAMENTALS AND APPLICATIONS
FOURTH EDITION IN SI UNITS
Adopted by
MEHMET KANOGLU
University of Gaziantep
YUNUS A.
GENGEL
JOHN M.
CIMBALA
me
Grau
E
Core 02020 Metin Edson. A gs reo. Pris diem © 201, 2010 and 206. No par of hs pain may
terca hu in an o yay mean. oe na abs eval tm, vna Di wen con he
‘usar cing bt tl nyse oh esi me D or dna ing
ti oc cam ep nh yo wich its by Mew Hl
Cover Image pena
Wen ora hte, SEN 978981491599 MID 91-8594
Grau
E
Core 02020 Metin Edson. A gs reo. Pris diem © 201, 2010 and 206. No par of hs pain may
terca hu in an o yay mean. oe na abs eval tm, vna Di wen con he
‘usar cing bt tl nyse oh esi me D or dna ing
ti oc cam ep nh yo wich its by Mew Hl
Cover Image pena
Wen ora hte, SEN 978981491599 MID 91-8594
Dedication
To all students, with the hope of stimulating
he desire ta explore aur marsctous world, of
which fluid mechanics is a small but fascinating
part. And te cur wives Zehra and Suzy for
cie unending support.
To all students, with the hope of stimulating
he desire ta explore aur marsctous world, of
which fluid mechanics is a small but fascinating
part. And te cur wives Zehra and Suzy for
cie unending support.
THIS PAGE HAS BEEN LEFT INTENTIONALLY BLANK.
BRIEF CONTENTS
CHAPTER ONE
INTRODUCTION AND BASIC CONCEPTS 1
CHAPTER TWO
PROPERTIES OF FLUIDS 37
CHAPTER THREE
CHAPTER FOUR
FLUID KINEMATICS 137
CHAPTER FIVE
BERNOULLI AND ENERGY EQUATIONS 169
CHAPTER SIX
MOMENTUM ANALYSIS OF FLOW SYSTEMS 249
CHAPTER SEVEN
DIMENSIONAL ANALYSIS AND MODELING 297
CHAPTER EIGHT
INTERNAL FLOW. 351
CHAPTER NINE
DIFFERENTIAL ANALYSIS OF FLUID FLOW 443
CHAPTER TEN
[APPROXIMATE SOLUTIONS OF THE NAVIER-STOKES
EQUATION 519
CHAPTER ELEVEN
EXTERNAL FLOW: DRAG AND LIFT 611
CHAPTER TWELVE
CHAPTER THIRTEEN
OPEN-CHANNEL FLOW 723
CHAPTER FOURTEEN
CHAPTER FIFTEEN
CHAPTER ONE
INTRODUCTION AND BASIC CONCEPTS 1
CHAPTER TWO
PROPERTIES OF FLUIDS 37
CHAPTER THREE
CHAPTER FOUR
FLUID KINEMATICS 137
CHAPTER FIVE
BERNOULLI AND ENERGY EQUATIONS 169
CHAPTER SIX
MOMENTUM ANALYSIS OF FLOW SYSTEMS 249
CHAPTER SEVEN
DIMENSIONAL ANALYSIS AND MODELING 297
CHAPTER EIGHT
INTERNAL FLOW. 351
CHAPTER NINE
DIFFERENTIAL ANALYSIS OF FLUID FLOW 443
CHAPTER TEN
[APPROXIMATE SOLUTIONS OF THE NAVIER-STOKES
EQUATION 519
CHAPTER ELEVEN
EXTERNAL FLOW: DRAG AND LIFT 611
CHAPTER TWELVE
CHAPTER THIRTEEN
OPEN-CHANNEL FLOW 723
CHAPTER FOURTEEN
CHAPTER FIFTEEN
THIS PAGE HAS BEEN LEFT INTENTIONALLY BLANK.
CONTENTS
CHAPTER ONE
INTRODUCTION AND BASIC
CONCEPTS 1
“
1-2. A Brief History of Fluid Mechanics 6
1-3. TheNoSlip Condition $
4-4 Classification of Fluid Flows 9
4-5. System and Con! Volume 15,
1-6 Importance of Dimensions and Units 16
e 7
1-7. Modeling in Engineering 22
1-8. Problem-Solving Technique 24
Sepa mien 2
ETES
1-9. Engineering Software Packages 26
140 Accuracy, Precision. and Significant Digis 28
Application Spit: What Nacler Blas and
Raindrops Haven Common 32
CHAPTER TWO
PROPERTIES OF FLUIDS 37
ES
12-2 Density and Specific Gravity 39
Vapor Pressure and Cavitation 41
Energy and Specific Heats 43
2-5 Compresibilty and Speed of Sound 45
Steeda! Saunt nd cotos 42
2-6 Viscosity SI
2-7. Surface Tension and Capillary Elfe 56
CHAPTER THREE
PRESSURE AND FLUID STATICS 77
34 Presae 78
3-2 Pressure Measurement Devices $4
3-3. Introduction to Fluid States 91
3-4. Hydrostatic Forces on Submerged
Plane Surfaces 92
Speck Case Strenge RecanguarPte 95
3-5 Hydrostatic Forces on Submerged Curved
Surfaces 97
346 Buoyancy and Stability 100
CHAPTER ONE
INTRODUCTION AND BASIC
CONCEPTS 1
“
1-2. A Brief History of Fluid Mechanics 6
1-3. TheNoSlip Condition $
4-4 Classification of Fluid Flows 9
4-5. System and Con! Volume 15,
1-6 Importance of Dimensions and Units 16
e 7
1-7. Modeling in Engineering 22
1-8. Problem-Solving Technique 24
Sepa mien 2
ETES
1-9. Engineering Software Packages 26
140 Accuracy, Precision. and Significant Digis 28
Application Spit: What Nacler Blas and
Raindrops Haven Common 32
CHAPTER TWO
PROPERTIES OF FLUIDS 37
ES
12-2 Density and Specific Gravity 39
Vapor Pressure and Cavitation 41
Energy and Specific Heats 43
2-5 Compresibilty and Speed of Sound 45
Steeda! Saunt nd cotos 42
2-6 Viscosity SI
2-7. Surface Tension and Capillary Elfe 56
CHAPTER THREE
PRESSURE AND FLUID STATICS 77
34 Presae 78
3-2 Pressure Measurement Devices $4
3-3. Introduction to Fluid States 91
3-4. Hydrostatic Forces on Submerged
Plane Surfaces 92
Speck Case Strenge RecanguarPte 95
3-5 Hydrostatic Forces on Submerged Curved
Surfaces 97
346 Buoyancy and Stability 100
3-7. Fluids in Rigid-Body Motion 106
Space sae atest 08
‘essen ona Seis Pan 108
Seotonine Ornanca Corner RO
CHAPTER FOUR
FLUID KINEMATICS 137
4-1 Lagrangian and Eulerian Descriptions 138.
4-2. Flow Parera and Flow Visualization 145
Plots of Fluid Flow Data 152
(Other Kinematic Descriptions 155
Voricity ad Rottionality 160,
The Reynolds Transport Theorem 164
ent Dane tte ya Test
Application Sporligh: Fluide Actumors 173
Application Sotligh: Selling Food; the
Human Airway 174
CHAPTER FIVE
BERNOULLI AND ENERGY EQUATIONS 189
5-1 Introduction 190
Conservation of Mass 191
Mechanical Energy and Eficiency 198
‘The Bernoulli Equation 203
Force uno sre Suenos 208
too Compro ew 207
Se Dame on Sgen Pressures 207
Fate Ge Ln Mc a Ey
(rage tne ec) 20
avolaten ae emo Ecutan 202
General Enerey Equation 219)
Ey nero 220
Energy me ot 20
Energy Analysis of Steady Flows 223
Arten ions ug, 734
54
ss
CHAPTER SIX
MOMENTUM ANALYSIS OF FLOW
SYSTEMS 249
6-1 Newton's Laws 250
‘Choosing a Cono! Volume 251
Forces Acting on a Control Volume 252
‘Te Linear Momentum Equation 255
Hower Conon acc) 257
Review of Rotational Moron and Angular
Momentum 269
“The Angular Momentum Equation 272
62
63
64
£
Space sae atest 08
‘essen ona Seis Pan 108
Seotonine Ornanca Corner RO
CHAPTER FOUR
FLUID KINEMATICS 137
4-1 Lagrangian and Eulerian Descriptions 138.
4-2. Flow Parera and Flow Visualization 145
Plots of Fluid Flow Data 152
(Other Kinematic Descriptions 155
Voricity ad Rottionality 160,
The Reynolds Transport Theorem 164
ent Dane tte ya Test
Application Sporligh: Fluide Actumors 173
Application Sotligh: Selling Food; the
Human Airway 174
CHAPTER FIVE
BERNOULLI AND ENERGY EQUATIONS 189
5-1 Introduction 190
Conservation of Mass 191
Mechanical Energy and Eficiency 198
‘The Bernoulli Equation 203
Force uno sre Suenos 208
too Compro ew 207
Se Dame on Sgen Pressures 207
Fate Ge Ln Mc a Ey
(rage tne ec) 20
avolaten ae emo Ecutan 202
General Enerey Equation 219)
Ey nero 220
Energy me ot 20
Energy Analysis of Steady Flows 223
Arten ions ug, 734
54
ss
CHAPTER SIX
MOMENTUM ANALYSIS OF FLOW
SYSTEMS 249
6-1 Newton's Laws 250
‘Choosing a Cono! Volume 251
Forces Acting on a Control Volume 252
‘Te Linear Momentum Equation 255
Hower Conon acc) 257
Review of Rotational Moron and Angular
Momentum 269
“The Angular Momentum Equation 272
62
63
64
£
Application Spottigh: Manta Ray
Swimming 280
CHAPTER SEVEN
DIMENSIONAL ANALYSIS AND
MODELING 297
74
72
Dimensions and Units 298
Dimensional Homogeneity 299
Dimensional Analysis ad Similar 305
‘The Method of Repeating Variables andthe
Buckingham Pi Theorem 309.
Historical Spoiligh: Persons Honored by
‘Nondimensional Parameters 317
Experimental Testing, Modeling, and Incomplete
Similarity 325,
Application Spotlight: How a Fly les 332
73
7-4
CHAPTER EIGHT
INTERNAL FLOW 351
84
a
Introduction 352
Laminar and Turbulent Flows 353
8-3 The Entrance Region 355
EnoyLengre 356
8-4 Laminar Flow in Pipes 357
as
‘Turbulent Flow in Pipes 365
Minor Losses 379
Piping
Fong Spams wi am Trans 388
Flow Rate and Velocity Measurement 396
Tote Forme 402
Tema evs Han)
Application Spoigh: PIV Applied to Cardiac
Flow 420
Application Spoigh: Multicolor Panicle
Shadow Velocimetry/Accelerometry 421
CHAPTER NINE
DIFFERENTIAL ANALYSIS OF FLUID
FLOW 443
91 Introduction 444
9-2 Conservation of Mass—The Continuity
ation ad
Bent vung the Ovegence There 445
nea core ae 4
Cos) Connon Crane Cowansis 450
pacas lime Cay Couto #50
9-3 The Steam Function 456
‘he Seam iron nace Cos 63
‘he Compre Seam Fonction 64
Swimming 280
CHAPTER SEVEN
DIMENSIONAL ANALYSIS AND
MODELING 297
74
72
Dimensions and Units 298
Dimensional Homogeneity 299
Dimensional Analysis ad Similar 305
‘The Method of Repeating Variables andthe
Buckingham Pi Theorem 309.
Historical Spoiligh: Persons Honored by
‘Nondimensional Parameters 317
Experimental Testing, Modeling, and Incomplete
Similarity 325,
Application Spotlight: How a Fly les 332
73
7-4
CHAPTER EIGHT
INTERNAL FLOW 351
84
a
Introduction 352
Laminar and Turbulent Flows 353
8-3 The Entrance Region 355
EnoyLengre 356
8-4 Laminar Flow in Pipes 357
as
‘Turbulent Flow in Pipes 365
Minor Losses 379
Piping
Fong Spams wi am Trans 388
Flow Rate and Velocity Measurement 396
Tote Forme 402
Tema evs Han)
Application Spoigh: PIV Applied to Cardiac
Flow 420
Application Spoigh: Multicolor Panicle
Shadow Velocimetry/Accelerometry 421
CHAPTER NINE
DIFFERENTIAL ANALYSIS OF FLUID
FLOW 443
91 Introduction 444
9-2 Conservation of Mass—The Continuity
ation ad
Bent vung the Ovegence There 445
nea core ae 4
Cos) Connon Crane Cowansis 450
pacas lime Cay Couto #50
9-3 The Steam Function 456
‘he Seam iron nace Cos 63
‘he Compre Seam Fonction 64
9-4 TheDifferential Linear Momentum Equation—
‘Cauchy's Equation 465
Arena Fom Cass Eaton 267
‘The Navier-Stokes Equation 470
In Conesa Comes #8
Oman Coocnates ar
Differential Analysis of Fluid Flow
Problems 476.
er Anat Sa aches in 499
Application potigh: The No-Sip Boundary
Condition 503
CHAPTER TEN
APPROXIMATE SOLUTIONS OF THE
NAVIER-STOKES EQUATION 519
10-1 Inroducton 520
10-2 Nondimensionalized Equations of Motion $21
10-3 The Creeping Flow Approximation $24
410-4 Approximation for nvscid Regions of Flow 529
10-5 The Iratsional Flow Approi
non m Yan pers ow 542
ES
10-6 The Boundary Layer Approximation 558,
Devlcener Themes 92
More ng Tocar y Layers 587
Rte nd Soc sano, 555
Application Spotlight: Droplet Formation $97
CHAPTER ELEVEN
EXTERNAL FLOW: DRAG AND LIFT 611
414 Invoduction 612
112 Drgand Lint 614
1-3. Friction and Pressure Drag 618
41-4 Drag Coefficient of Common Geometries 621
Balog Sts and a9 622
Sieeposton 627
41-5 Parallel Flow over Flt Pates 629
1-6. Flow over Cylinders and Spheres 633
oct Seca Ros 636
17 Lin 638
Free Spon ng and Ong 642
Lire perra 683
Applicaton Spotlight: Drag Reduction 652
Pr on ns Aug 659
CHAPTER TWELVE
COMPRESSIBLE FLOW 667
12-1 Stagnation Properties 668
12-2 One-Dimensional scnropi Flow 671
‘Cauchy's Equation 465
Arena Fom Cass Eaton 267
‘The Navier-Stokes Equation 470
In Conesa Comes #8
Oman Coocnates ar
Differential Analysis of Fluid Flow
Problems 476.
er Anat Sa aches in 499
Application potigh: The No-Sip Boundary
Condition 503
CHAPTER TEN
APPROXIMATE SOLUTIONS OF THE
NAVIER-STOKES EQUATION 519
10-1 Inroducton 520
10-2 Nondimensionalized Equations of Motion $21
10-3 The Creeping Flow Approximation $24
410-4 Approximation for nvscid Regions of Flow 529
10-5 The Iratsional Flow Approi
non m Yan pers ow 542
ES
10-6 The Boundary Layer Approximation 558,
Devlcener Themes 92
More ng Tocar y Layers 587
Rte nd Soc sano, 555
Application Spotlight: Droplet Formation $97
CHAPTER ELEVEN
EXTERNAL FLOW: DRAG AND LIFT 611
414 Invoduction 612
112 Drgand Lint 614
1-3. Friction and Pressure Drag 618
41-4 Drag Coefficient of Common Geometries 621
Balog Sts and a9 622
Sieeposton 627
41-5 Parallel Flow over Flt Pates 629
1-6. Flow over Cylinders and Spheres 633
oct Seca Ros 636
17 Lin 638
Free Spon ng and Ong 642
Lire perra 683
Applicaton Spotlight: Drag Reduction 652
Pr on ns Aug 659
CHAPTER TWELVE
COMPRESSIBLE FLOW 667
12-1 Stagnation Properties 668
12-2 One-Dimensional scnropi Flow 671
12-3 Lenropie Flow through Nozzes 677
12-4 Shock Waves and Expansion
Waves 685
12-5 Duct Flow with Heat Tran and Negligible
Friction (RaykighFow) 701
Pope atar lor Rah an 706
Grated ntegnro 708
12-6 Adiabatic Duct Flow with Friction
(anno Flow) 710
Grated amma om 76
Application Spotlight: Shock Wavel
‘Boundary-Layer interactions 720
CHAPTER THIRTEEN
OPEN-CHANNEL FLOW 733
13-4 Classification of Open-Channe Flows 734
418-2 Froude Number and Wave Spood 737
Speed ou Wives 730
13-3 Specific Energy 741
13-4 Conservation of Mass and Energy
Fquations 744
13-5 Uniform Flow in Channels 745
13-6 Best Hydraulic Cross Sections 751
13-7 GradallyVaried Flow 755
13-8 Rapidly Varied Flow and the Hydraulic
Jump 765
13-9 Flow Control and Measurement 769
Application Spoigh: Bridge Scour 779
CHAPTER FOURTEEN
TURBOMACHINERY 793
14-41 Classifications and Terminology 794
Porte Depcemer Pugs 809
Syme npr 82
rtp ge 82
14-3 Pump Scaling Lans 830
Omensenu Ants. 830
Poste Ses 835
14-4 Turbines 839
Fone cores 88
14-5 Turbine Sealing Laws 861
Application polig: Rey Ful Atomizers 867
CHAPTER FIFTEEN
INTRODUCTION TO COMPUTATIONAL
FLUID DYNAMICS 885
15-1 Introduction and Fundamentals 886
Menasen 886
12-4 Shock Waves and Expansion
Waves 685
12-5 Duct Flow with Heat Tran and Negligible
Friction (RaykighFow) 701
Pope atar lor Rah an 706
Grated ntegnro 708
12-6 Adiabatic Duct Flow with Friction
(anno Flow) 710
Grated amma om 76
Application Spotlight: Shock Wavel
‘Boundary-Layer interactions 720
CHAPTER THIRTEEN
OPEN-CHANNEL FLOW 733
13-4 Classification of Open-Channe Flows 734
418-2 Froude Number and Wave Spood 737
Speed ou Wives 730
13-3 Specific Energy 741
13-4 Conservation of Mass and Energy
Fquations 744
13-5 Uniform Flow in Channels 745
13-6 Best Hydraulic Cross Sections 751
13-7 GradallyVaried Flow 755
13-8 Rapidly Varied Flow and the Hydraulic
Jump 765
13-9 Flow Control and Measurement 769
Application Spoigh: Bridge Scour 779
CHAPTER FOURTEEN
TURBOMACHINERY 793
14-41 Classifications and Terminology 794
Porte Depcemer Pugs 809
Syme npr 82
rtp ge 82
14-3 Pump Scaling Lans 830
Omensenu Ants. 830
Poste Ses 835
14-4 Turbines 839
Fone cores 88
14-5 Turbine Sealing Laws 861
Application polig: Rey Ful Atomizers 867
CHAPTER FIFTEEN
INTRODUCTION TO COMPUTATIONAL
FLUID DYNAMICS 885
15-1 Introduction and Fundamentals 886
Menasen 886
¡renato nd Ci ntpendence 899 TABLE A-2 Boiling and Freeing Point
Sour Connors. 858 Properties 949)
ate we TABLE A-3 Properties of Saturated Water 950
TABLE A4 Properties of Saturated
pe FwEraance Repo ate =500 89 a 991
ow reuse Creat Cynder se 50 203 Refrigerant
45-3 Turbulent CFD Calculations 908 TABLE A-S Properties of Saturated Ammonia 952
wein Creer Cynder a = 0000 9 TABLEA-6 Properties ofSaturted Propane 953
aupa Cred Create = D 90 TABLEA-7 —ProperiesofLiguds 958
Deon tne Sree are ow Fan 9 METS une 5
REAL wih Heat Tastee 22! TABLEA-9 Prperies of Airat | am Pressure 956
pa TABLEA-10 Properties ol Gass at 1 atm
Cong tan are logra Creat ips 923 Pressure 957
15-5 Compressible Flow CFD Calculations 928 TABLEA-T1_ Properties ofthe Atmosphere at High
Congest wea Canwrgmg-Overong Autude 959
ozo 929 FIGURE A-12 The Moody Char for the Friction
15-6 Open-Channel Flow CFD Calculaions 936
rca Sc Gu pija argh 287
Factor fr Fully Developed Flow in
Circular Pipes 960
TABLEA-13 One-Dimensional hentropie
‘Compressible Flow Functions for an
‘eal Gas with k= LA 961
Le TABLEA-14 One-Dimensional Normal Shock
Application Spotigh: À Virtual Stomach 939 ns ll Ci ve
Artrnces ons Suppested Reosng 980 1a 962
ns TABLEA-1S Rayleigh Flow Functions for an Kal
Gas with k= 14 963,
APPENDIX TABLE A-16 Fanno Flow Functions for an Ideal Gas
PROPERTY TABLES AND CHARTS 947 na os
TABLEA-S Mol Mass Gas Consta, and tne 7
Léa Gas Spec Heats ol Some Comrie Faas 95
Substances 948 Rendu 387
Sour Connors. 858 Properties 949)
ate we TABLE A-3 Properties of Saturated Water 950
TABLE A4 Properties of Saturated
pe FwEraance Repo ate =500 89 a 991
ow reuse Creat Cynder se 50 203 Refrigerant
45-3 Turbulent CFD Calculations 908 TABLE A-S Properties of Saturated Ammonia 952
wein Creer Cynder a = 0000 9 TABLEA-6 Properties ofSaturted Propane 953
aupa Cred Create = D 90 TABLEA-7 —ProperiesofLiguds 958
Deon tne Sree are ow Fan 9 METS une 5
REAL wih Heat Tastee 22! TABLEA-9 Prperies of Airat | am Pressure 956
pa TABLEA-10 Properties ol Gass at 1 atm
Cong tan are logra Creat ips 923 Pressure 957
15-5 Compressible Flow CFD Calculations 928 TABLEA-T1_ Properties ofthe Atmosphere at High
Congest wea Canwrgmg-Overong Autude 959
ozo 929 FIGURE A-12 The Moody Char for the Friction
15-6 Open-Channel Flow CFD Calculaions 936
rca Sc Gu pija argh 287
Factor fr Fully Developed Flow in
Circular Pipes 960
TABLEA-13 One-Dimensional hentropie
‘Compressible Flow Functions for an
‘eal Gas with k= LA 961
Le TABLEA-14 One-Dimensional Normal Shock
Application Spotigh: À Virtual Stomach 939 ns ll Ci ve
Artrnces ons Suppested Reosng 980 1a 962
ns TABLEA-1S Rayleigh Flow Functions for an Kal
Gas with k= 14 963,
APPENDIX TABLE A-16 Fanno Flow Functions for an Ideal Gas
PROPERTY TABLES AND CHARTS 947 na os
TABLEA-S Mol Mass Gas Consta, and tne 7
Léa Gas Spec Heats ol Some Comrie Faas 95
Substances 948 Rendu 387
PREFACE
BACKGROUND
Fluid mechanics is an exching and fascinating subject with unlimited prot
cal applications ranging rom microscopic biological systems to automobiles,
planes, and spaceerft propulsion, Fluid mechancs has alo Historical
een one ofthe most challenging subjects for undergraduate students because
proper analysis of fluid mechanies problems requires nor only knowledge
‘ofthe concepts but also physical intuition and experience. Our hope is hat.
this book, through its careful explanations of concepts and is use of numer
ous practical examples, sketches. figures. and photographs, bridges the gap
bete knowledge andthe proper application of that knowledge
Fluid mechanics isa mature subject the basic equations and aproxima
ons are well established and can be found in any introductory textbook, Our
book is distinguished from other introductory books because we presen the
subject in a progressive order from simple to more dificult, building each
‘chapter upon foundations lid down in cac chapters, We provide more día
trams and photographs han other books because fluid mechanics i, by i
nature, a highly visual subject. Only by illustrating the concepts discussed,
an students fly appreciate the mathematica significance ofthe materia,
OBJECTIVES
‘This book has been writen forthe Fist uid mechanics course for under
graduate engineering students, There is suficien material for a wwo-coune
Sequence, if desired. We asume that readers will have an adequate back
ground in calculus, physics, engineering mechanics, and thermodynamics,
‘The objectives ofthis ext are
+ To present the base principles and equations of fluid mechanics.
+ To show numerous and diverse real-world engineering examples to
sive the student the intuition necessary or correct application of fluid
‘mechanics principles in engineering applications.
+ To develop an inte understanding of fluid mechanics by emphasi
ing the physics. and reinforcing that understanding through illsrative
figures and photographs.
‘The book contains enough material tallow considerable Nexbility in tech
ing the course. Aeronautics and aerospace engincers might emphasize poten
tial flow, drag and lif, compressible flow turbomachinery, and CED. while
mechanical or evil engineering instructors might choose to emphasize pipe
‘ows and open-channel lows, respectively
NEW TO THE FOURTH EDITION
Alle popular features o the previous editions have ben retained while new
ones hate been added. The main body ofthe ex remain largely unchanged.
[A noticeable change isthe addition of a number of exciting new pictures
{throughout the book.
BACKGROUND
Fluid mechanics is an exching and fascinating subject with unlimited prot
cal applications ranging rom microscopic biological systems to automobiles,
planes, and spaceerft propulsion, Fluid mechancs has alo Historical
een one ofthe most challenging subjects for undergraduate students because
proper analysis of fluid mechanies problems requires nor only knowledge
‘ofthe concepts but also physical intuition and experience. Our hope is hat.
this book, through its careful explanations of concepts and is use of numer
ous practical examples, sketches. figures. and photographs, bridges the gap
bete knowledge andthe proper application of that knowledge
Fluid mechanics isa mature subject the basic equations and aproxima
ons are well established and can be found in any introductory textbook, Our
book is distinguished from other introductory books because we presen the
subject in a progressive order from simple to more dificult, building each
‘chapter upon foundations lid down in cac chapters, We provide more día
trams and photographs han other books because fluid mechanics i, by i
nature, a highly visual subject. Only by illustrating the concepts discussed,
an students fly appreciate the mathematica significance ofthe materia,
OBJECTIVES
‘This book has been writen forthe Fist uid mechanics course for under
graduate engineering students, There is suficien material for a wwo-coune
Sequence, if desired. We asume that readers will have an adequate back
ground in calculus, physics, engineering mechanics, and thermodynamics,
‘The objectives ofthis ext are
+ To present the base principles and equations of fluid mechanics.
+ To show numerous and diverse real-world engineering examples to
sive the student the intuition necessary or correct application of fluid
‘mechanics principles in engineering applications.
+ To develop an inte understanding of fluid mechanics by emphasi
ing the physics. and reinforcing that understanding through illsrative
figures and photographs.
‘The book contains enough material tallow considerable Nexbility in tech
ing the course. Aeronautics and aerospace engincers might emphasize poten
tial flow, drag and lif, compressible flow turbomachinery, and CED. while
mechanical or evil engineering instructors might choose to emphasize pipe
‘ows and open-channel lows, respectively
NEW TO THE FOURTH EDITION
Alle popular features o the previous editions have ben retained while new
ones hate been added. The main body ofthe ex remain largely unchanged.
[A noticeable change isthe addition of a number of exciting new pictures
{throughout the book.
Four new subsections have been added: “Uniform versus Nonuniform
Flow” and "Equation Solvers to Chap I "Flying in Nature” by guet author
‘Azar slam Panah of Penn State Berks to Chap. 11, and "CFD Methods for
‘Two-Phase Flows” by guest author Alex Rate of Penn State to Chap. 15. In
‘Chap. 8, we now highlight the explicit Churchill equation as an atea o
{he implicit Colebrook equation.
“Two new Application Spolighs, have been added: “Smelling Food: the
Human Airway” by Rui Ni of Penn State, o Chap. 4, and "Multicolor Par
tice Shadow Velocimetry/Accelerometty” by Michael MePiail and Michal
Krane of Penn Stat to Chap 8
A large number of he end-f-chaper problems inthe text have been mod:
‘tied and many problems were replaced by new ones. Also, several of the
solv example problems have ben replaced,
PHILOSOPHY AND GOAL
“The Fourth Edition of Fluid Mechanics: Fundamentals and Applications has
the same goals and philosophy asthe eter texts by lead autho Yunus Geng
+ Communicates direc with tomorrow's engineers in a simple yer
precise manner
+ Leads students toward a clear understanding and firm grasp ofthe basic
principles o id mechanics
+ Encourage creative thinking and development of deeper understand.
ing and nite fee or lid mechanics
+ As read by students with intrest and enthusiasm rater than merely as a
guide 10 solve homework problems
‘The best way to lean is by practice. Special effort is made throughout the
‘book o reinforce the material that was presented earlier (in each chapter
as well asin material from previous chapters). Many of the ¡lustrated
example problems and end-of-chapter problems are comprehensive and
encourage students o review and revisit concepts and imuitions gained
previously.
“Throughout the book, we show examples generate by computational Mid
dynamics (CFD), We alsoprovid an introductory chapter onthe subject. Our
goals mot 1 teach the details about numerical algorithms associated with,
‘CED asi more properly presented in a separate couse. Rather urinten
isto introduce undergraduate students to the capabilities and limitations of
{CFD as an engineering tol. We use CFD solutions in much the same way
as experimental results ae used from wind tunnel tests (i. to reinforce
‘understanding ofthe physics of Nui lows and o provide quality flow vis:
izations tat hep explain ui behavior) With dozens of CFD end-of chapter
problems posted on the website, instructors have ample opportunity to it
{duce the basis of CFD throughout the course
CONTENT AND ORGANIZATION
‘This book is organized inc 1S chapters beginning wit fundamental concepts
‘of Msi, Aid properties, and Tad flows and ending with an introduction o
Computational id dynes
+ Chapter | provides basic introduction to ds, classifications of id
flow, contol volume versus system formulations, dimensions, units,
significan digits, and problem-solving techniques.
Flow” and "Equation Solvers to Chap I "Flying in Nature” by guet author
‘Azar slam Panah of Penn State Berks to Chap. 11, and "CFD Methods for
‘Two-Phase Flows” by guest author Alex Rate of Penn State to Chap. 15. In
‘Chap. 8, we now highlight the explicit Churchill equation as an atea o
{he implicit Colebrook equation.
“Two new Application Spolighs, have been added: “Smelling Food: the
Human Airway” by Rui Ni of Penn State, o Chap. 4, and "Multicolor Par
tice Shadow Velocimetry/Accelerometty” by Michael MePiail and Michal
Krane of Penn Stat to Chap 8
A large number of he end-f-chaper problems inthe text have been mod:
‘tied and many problems were replaced by new ones. Also, several of the
solv example problems have ben replaced,
PHILOSOPHY AND GOAL
“The Fourth Edition of Fluid Mechanics: Fundamentals and Applications has
the same goals and philosophy asthe eter texts by lead autho Yunus Geng
+ Communicates direc with tomorrow's engineers in a simple yer
precise manner
+ Leads students toward a clear understanding and firm grasp ofthe basic
principles o id mechanics
+ Encourage creative thinking and development of deeper understand.
ing and nite fee or lid mechanics
+ As read by students with intrest and enthusiasm rater than merely as a
guide 10 solve homework problems
‘The best way to lean is by practice. Special effort is made throughout the
‘book o reinforce the material that was presented earlier (in each chapter
as well asin material from previous chapters). Many of the ¡lustrated
example problems and end-of-chapter problems are comprehensive and
encourage students o review and revisit concepts and imuitions gained
previously.
“Throughout the book, we show examples generate by computational Mid
dynamics (CFD), We alsoprovid an introductory chapter onthe subject. Our
goals mot 1 teach the details about numerical algorithms associated with,
‘CED asi more properly presented in a separate couse. Rather urinten
isto introduce undergraduate students to the capabilities and limitations of
{CFD as an engineering tol. We use CFD solutions in much the same way
as experimental results ae used from wind tunnel tests (i. to reinforce
‘understanding ofthe physics of Nui lows and o provide quality flow vis:
izations tat hep explain ui behavior) With dozens of CFD end-of chapter
problems posted on the website, instructors have ample opportunity to it
{duce the basis of CFD throughout the course
CONTENT AND ORGANIZATION
‘This book is organized inc 1S chapters beginning wit fundamental concepts
‘of Msi, Aid properties, and Tad flows and ending with an introduction o
Computational id dynes
+ Chapter | provides basic introduction to ds, classifications of id
flow, contol volume versus system formulations, dimensions, units,
significan digits, and problem-solving techniques.
(Chapter 2is devoted to uid properties such as density, vapor pressure,
specific heats, speed of sound, viscosity and surface tension,
Chapter 3 deals with fluid statis and pressure, including manometer
and barometers, hydrostatic forces on submerged surfaces, buoyancy
and stability, and ids in sii body mation.
Chapter 4 covers topics related to fluid kinematics, such as the differ
ences between Lagrangian and Eulerian descriptions of fluid flows,
Flow paterns, flow visualization, vorticity and rotationality, andthe
Reynolds transport here.
Chapter $ introduces the fundamental conservation laws of mass
‘momentum, and energy. with emphasi on the proper use ofthe mass,
Bernoulli and energy equations and the engineering applications of
these equations.
Chapter 6 applies the Reynolds transport theorem to linear momentum
and angular momentum and emphasizes practical engineering applic
tions ol fine contol volume momentum analysis
Chapter reinforces the concep of dimensional homogeneity and into
duces the Buckingham Pi theorem of dimensional analysis, dynamic
Similarity and the method of repeating variables material ha is use
ful throughout the rest ofthe book and in many disciplines in science
and engineering
Chapter is devoted 0 flow in pies and ducts. We discuss the di
ferences between laminar and turbulent flow Fiction lose in pipes
and dct, and minor losses in piping networks. We alo explain how
to properly selec pump e fan to math a piping network Finally, we
discuss various experimental devices that ae sed to measure Flow fte
and velocity. and provide a brie introduction to biotluid mechanics.
CChapter9 deals with differential analysis of fluid low and includes der
‘vation and application o the continuity equation, he Cauchy equation,
and the Navier-Stokes equation, We alo introduce the steam function
and describe it usefulness in analysis of ui Flows, and we provide à
brief introduction to bioluks Finally. we point out some of the unique
aspects of differential analysis related 1 biofluid mechanics
Chapter 10 iscusses several approximations o the Navier-Stokes oqua-
ion and provides example solutions for each approximation, including
reeping flow, ivisid flow, irosional (potential) ow, and boundary
Mayen.
Chapter 11 covers forces on living and non-living bodies (drag and
Jif), explaining the distincion between friction and pressure dag,
and providing drag coefficients for many common geomerris. This
Chapter emphasizes the practical application of wind tunnel mea
surement coupled with dynamic similarity and dimensional analysis
concepts introduced earlier in Chap 7.
Chapter 12 extends fluid flow analysis to compresibe flow, whee the
behavior of gases is greatly affected by the Mach number. In his chapter,
the concepts of expansion waves, normal and oblique shock waves, and
choked low are introduced,
Chapter 13 deals with open-channel flow and some ofthe unique fe
tures associated with th flow of quid with a fee surface, such as
surface waves and hydraulic jumps.
specific heats, speed of sound, viscosity and surface tension,
Chapter 3 deals with fluid statis and pressure, including manometer
and barometers, hydrostatic forces on submerged surfaces, buoyancy
and stability, and ids in sii body mation.
Chapter 4 covers topics related to fluid kinematics, such as the differ
ences between Lagrangian and Eulerian descriptions of fluid flows,
Flow paterns, flow visualization, vorticity and rotationality, andthe
Reynolds transport here.
Chapter $ introduces the fundamental conservation laws of mass
‘momentum, and energy. with emphasi on the proper use ofthe mass,
Bernoulli and energy equations and the engineering applications of
these equations.
Chapter 6 applies the Reynolds transport theorem to linear momentum
and angular momentum and emphasizes practical engineering applic
tions ol fine contol volume momentum analysis
Chapter reinforces the concep of dimensional homogeneity and into
duces the Buckingham Pi theorem of dimensional analysis, dynamic
Similarity and the method of repeating variables material ha is use
ful throughout the rest ofthe book and in many disciplines in science
and engineering
Chapter is devoted 0 flow in pies and ducts. We discuss the di
ferences between laminar and turbulent flow Fiction lose in pipes
and dct, and minor losses in piping networks. We alo explain how
to properly selec pump e fan to math a piping network Finally, we
discuss various experimental devices that ae sed to measure Flow fte
and velocity. and provide a brie introduction to biotluid mechanics.
CChapter9 deals with differential analysis of fluid low and includes der
‘vation and application o the continuity equation, he Cauchy equation,
and the Navier-Stokes equation, We alo introduce the steam function
and describe it usefulness in analysis of ui Flows, and we provide à
brief introduction to bioluks Finally. we point out some of the unique
aspects of differential analysis related 1 biofluid mechanics
Chapter 10 iscusses several approximations o the Navier-Stokes oqua-
ion and provides example solutions for each approximation, including
reeping flow, ivisid flow, irosional (potential) ow, and boundary
Mayen.
Chapter 11 covers forces on living and non-living bodies (drag and
Jif), explaining the distincion between friction and pressure dag,
and providing drag coefficients for many common geomerris. This
Chapter emphasizes the practical application of wind tunnel mea
surement coupled with dynamic similarity and dimensional analysis
concepts introduced earlier in Chap 7.
Chapter 12 extends fluid flow analysis to compresibe flow, whee the
behavior of gases is greatly affected by the Mach number. In his chapter,
the concepts of expansion waves, normal and oblique shock waves, and
choked low are introduced,
Chapter 13 deals with open-channel flow and some ofthe unique fe
tures associated with th flow of quid with a fee surface, such as
surface waves and hydraulic jumps.
+ Chapter 14 examines turbomachinry in more detail including pumps,
fans, and turbines. An emphasis is placed on how pumps and turbines
‘work rather than on ther detailed design We also discuss overall pump
and turbine design, based on dynamic simiarity laws and simplified
Velocity veto analyses.
+ Chapter 15 describes the fundamental concepts of computational fluid
dyamios (CFD) and shows students how t use commercial CFD codes
A tools o sole comple fluid mechanics problems. We emphasize the
Application of CFD rather than the algorithms use in CFD codes,
Each chapter contains a wealth of end-of-chapter homework problems. A
comprehensive se of appendices is provided giving the thermodynamic and
‘uid properties of several material, in addition to ar and water, along with,
some useful plots and tables. Many of the end-of-chapter problems require
the use of material properties from the appendices 0 enhance the realism of
the problems.
LEARNING TOOLS
EMPHASIS ON PHYSICS
A distinctive feature of this book is ts emphasis on the physical aspects
of the subject matter in addition to mathematical representations and
manipulations. The authors believe thatthe emphasis in undergraduate
education should remain on developing a sense of underlying physical
‘mechanisms and a mastery of solving practical problems that an engineer
is likely to face in the eal world, Developing an intuitive understanding
should also make the course a more motivating and worthwhile exper:
fence for the students.
EFFECTIVE USE OF ASSOCIATION
‘An observant mind should have no difficulty understanding engineering
Sciences. After all the principles of engineering sciences are based on our
everyday experiences and experimental observations. Therefor, a physi
‘al intuitive approach is used throughout this ex, Frequently, parallels are
dran between the subject mater and students everyday experiences so that
‘ey can late the subject matter (0 what they already Know
SELF-INSTRUCTING
“The material in the text is introduced at a level ha an average student can
follow comfortably. I speak o students, not ner students. Infact. ii el
insruetve. Noting hat he principles of science are based on experimental
‘observations, most ofthe derivations in his tet are largely base on physical
arguments, and thus they are easy 1 follow and understand
EXTENSIVE USE OF ARTWORK AND PHOTOGRAPHS
Figures are important learning tools that help the Students “get the picture
and the text makes effective use of graphics. It contains more figures, photo
graph. and illustrations than any oer book inthis category. Figures attract
tention and stimulate curiosity and interes. Most ofthe figures in this text,
fans, and turbines. An emphasis is placed on how pumps and turbines
‘work rather than on ther detailed design We also discuss overall pump
and turbine design, based on dynamic simiarity laws and simplified
Velocity veto analyses.
+ Chapter 15 describes the fundamental concepts of computational fluid
dyamios (CFD) and shows students how t use commercial CFD codes
A tools o sole comple fluid mechanics problems. We emphasize the
Application of CFD rather than the algorithms use in CFD codes,
Each chapter contains a wealth of end-of-chapter homework problems. A
comprehensive se of appendices is provided giving the thermodynamic and
‘uid properties of several material, in addition to ar and water, along with,
some useful plots and tables. Many of the end-of-chapter problems require
the use of material properties from the appendices 0 enhance the realism of
the problems.
LEARNING TOOLS
EMPHASIS ON PHYSICS
A distinctive feature of this book is ts emphasis on the physical aspects
of the subject matter in addition to mathematical representations and
manipulations. The authors believe thatthe emphasis in undergraduate
education should remain on developing a sense of underlying physical
‘mechanisms and a mastery of solving practical problems that an engineer
is likely to face in the eal world, Developing an intuitive understanding
should also make the course a more motivating and worthwhile exper:
fence for the students.
EFFECTIVE USE OF ASSOCIATION
‘An observant mind should have no difficulty understanding engineering
Sciences. After all the principles of engineering sciences are based on our
everyday experiences and experimental observations. Therefor, a physi
‘al intuitive approach is used throughout this ex, Frequently, parallels are
dran between the subject mater and students everyday experiences so that
‘ey can late the subject matter (0 what they already Know
SELF-INSTRUCTING
“The material in the text is introduced at a level ha an average student can
follow comfortably. I speak o students, not ner students. Infact. ii el
insruetve. Noting hat he principles of science are based on experimental
‘observations, most ofthe derivations in his tet are largely base on physical
arguments, and thus they are easy 1 follow and understand
EXTENSIVE USE OF ARTWORK AND PHOTOGRAPHS
Figures are important learning tools that help the Students “get the picture
and the text makes effective use of graphics. It contains more figures, photo
graph. and illustrations than any oer book inthis category. Figures attract
tention and stimulate curiosity and interes. Most ofthe figures in this text,
are intended 10 serve as a means of emphasizing some key concepts that
"Would otherwise go unnoticed some serve as page summaries,
NUMEROUS WORKED-OUT EXAMPLES
All chapters contain numerous worked-out examples that both early the
‘material and illustrate the use of basic principles in a context that eps
develop the student's intuition. An nie and systematic approach is used
inthe solution of all example problems. The solution methodology sais with
statement of the problem, and all objectives are identified. The assumptions
and approximations are then stated together wit their justifications. Any
properties needed to solve the problem ae lied separately. Numerical values
are used together with numbers to emphasize that without units, numbers are
‘meaningless. The significance ofeach example’ results discussed following
the solution. This methodical approach is also followed and provided inthe
solutions tothe end-of-chapter problems, avaiable to instructors.
A WEALTH OF REALISTIC END-OF-CHAPTER PROBLEMS
‘The end-of-chapter problems are grouped under specific topes to make
problem selection esie for both insuctors and students, Within each
group of problems are Concept Questions, indicated by °C." w check the
Students’ level of understanding of basic concept. Problems under Funda.
‘mental of Engineering (FE) Exam Problems ate designed to help students
prepare for the Fundamentals of Engineering exam, as they prepare
{or their Professional Engineering license. The problems under Review
Problems are more comprehensive in nature and are not directly tied
to any specific Section or a chapter—in some cases they require review
of material learned in previous chapters. Problems designated as
Design and Essay are intended to encourage students 10 make engineering
judgments, to conduct independent exploration of topics of interest, and to
‘communicate their finding’ in profesional manner, Problems withthe
E icon are comprehensive in nature and ae intended to be solved with a
Computer using aproprate software. Several economics and safety-related
problems are incorporated throughout o enhance cos and safety awareness
mong engineering students, Answers o selected problems are sed imme:
¿ley folowing the problem for convenience to students
USE OF COMMON NOTATION
‘The use of diferent notation or the same quate in deremtenginceing
‘courses as long been a source of discontent and confusion. A student aking
both fluid mechanics and heat transfer for example, as to us the notation Q
for volume Now rte in one coune, and for heat tante inthe other, Th need
Lo unify notation in engineering education has olen ben raised, ven in some
repart of conferences sponsored by the National Science Foundation though
Foundation Coalitions, but ite effort has been made to date inthis regard.
For example, refer tothe final epor ofthe Mini Conference on Energy Sem
Innovations, May 28 and 29,2003, University of Wisconsin, In this tet we
made a conscious ello to minimize ths conflict by adopting the familar
{ermodynanic notation Ur volume ow rate this reserving the notation ©
"Would otherwise go unnoticed some serve as page summaries,
NUMEROUS WORKED-OUT EXAMPLES
All chapters contain numerous worked-out examples that both early the
‘material and illustrate the use of basic principles in a context that eps
develop the student's intuition. An nie and systematic approach is used
inthe solution of all example problems. The solution methodology sais with
statement of the problem, and all objectives are identified. The assumptions
and approximations are then stated together wit their justifications. Any
properties needed to solve the problem ae lied separately. Numerical values
are used together with numbers to emphasize that without units, numbers are
‘meaningless. The significance ofeach example’ results discussed following
the solution. This methodical approach is also followed and provided inthe
solutions tothe end-of-chapter problems, avaiable to instructors.
A WEALTH OF REALISTIC END-OF-CHAPTER PROBLEMS
‘The end-of-chapter problems are grouped under specific topes to make
problem selection esie for both insuctors and students, Within each
group of problems are Concept Questions, indicated by °C." w check the
Students’ level of understanding of basic concept. Problems under Funda.
‘mental of Engineering (FE) Exam Problems ate designed to help students
prepare for the Fundamentals of Engineering exam, as they prepare
{or their Professional Engineering license. The problems under Review
Problems are more comprehensive in nature and are not directly tied
to any specific Section or a chapter—in some cases they require review
of material learned in previous chapters. Problems designated as
Design and Essay are intended to encourage students 10 make engineering
judgments, to conduct independent exploration of topics of interest, and to
‘communicate their finding’ in profesional manner, Problems withthe
E icon are comprehensive in nature and ae intended to be solved with a
Computer using aproprate software. Several economics and safety-related
problems are incorporated throughout o enhance cos and safety awareness
mong engineering students, Answers o selected problems are sed imme:
¿ley folowing the problem for convenience to students
USE OF COMMON NOTATION
‘The use of diferent notation or the same quate in deremtenginceing
‘courses as long been a source of discontent and confusion. A student aking
both fluid mechanics and heat transfer for example, as to us the notation Q
for volume Now rte in one coune, and for heat tante inthe other, Th need
Lo unify notation in engineering education has olen ben raised, ven in some
repart of conferences sponsored by the National Science Foundation though
Foundation Coalitions, but ite effort has been made to date inthis regard.
For example, refer tothe final epor ofthe Mini Conference on Energy Sem
Innovations, May 28 and 29,2003, University of Wisconsin, In this tet we
made a conscious ello to minimize ths conflict by adopting the familar
{ermodynanic notation Ur volume ow rate this reserving the notation ©
{oe heat transfer. Also, we consistently use an overdo to denote time rae, We
think tha both students and instuctrs will appreciate this effr to promote
‘COMBINED COVERAGE OF BERNOULLI
AND ENERGY EQUATIONS:
‘The Bemoalli equation is one ofthe mos frequently used equations in uid
mechanics, but it i also one ofthe most misused. Therefore, itis importan
o emphasize the limitations on the use ofthis idealized equation and to
show how to properly account for imperfections and ireversibl loses.
In Chap. 5, we do this by introducing the energy equation right after the
Bemoulli equation and demonstrating how the solutions of many practical
engineering problems differ rom those obtained using the Bernoul equa
tion. This helps students develop a realistic view o the Bernoulli equation
A SEPARATE CHAPTER ON CFD
‘Commercial Computational Fluid Dynamics (CFD) codes ate widely used
in engineering practice in the design and analysis of flow systems, and it has
become exceedingly important for engineers to havea solid understanding of
the fundamental aspects, capabilities, and limitations of CFD. Recognizing
‘that most undergraduate engineering curriculums do not have room fora fll,
course on CFD, a separate chapter include ere 10 make up or this def
tency and to equip students with an adequate background on the strengths
and weaknesses of CFD.
APPLICATION SPOTLIGHTS
‘Throughout the book are highlighted examples called Applicaton Spotlights
‘where a real-world application of Muid mechanics is shown. A unique fea
ture of these special examples is that they are writen by guest authors. The
Application Spotlights ae designed to show students how uid mechanies
has divene applications in a wide variety’ of fields, They aso include eye
catching photographs rom the guest author research
CONVERSION FACTORS
Frequently used conversion factors, physical constants, and properties of ir
and water at 20°C and atmospheric presure ae ised atthe very end ofthe
book for easy reference
NOMENCLATURE
A list of the majo symbols, subscripts, and superscripts used inthe text is
provided near the end ofthe book for easy reference
think tha both students and instuctrs will appreciate this effr to promote
‘COMBINED COVERAGE OF BERNOULLI
AND ENERGY EQUATIONS:
‘The Bemoalli equation is one ofthe mos frequently used equations in uid
mechanics, but it i also one ofthe most misused. Therefore, itis importan
o emphasize the limitations on the use ofthis idealized equation and to
show how to properly account for imperfections and ireversibl loses.
In Chap. 5, we do this by introducing the energy equation right after the
Bemoulli equation and demonstrating how the solutions of many practical
engineering problems differ rom those obtained using the Bernoul equa
tion. This helps students develop a realistic view o the Bernoulli equation
A SEPARATE CHAPTER ON CFD
‘Commercial Computational Fluid Dynamics (CFD) codes ate widely used
in engineering practice in the design and analysis of flow systems, and it has
become exceedingly important for engineers to havea solid understanding of
the fundamental aspects, capabilities, and limitations of CFD. Recognizing
‘that most undergraduate engineering curriculums do not have room fora fll,
course on CFD, a separate chapter include ere 10 make up or this def
tency and to equip students with an adequate background on the strengths
and weaknesses of CFD.
APPLICATION SPOTLIGHTS
‘Throughout the book are highlighted examples called Applicaton Spotlights
‘where a real-world application of Muid mechanics is shown. A unique fea
ture of these special examples is that they are writen by guest authors. The
Application Spotlights ae designed to show students how uid mechanies
has divene applications in a wide variety’ of fields, They aso include eye
catching photographs rom the guest author research
CONVERSION FACTORS
Frequently used conversion factors, physical constants, and properties of ir
and water at 20°C and atmospheric presure ae ised atthe very end ofthe
book for easy reference
NOMENCLATURE
A list of the majo symbols, subscripts, and superscripts used inthe text is
provided near the end ofthe book for easy reference
ACKNOWLEDGMENTS
‘The authors would like to acknowledge with appreciation the numerous and
‘valuable comments, suggestions, consructive encima praise fom the
following evaluators and viewers
ass Abusos Jonatan ok
Per
DS
Sala Ganga ms
We also thank those who were acknowledged in the fist, second, and
bird editions ofthis book, but are too numerous 10 mention again here
‘The authors are particularly grateful to Mehmet Kanoÿl of University of
Gaziantep for his valuable contributions, particularly his modifications of
end-of-chapter problems, his editing and updating ofthe solutions man-
{al and his critical review of the entire manuscript, We also thank Tahsin
Engin of Sakarya University and Suar Canbazoplu of Inonu University for
contributing several end-of-chapter problems, and Mohsen Hassan Vand
Tor reviewing the book and pointing out a number of emos
Finally, special hanks must goto cur families, especially our wives, Zea
Gengel and Suzanne Cimbala, for their continued patience, understanding,
and support throughout the preparation ofthis book, which involved many
Tong hours when they had t handle family concerns on their own because
their husbands aces wee glued 10 à computer sree.
Publishers ae also thankful othe following faculty members for critically
eviwing the manuscrits
Lajpat Rai Masood Ahmed
Manoj Langbi
Yunus A. Gengel
John M. Cimbata
‘The authors would like to acknowledge with appreciation the numerous and
‘valuable comments, suggestions, consructive encima praise fom the
following evaluators and viewers
ass Abusos Jonatan ok
Per
DS
Sala Ganga ms
We also thank those who were acknowledged in the fist, second, and
bird editions ofthis book, but are too numerous 10 mention again here
‘The authors are particularly grateful to Mehmet Kanoÿl of University of
Gaziantep for his valuable contributions, particularly his modifications of
end-of-chapter problems, his editing and updating ofthe solutions man-
{al and his critical review of the entire manuscript, We also thank Tahsin
Engin of Sakarya University and Suar Canbazoplu of Inonu University for
contributing several end-of-chapter problems, and Mohsen Hassan Vand
Tor reviewing the book and pointing out a number of emos
Finally, special hanks must goto cur families, especially our wives, Zea
Gengel and Suzanne Cimbala, for their continued patience, understanding,
and support throughout the preparation ofthis book, which involved many
Tong hours when they had t handle family concerns on their own because
their husbands aces wee glued 10 à computer sree.
Publishers ae also thankful othe following faculty members for critically
eviwing the manuscrits
Lajpat Rai Masood Ahmed
Manoj Langbi
Yunus A. Gengel
John M. Cimbata
Online Resources available at
http://www.mhhe.com/cengel/fma.
Your home page for teaching ld mechanics the Aid Mechonie:
Fundomentols and Applications ex-specii website 1 password protected
and offers resources for instructors.
= Electron Solutions Manual—pxovides PDF es with detailed ped
solutions 1 al te homework problems.
= Lecture Slides provide PowerPoint lecture ses for al chapters.
http://www.mhhe.com/cengel/fma.
Your home page for teaching ld mechanics the Aid Mechonie:
Fundomentols and Applications ex-specii website 1 password protected
and offers resources for instructors.
= Electron Solutions Manual—pxovides PDF es with detailed ped
solutions 1 al te homework problems.
= Lecture Slides provide PowerPoint lecture ses for al chapters.
INTRODUCTION AND
BASIC CONCEPTS
usd in he analysis of ui flow. We star his chapter with a discussion
ofthe phases of matter and the numerous ways of classification of fluid
flow, such as viscous versus imvisci regions of flow, internal versus exter
I this introductory chapter, we present the basic concepts commonly
al flow, compressible versus incompressible low, laminar versus turbulent
‘flow, natural versus forced flow, and steady versus unsteady low. We also
discuss the nop condition at soid-ud interfaces and present a brie his
tory of the development of Mid mechanics.
‘After presenting the concepts of system and control volume, we review
the uni systems tht willbe used. We then discuss how mathematical mod:
els for enginering problems are prepared and how to interpret the re
‘obtained from the analysis of such models. This is followed by a presenta
‘ion of an intuitive systematic problem-solving technique that can be used as
a model in solving engineering problems. Finals, we discuss accuracy, pre
cision, and significant digits in engineering measurements and calculations.
Siren image showing the thermal
plume produced by Profesor Cimbala
Sse welcomes yout the Escinating
‘orld o id mechanics,
CHAPTER
OBJECTIVES
en yo ish eacng his caper,
you shodd be abe
‘= Understandine bas concepts
od mechanics
= Recognize tados pes
ffi fon ries cru
rein price
= Modelengneeing problems
nov tem in asjtematic
= Havea working knowledge
faccagy reo,
sigan digs, ana
recagnie the importance of
imensonalnamogeniy n
engineering cuts
BASIC CONCEPTS
usd in he analysis of ui flow. We star his chapter with a discussion
ofthe phases of matter and the numerous ways of classification of fluid
flow, such as viscous versus imvisci regions of flow, internal versus exter
I this introductory chapter, we present the basic concepts commonly
al flow, compressible versus incompressible low, laminar versus turbulent
‘flow, natural versus forced flow, and steady versus unsteady low. We also
discuss the nop condition at soid-ud interfaces and present a brie his
tory of the development of Mid mechanics.
‘After presenting the concepts of system and control volume, we review
the uni systems tht willbe used. We then discuss how mathematical mod:
els for enginering problems are prepared and how to interpret the re
‘obtained from the analysis of such models. This is followed by a presenta
‘ion of an intuitive systematic problem-solving technique that can be used as
a model in solving engineering problems. Finals, we discuss accuracy, pre
cision, and significant digits in engineering measurements and calculations.
Siren image showing the thermal
plume produced by Profesor Cimbala
Sse welcomes yout the Escinating
‘orld o id mechanics,
CHAPTER
OBJECTIVES
en yo ish eacng his caper,
you shodd be abe
‘= Understandine bas concepts
od mechanics
= Recognize tados pes
ffi fon ries cru
rein price
= Modelengneeing problems
nov tem in asjtematic
= Havea working knowledge
faccagy reo,
sigan digs, ana
recagnie the importance of
imensonalnamogeniy n
engineering cuts
FIGURE 1-1
Fluid mechanics deals wid liquido and
ass in mation orate,
FIGURE 1-2
Deformation of rubi lok paced
esse two paral plates under he
inflence ofa shear foros Te shear
Stress how i (hat om he rubber
qual but opposite shear stress ats on
the upper ple
1-1 = INTRODUCTION
Mechanic is the oldest physical science hat deals with both stationary and
moving bodies under the influence of forces The branch of mechanics that
‘deals with bodies at rest is called statis, while the branch that deals wi
bodies in motion under the action of forces i called dynamics. The subeat-
‘gory Mid mechanie is defined as he science that deals withthe behavior
Of Mid at rest (id sais) or in motion (ui dynamic), and the intra
tion of fluids with solis oF oer fluids atthe boundaries. Fluid mechanics
is also refered to as Muid dynamics by considering fluids at es as a spe
cial case of motion with ero velciy (Fi. 1-1.
Fluid mechanics itself also divided into several categories. The study
of the motion of ds that can be approximated as incompressible (Such
as liquid, especially water, and gases at low specds) is usually refered (0
35 hydrodynamics. A subcategory of hydrodynamics is hydraulics, which
als with liquid flows in pipes and open channels. Gas dynamics deals
‘with he flow of fluids that undergo significant density changes. such a the
Flow of gases trough nozzles at high speeds. The category aerodynamics
seals with the flow of gases (especialy ai) over bodies such as area,
rockets, and automobiles at high or low speeds. Some other specialized
‘ategories such as meteorology, oceanography and hydrology deal with
‘naturally curring flows,
What Is a Fluid?
You will recall from physics that a substance exists in three primary phases
solid, liquid and gas. (At very high temperatures it also exists as plasma)
‘A substance in the liquid or gas phases referred to as a ud, Distinction
between solid and a fluid ts made on the basis of the substance’ a
ity to resis an applied shear (or tangential) stress that tends to change is
shape. A solid can resist an applied shear ses by deforming, whereas a
Jud deforms continuously under the influence of a shear ses, no mater
how smal. In solid, stress is proportional to strain, Du in ds, sess is
‘proportional o sin rate, When a constant shea force is applied. a sold
eventual stops deforming at some fixed nin angle, whereas a lud never
‘ops deforming and approaches constant rte of si
‘Consider a rectangular rubber block tightly placed between wo
the upper plat is pulled with a force F while he lower plate is held fixe
the rubber block deforms, as shown in Fig. 1-2. The angle of deformation a
(called the shea strain or angular displacement) increases in proportion to
the applied force F. Assuming there ts no sip between the rubber and the
plates, the upper surface of the rubber is displaced by an amount equal to
the displacement ofthe upper plate while the lower surface remains sation
ar. In equilibrium, the nt Tore ating on the upper plate in the horizontal
direction must be zero, and thus a force equal and opposite 10 F must be
acting on the plate. This opposing force that develops atthe plate-rubber
interface due 0 friction is expressed as F = 24. where «isthe shear stress
and A i the contact arca between the upper plate and the rubber. When the
force i removed, the rubber returns to Hs original poston. This phenome:
‘hon would also be observed with eter solis such a a sel block povided
that the applied force does not exceed the casi range. If this experiment
‘were epeated with fluid (ith two large parallel plates placed in a large
Fluid mechanics deals wid liquido and
ass in mation orate,
FIGURE 1-2
Deformation of rubi lok paced
esse two paral plates under he
inflence ofa shear foros Te shear
Stress how i (hat om he rubber
qual but opposite shear stress ats on
the upper ple
1-1 = INTRODUCTION
Mechanic is the oldest physical science hat deals with both stationary and
moving bodies under the influence of forces The branch of mechanics that
‘deals with bodies at rest is called statis, while the branch that deals wi
bodies in motion under the action of forces i called dynamics. The subeat-
‘gory Mid mechanie is defined as he science that deals withthe behavior
Of Mid at rest (id sais) or in motion (ui dynamic), and the intra
tion of fluids with solis oF oer fluids atthe boundaries. Fluid mechanics
is also refered to as Muid dynamics by considering fluids at es as a spe
cial case of motion with ero velciy (Fi. 1-1.
Fluid mechanics itself also divided into several categories. The study
of the motion of ds that can be approximated as incompressible (Such
as liquid, especially water, and gases at low specds) is usually refered (0
35 hydrodynamics. A subcategory of hydrodynamics is hydraulics, which
als with liquid flows in pipes and open channels. Gas dynamics deals
‘with he flow of fluids that undergo significant density changes. such a the
Flow of gases trough nozzles at high speeds. The category aerodynamics
seals with the flow of gases (especialy ai) over bodies such as area,
rockets, and automobiles at high or low speeds. Some other specialized
‘ategories such as meteorology, oceanography and hydrology deal with
‘naturally curring flows,
What Is a Fluid?
You will recall from physics that a substance exists in three primary phases
solid, liquid and gas. (At very high temperatures it also exists as plasma)
‘A substance in the liquid or gas phases referred to as a ud, Distinction
between solid and a fluid ts made on the basis of the substance’ a
ity to resis an applied shear (or tangential) stress that tends to change is
shape. A solid can resist an applied shear ses by deforming, whereas a
Jud deforms continuously under the influence of a shear ses, no mater
how smal. In solid, stress is proportional to strain, Du in ds, sess is
‘proportional o sin rate, When a constant shea force is applied. a sold
eventual stops deforming at some fixed nin angle, whereas a lud never
‘ops deforming and approaches constant rte of si
‘Consider a rectangular rubber block tightly placed between wo
the upper plat is pulled with a force F while he lower plate is held fixe
the rubber block deforms, as shown in Fig. 1-2. The angle of deformation a
(called the shea strain or angular displacement) increases in proportion to
the applied force F. Assuming there ts no sip between the rubber and the
plates, the upper surface of the rubber is displaced by an amount equal to
the displacement ofthe upper plate while the lower surface remains sation
ar. In equilibrium, the nt Tore ating on the upper plate in the horizontal
direction must be zero, and thus a force equal and opposite 10 F must be
acting on the plate. This opposing force that develops atthe plate-rubber
interface due 0 friction is expressed as F = 24. where «isthe shear stress
and A i the contact arca between the upper plate and the rubber. When the
force i removed, the rubber returns to Hs original poston. This phenome:
‘hon would also be observed with eter solis such a a sel block povided
that the applied force does not exceed the casi range. If this experiment
‘were epeated with fluid (ith two large parallel plates placed in a large
body of water, for example), the fluid ayer in contact with the upper plate
‘would move with the plate continuously at the velocity of the plate no mat
ter how small he foros F. The fluid velocity would decrease with depth
Because of friction between fui layer, reaching zero a he lower plate.
"You will recall fom satis that stress is defined as force por un arca
and is determined by dividing the force by the area upon which i ats. The
normal component of a force ating on a surface per uni area is called the
‘normal stress, and the tangential component of a force acting on a surface
per unit area is called shear stress (Fig. 1-3) ln a fluid at res the normal
‘resis called pressure. A fluid at rex is at state of zero shear re,
‘When the wall are removed ora liquid container is ited «shear develops
as the liquid moves to re-establish a horizontal re surface.
Ina quid, groups of molecules can move relative 1 cach cher, but he vo
‘une remains relatively constant because ofthe strong cohesive forces between
the molecules. Asa result, a liquid takes the shape ofthe container itis in,
and it forms a fee surface In a larger container in gravitational fil. À gas
on the eter hand, expand unt encouner the walls ofthe container and
ls the entre available space. This is because the gas molecules are widely
spaced, and the cohesive forces between them are very smal, Unlike liquids,
as in an open container cannot form a free surface (Fig. 1-4)
“Although solids and lads ae easily distinguished in mos cases this distin
fon is not so clear in some borden cases Fr example asphal apcan and
hives as a solid since i esis shear ses for short periods of time, When
these Iron are exert overextended periods of time, however, he asphalt
deforms slowly, behaving as a Maid. Some plastics, lad, and durry mixtures
exhibit similar behavior. Sch borderline cases ac beyond the scope of this
text. The figs me deal with in this text will be clearly reognizhle a Ti,
Intermolecular bonds are strongest in solids and weakest in gases. One
reason is that molecules in solids are closely packed together, whereas in
ases they are separated by relatively large distances (Fig. 1-5). The mole:
‘ules in solid are aranged ina pater that is epestd throughout. Because
‘ofthe small distances between molecules in a sold the attractive forces of
molecules on cach aber are large and keep the molecules at fixed positions.
‘The molecular spacing inthe quid phase 3 ot much diferent from that of
FIGURE 1-3
“The normal ses nd shear sees a
the surface fa ui elemen, For
‘ude rest the shear res er
and presse i the ony normal res,
FIGURE 1-4
Unie a tigi agas does not frm a
face ur, a expands t il the
elie salable space.
8.09
O»
e
FIGURE 1-5
‘The arrangement of atoms in diferent phases (a) molecules are at reale inc positions
"ma solid.) groups of molecules move aout cach other in the quid phase, and
(e) individ molecules move about at random in the as pas.
‘would move with the plate continuously at the velocity of the plate no mat
ter how small he foros F. The fluid velocity would decrease with depth
Because of friction between fui layer, reaching zero a he lower plate.
"You will recall fom satis that stress is defined as force por un arca
and is determined by dividing the force by the area upon which i ats. The
normal component of a force ating on a surface per uni area is called the
‘normal stress, and the tangential component of a force acting on a surface
per unit area is called shear stress (Fig. 1-3) ln a fluid at res the normal
‘resis called pressure. A fluid at rex is at state of zero shear re,
‘When the wall are removed ora liquid container is ited «shear develops
as the liquid moves to re-establish a horizontal re surface.
Ina quid, groups of molecules can move relative 1 cach cher, but he vo
‘une remains relatively constant because ofthe strong cohesive forces between
the molecules. Asa result, a liquid takes the shape ofthe container itis in,
and it forms a fee surface In a larger container in gravitational fil. À gas
on the eter hand, expand unt encouner the walls ofthe container and
ls the entre available space. This is because the gas molecules are widely
spaced, and the cohesive forces between them are very smal, Unlike liquids,
as in an open container cannot form a free surface (Fig. 1-4)
“Although solids and lads ae easily distinguished in mos cases this distin
fon is not so clear in some borden cases Fr example asphal apcan and
hives as a solid since i esis shear ses for short periods of time, When
these Iron are exert overextended periods of time, however, he asphalt
deforms slowly, behaving as a Maid. Some plastics, lad, and durry mixtures
exhibit similar behavior. Sch borderline cases ac beyond the scope of this
text. The figs me deal with in this text will be clearly reognizhle a Ti,
Intermolecular bonds are strongest in solids and weakest in gases. One
reason is that molecules in solids are closely packed together, whereas in
ases they are separated by relatively large distances (Fig. 1-5). The mole:
‘ules in solid are aranged ina pater that is epestd throughout. Because
‘ofthe small distances between molecules in a sold the attractive forces of
molecules on cach aber are large and keep the molecules at fixed positions.
‘The molecular spacing inthe quid phase 3 ot much diferent from that of
FIGURE 1-3
“The normal ses nd shear sees a
the surface fa ui elemen, For
‘ude rest the shear res er
and presse i the ony normal res,
FIGURE 1-4
Unie a tigi agas does not frm a
face ur, a expands t il the
elie salable space.
8.09
O»
e
FIGURE 1-5
‘The arrangement of atoms in diferent phases (a) molecules are at reale inc positions
"ma solid.) groups of molecules move aout cach other in the quid phase, and
(e) individ molecules move about at random in the as pas.
FIGURE 1-6
On a microscopic scale, prssoe
is termine by the interaction of
individual gas molecules. However,
e can mesure the pressure ona
Imacrscopie scale witha pressure
se
FIGURE +-7
Fluid dynamics is wed extensively in
the design of ac hearts. Shown
hers the Pen State Electric Total
‘tical Hear
the solid phase, except the molecules are no longer at fixed postions relative
to each other and they can rotat and translate freely. In a liquid, de intr
molecular forces are weaker relaie t solids, but sill rong compared with
ases, The distances between molecules generally increase slighty as à sold
turns liquid, with water being a notable exception.
In the gas phase, the molecules ar ar apar from each othe, and mc
lar owering is nonexistent. Gas molecules move about a random, continu
ally colliding with ach other andthe walls of the container in which they
re confined, Particularly at low denses, the intermolecular forces are very
small and colisons are the only mode of interaction between the mole
us. Molecules in he gas phase are a considerably higher energy level
han they are in the guid or sold phase. Therefore, the gas mus release a
large amount of is energy before i can condense or freeze.
‘Gas and vapor are often used as synonymous words. The vapor phase of
substances customarily called a gas when is above the critical tempera
ture, Vapor usually implies thatthe curren phase is not far fom a state of
condematon.
“Any practical ul system const of large number of molecules, and the
properties ofthe system naturally depend on the behavior ofthese molecules.
For example the pressure of a gas in a container isthe sult of momentum
transfer between the molecules andthe walls of the container. However, one
does ot need to know the behavior o the gas molecules determine the pes
‘ure in the container eis sffcen o atach a presse gage tothe container
(ig. 1-6), This macroscopic or classical approach does not require a knoul
edge ofthe behavior of individual molecules and provides a diet and easy
‘way to analyze engineering problems. The more elaborate microscopic ost
Hal approach based on the average behavior of lage groups of individual
‘molecules rather involve and wed inthis ext only in a supporting role
Application Areas of Fluid Mechanics
Tes important to develop a good understanding ofthe basic principles of
‘uid mechanics, since fluid mechanic is widely used bah in every
activities and in the design of modern engineering systems from vacuum
leaner o supersonic aeraft For example, uid mechanics plays à vial
role inthe human body. The heat constantly pumping blow! 1 all parts
‘ofthe human body trough theatres and veins, andthe lungs are the ies
OFairflow in alternating directions. Al aiii hearts, breathing machines,
and dialysis systems are designed using fui dynamics Fig. 1-7)
"An onlnary house some spect, an exibition hall ied With ap
cations of id mechanics. The piping stems for water, natura gs. and
Sage for an individual howe and the entire city ae designed primarily on
the bas of uid mechanic. The same i alo tue forthe piping and dicing
network of heating and airconditioning systems, A relier imohes tubes
through which the refrigerar lows, a compressor that pressuries the eg
ant and two heat exchangers where the regan absorbs and rejas ea.
Fluid mechanics plays a major role in the design of all these components
Even the operation of ordinary facets is based on (lid mechani
We can also sce numerou application ol lid mechanics in an atomo-
bile. AN components associated with the transportation ofthe fu from the
fuel tank 0 the eyinder-—the Fel fine, fuel pump. and fuel injectors or
On a microscopic scale, prssoe
is termine by the interaction of
individual gas molecules. However,
e can mesure the pressure ona
Imacrscopie scale witha pressure
se
FIGURE +-7
Fluid dynamics is wed extensively in
the design of ac hearts. Shown
hers the Pen State Electric Total
‘tical Hear
the solid phase, except the molecules are no longer at fixed postions relative
to each other and they can rotat and translate freely. In a liquid, de intr
molecular forces are weaker relaie t solids, but sill rong compared with
ases, The distances between molecules generally increase slighty as à sold
turns liquid, with water being a notable exception.
In the gas phase, the molecules ar ar apar from each othe, and mc
lar owering is nonexistent. Gas molecules move about a random, continu
ally colliding with ach other andthe walls of the container in which they
re confined, Particularly at low denses, the intermolecular forces are very
small and colisons are the only mode of interaction between the mole
us. Molecules in he gas phase are a considerably higher energy level
han they are in the guid or sold phase. Therefore, the gas mus release a
large amount of is energy before i can condense or freeze.
‘Gas and vapor are often used as synonymous words. The vapor phase of
substances customarily called a gas when is above the critical tempera
ture, Vapor usually implies thatthe curren phase is not far fom a state of
condematon.
“Any practical ul system const of large number of molecules, and the
properties ofthe system naturally depend on the behavior ofthese molecules.
For example the pressure of a gas in a container isthe sult of momentum
transfer between the molecules andthe walls of the container. However, one
does ot need to know the behavior o the gas molecules determine the pes
‘ure in the container eis sffcen o atach a presse gage tothe container
(ig. 1-6), This macroscopic or classical approach does not require a knoul
edge ofthe behavior of individual molecules and provides a diet and easy
‘way to analyze engineering problems. The more elaborate microscopic ost
Hal approach based on the average behavior of lage groups of individual
‘molecules rather involve and wed inthis ext only in a supporting role
Application Areas of Fluid Mechanics
Tes important to develop a good understanding ofthe basic principles of
‘uid mechanics, since fluid mechanic is widely used bah in every
activities and in the design of modern engineering systems from vacuum
leaner o supersonic aeraft For example, uid mechanics plays à vial
role inthe human body. The heat constantly pumping blow! 1 all parts
‘ofthe human body trough theatres and veins, andthe lungs are the ies
OFairflow in alternating directions. Al aiii hearts, breathing machines,
and dialysis systems are designed using fui dynamics Fig. 1-7)
"An onlnary house some spect, an exibition hall ied With ap
cations of id mechanics. The piping stems for water, natura gs. and
Sage for an individual howe and the entire city ae designed primarily on
the bas of uid mechanic. The same i alo tue forthe piping and dicing
network of heating and airconditioning systems, A relier imohes tubes
through which the refrigerar lows, a compressor that pressuries the eg
ant and two heat exchangers where the regan absorbs and rejas ea.
Fluid mechanics plays a major role in the design of all these components
Even the operation of ordinary facets is based on (lid mechani
We can also sce numerou application ol lid mechanics in an atomo-
bile. AN components associated with the transportation ofthe fu from the
fuel tank 0 the eyinder-—the Fel fine, fuel pump. and fuel injectors or
carburetors—as well as the mixing ofthe fuel and the air in the clinders
and the purging of combustion gases in exhaust pipes are analyzed using
"uid mechanics. Fluid mochanies i also used inthe design of the heating
and airconditioning sytem. the hydraulic brakes, the power steering, the
automate transmision, the Ibricaton systems the cooling system of the
engine block including the radiator and the water pump, and even the tes.
‘The sleek sreamlined shape of recent model cars isthe result of efforts to
minimize drag by using extensive analysis of flow over surfaces.
‘On a broader scale. fluid mechanics plays a major part in he design and
analysis of aireat, bots, submarines, rocket, jet engines, wind turbines,
biomedical devices, cooling systems for electonic components, and ts:
portation systems for moving wate, crude il, and natural gas. It alo
‘Considered in the design of building, bridges, and even billboards to make
Sure thatthe structures can withstand wind loading. Numerous natural phe
‘nomena such as the rain cycle, weather patterns, the rise of ground Wate to
the tops of res, winds, ocean waves and currents in lange water bodies re
ako governed by the principles of Haid mechanics (Fig, 1-8)
Poner Para ay
OS ar Rey Comisión MRC) at rn i LLP
Foi mania re
Inds gto
FIGURE 1-8
Some aplication res of fluid mechas
and the purging of combustion gases in exhaust pipes are analyzed using
"uid mechanics. Fluid mochanies i also used inthe design of the heating
and airconditioning sytem. the hydraulic brakes, the power steering, the
automate transmision, the Ibricaton systems the cooling system of the
engine block including the radiator and the water pump, and even the tes.
‘The sleek sreamlined shape of recent model cars isthe result of efforts to
minimize drag by using extensive analysis of flow over surfaces.
‘On a broader scale. fluid mechanics plays a major part in he design and
analysis of aireat, bots, submarines, rocket, jet engines, wind turbines,
biomedical devices, cooling systems for electonic components, and ts:
portation systems for moving wate, crude il, and natural gas. It alo
‘Considered in the design of building, bridges, and even billboards to make
Sure thatthe structures can withstand wind loading. Numerous natural phe
‘nomena such as the rain cycle, weather patterns, the rise of ground Wate to
the tops of res, winds, ocean waves and currents in lange water bodies re
ako governed by the principles of Haid mechanics (Fig, 1-8)
Poner Para ay
OS ar Rey Comisión MRC) at rn i LLP
Foi mania re
Inds gto
FIGURE 1-8
Some aplication res of fluid mechas
FIGURE 1-9
Segment of Pergamon pipeline,
Each ly pipe section was
1310 ¡Som ia diameter
FIGURE 1-10
Amine hoist powered
byarevesible water whee,
1-2 » ABRIEF HISTORY OF FLUID MECHANICS!
One ofthe fis engineering problems humanki faced a cites were devel-
‘oped was the supply of water for domestic use and ration of crops. Our
ban lifestyles can be retained only with abundant water, and ii clar
from archeology that every succesful civilization of prehistory invested in
the construction and maintenance of water systems. The Roman aqueduc,
some of which ae sll in use, are the best known examples. However, pe.
aps the most impressive engineering from a technical viewpoint vas done
atthe Hallenis iy of Pergamon in presentday Turkey. There, rom 28310
133 vc, they built a series of pressurized Teal and clay pipelines (Fi. 1-9),
up to 45 km long that operated at pressures exceeding 1.7 MPa (180 m of
head). Unfortunately, the names of almost all thse early builders are lot 40
history.
“The caries recognized contribution to lid mechanies theory was made
by the Greek mathematician Archimedes (285-212 nc). He formulated and
applied the Duoyancy principle in history" is nondestuctive tes to deter»
ie the gold content of the crown of King Hier I. The Romans built great
‘aqueduct: and educated many conquered people on the benefits of clean
Water, but overall had a poor understanding of fluids theory, (Perhaps they
Shouldn't have Killed Archimedes when they sicked Syracuse)
During the Middle Ages, the application of fuid machinery slowly but
study expanded. Elegant piton pumps were developed for dewatering
mines, and the watermill and windmil were perfected 0 grind grin forge
meal, and fr other tasks. For the first time in record human history. si
nificant work was being done without the power of a muscle supplied by a
person or animal, and these inventions are generally credited with enabling
the later industrial revolution. Again the creator of most of the progress
are unknown, but the devices themselves were well document by several
{echnical writers such as Georgias Agricola (Fig. 1-10)
“The Renaissance brought continued development of fluid systems and
machines, but more importantly. the scientific method was perfected and
‘doped throughout Europe, Simon Stevin (1548-1617), Galileo Galilei
(1564-1642. Edme Marine (1620-1684), and Evangelista Tortel
(1608-1647) were among the first to apply the method to ido a they
investigated hydrostatic presure disribucions and vacuums. That work
as integrated and refined by the brilliant mathematician and philosopher,
Blaise Pascal (1623-1662). The Hallan monk, Benedeto Castell (1577.
16-44) was the frst person to publish a statement ofthe continuity principle
for fluids, Besides formulating his equations of mation for solid, Sir Isaac
Newton (1643-1727) appli his laws to Kids and explored fluid inertia
and resistance, fee jets and viscosity. That effort was built upon by Daniel
Bemoull (1700-1782), a Swiss, and his associate Leonard Euler (1707
1783). Together, their work defined the energy and momentum equations
Bemoull's 1738 classic teatie Hydrodynamica may be considered the ira
Fluid mechanics text. Final, Jean d'Alembert (1717-1789) developed the
idea of velocity and acceleration components, a differential expression of
ri sio conned y Pre Gir Bern of Oo Ste Ur
Segment of Pergamon pipeline,
Each ly pipe section was
1310 ¡Som ia diameter
FIGURE 1-10
Amine hoist powered
byarevesible water whee,
1-2 » ABRIEF HISTORY OF FLUID MECHANICS!
One ofthe fis engineering problems humanki faced a cites were devel-
‘oped was the supply of water for domestic use and ration of crops. Our
ban lifestyles can be retained only with abundant water, and ii clar
from archeology that every succesful civilization of prehistory invested in
the construction and maintenance of water systems. The Roman aqueduc,
some of which ae sll in use, are the best known examples. However, pe.
aps the most impressive engineering from a technical viewpoint vas done
atthe Hallenis iy of Pergamon in presentday Turkey. There, rom 28310
133 vc, they built a series of pressurized Teal and clay pipelines (Fi. 1-9),
up to 45 km long that operated at pressures exceeding 1.7 MPa (180 m of
head). Unfortunately, the names of almost all thse early builders are lot 40
history.
“The caries recognized contribution to lid mechanies theory was made
by the Greek mathematician Archimedes (285-212 nc). He formulated and
applied the Duoyancy principle in history" is nondestuctive tes to deter»
ie the gold content of the crown of King Hier I. The Romans built great
‘aqueduct: and educated many conquered people on the benefits of clean
Water, but overall had a poor understanding of fluids theory, (Perhaps they
Shouldn't have Killed Archimedes when they sicked Syracuse)
During the Middle Ages, the application of fuid machinery slowly but
study expanded. Elegant piton pumps were developed for dewatering
mines, and the watermill and windmil were perfected 0 grind grin forge
meal, and fr other tasks. For the first time in record human history. si
nificant work was being done without the power of a muscle supplied by a
person or animal, and these inventions are generally credited with enabling
the later industrial revolution. Again the creator of most of the progress
are unknown, but the devices themselves were well document by several
{echnical writers such as Georgias Agricola (Fig. 1-10)
“The Renaissance brought continued development of fluid systems and
machines, but more importantly. the scientific method was perfected and
‘doped throughout Europe, Simon Stevin (1548-1617), Galileo Galilei
(1564-1642. Edme Marine (1620-1684), and Evangelista Tortel
(1608-1647) were among the first to apply the method to ido a they
investigated hydrostatic presure disribucions and vacuums. That work
as integrated and refined by the brilliant mathematician and philosopher,
Blaise Pascal (1623-1662). The Hallan monk, Benedeto Castell (1577.
16-44) was the frst person to publish a statement ofthe continuity principle
for fluids, Besides formulating his equations of mation for solid, Sir Isaac
Newton (1643-1727) appli his laws to Kids and explored fluid inertia
and resistance, fee jets and viscosity. That effort was built upon by Daniel
Bemoull (1700-1782), a Swiss, and his associate Leonard Euler (1707
1783). Together, their work defined the energy and momentum equations
Bemoull's 1738 classic teatie Hydrodynamica may be considered the ira
Fluid mechanics text. Final, Jean d'Alembert (1717-1789) developed the
idea of velocity and acceleration components, a differential expression of
ri sio conned y Pre Gir Bern of Oo Ste Ur
continuity, and his “paradox” of ero resistance to steady uniform mation
‘over a body
The development of fluid mechanics theory through the end ofthe cih:
teenth century had litle impact on engineering since fluid properties and
parameters were poorly quanificd and mont theories were abstractions tha
‘ould not be quantified for design purposes. That was to change withthe
development of the French school of engineering led by Riche de Prony
(1755-1839). Prony (sill known for his brake to measure shaft powcr) and
his associates in Paris atthe Ecole Polytechnique and the École des Ponts
et Chaussées were the fis o integrate calculus and sient theory into
the engineering curiculum, which became the model for the fest of the
‘world. (So now you know whom to Dame for you painful reshman year)
‘Antonie Chery (1718-1798), Louis Naver (1785-1836), Gaspard Coriolis
(1792-1843), Henry Darcy (1803-1858). and many other contnibutors to
fluid engineering and theory were students andlor instructors at the schools,
By the mid nineteenth century. fundamental advances were coming on
several fronts The physician Jean Poisuile (1799-1869) had accurately
‘measured flow in capillary tubes for multiple uid, while in Germany
Got Hagen (1797-1884) had differentiated between laminar and tub
lent flow in pipes. In England, Lord Osborne Reynolds (1842-1912) con
‘inuod that work (Fig. 1-11) and developed the dimensionless number that
bears his name. Similar. in parallel 10 the early work of Navier. George
Stokes (1819-1903) completed the general equation of uid motion (with,
fit) that takes thei names, William Froude (1810-1879) almost single
handedly developed the procedures and proved the value of physical model
testing. American experte had become equal 10 the Europeans as demon:
strate by James Francis (1815-1892) and Lester Peton's (1829-1908) pio
neering work in turbines and Clemens Henchel's (1842-1930) invention of
the Vent meter
Tn alton to Reynolds and Stokes, many notable contributions were made
to fluid theory in the late nineteenth century by lsh and English sien,
including Wiliam Thomson, Lord Kelvin (1824-1907), William Swut, Lord
Rayleigh (1842-1919) and Sir Horace Lamb (1849-1934) These individu
I investigated a large number of problems, including dimensional analysis,
Frrtational flow, vortex motion, cavitation, and wanes. In a broader sense
Figure +1
‘Osborne Reynold’ original apparatus
for demonstrating the onset o ut
Tence in pipes, being operated
by John enka tthe University
‘of Manchester in 197,
‘over a body
The development of fluid mechanics theory through the end ofthe cih:
teenth century had litle impact on engineering since fluid properties and
parameters were poorly quanificd and mont theories were abstractions tha
‘ould not be quantified for design purposes. That was to change withthe
development of the French school of engineering led by Riche de Prony
(1755-1839). Prony (sill known for his brake to measure shaft powcr) and
his associates in Paris atthe Ecole Polytechnique and the École des Ponts
et Chaussées were the fis o integrate calculus and sient theory into
the engineering curiculum, which became the model for the fest of the
‘world. (So now you know whom to Dame for you painful reshman year)
‘Antonie Chery (1718-1798), Louis Naver (1785-1836), Gaspard Coriolis
(1792-1843), Henry Darcy (1803-1858). and many other contnibutors to
fluid engineering and theory were students andlor instructors at the schools,
By the mid nineteenth century. fundamental advances were coming on
several fronts The physician Jean Poisuile (1799-1869) had accurately
‘measured flow in capillary tubes for multiple uid, while in Germany
Got Hagen (1797-1884) had differentiated between laminar and tub
lent flow in pipes. In England, Lord Osborne Reynolds (1842-1912) con
‘inuod that work (Fig. 1-11) and developed the dimensionless number that
bears his name. Similar. in parallel 10 the early work of Navier. George
Stokes (1819-1903) completed the general equation of uid motion (with,
fit) that takes thei names, William Froude (1810-1879) almost single
handedly developed the procedures and proved the value of physical model
testing. American experte had become equal 10 the Europeans as demon:
strate by James Francis (1815-1892) and Lester Peton's (1829-1908) pio
neering work in turbines and Clemens Henchel's (1842-1930) invention of
the Vent meter
Tn alton to Reynolds and Stokes, many notable contributions were made
to fluid theory in the late nineteenth century by lsh and English sien,
including Wiliam Thomson, Lord Kelvin (1824-1907), William Swut, Lord
Rayleigh (1842-1919) and Sir Horace Lamb (1849-1934) These individu
I investigated a large number of problems, including dimensional analysis,
Frrtational flow, vortex motion, cavitation, and wanes. In a broader sense
Figure +1
‘Osborne Reynold’ original apparatus
for demonstrating the onset o ut
Tence in pipes, being operated
by John enka tthe University
‘of Manchester in 197,
FIGURE 1-12
“The Wright bothers take
Flight at Kiny Hank.
ary tia Car Ps
‘Poca De DIE pe 2006)
FIGURE 1-13
‘Old and new wind turbine technologies
noah of Woodward, OK. The mode
turbines have vpo $ MW cape,
{heir work also explored the links between fluid mechanic, hermodynam-
ies and heat traste
‘The dawn ofthe twentieth century brought two monumental development.
Fin, in 1903, the self-taught Wright bothers (Wilbur. 1867-1912: Orville,
1871-1948) invented the airplane through application of theory and deter
mined experimentation. Ther primitive invention was complete and contained
“lt major aspects of modern aircraft (Fig. 1-12). The Navier-Stokes equa-
‘ions were of litle use upto this time because they wer o0 dificult sole.
In a pioneering paper in 1904, the German Ludwig Prandtl (1875-1953)
‘showed that id hws can be divided ino à aye nar he walls the bound-
fry layer where the fiction effecs are significant and an outer Layer where
Such effets are negligible and the simplified Euler and Bemoul equations
are applicable, His students. Teodor von Kármán (1881-1963), Paul Blasius
(1883-1970) Johann Nikuradse (1894-1979), and thes, ui on that theory
in both hydraulic and aerodynamic applications. (During World War Hl bah
‘ies benefited from the theory as Prandd remsined in Germany while his
best tent, the Hungarian-bern von Kärmän, worked in America]
‘The mid twentieth century could be considered a golden age of fluid
mechanics applications. Existing theories were adequate for the tasks at
hand, and fluid properties and parameters were well defined. These sup-
ported a huge expansion of the aeronautical, chemical. industrial, and
Water resources sectors; each of which pushed fluid mechanics in new
iections Fluid mechanic research and work i the ate twentieth century
were dominated by the development of the digital computer in America.
‘The ability o solve large complex problems, such as global climate mod-
cling or the optimization ofa turbine blade has provided a benefit to our
Society thatthe eighteenth-century developers of fluid mechanics could
ever have imagined (Fig. 1-13). The principles presented in the folowing
pages have been applied to flows ranging from à moment at the micro.
copie seal to 50 years of simulation for an entre river basin. ts truly
mind boggling
Where will fluid mechanics go in the twenty-first century and beyond?
Frankly, even limited extrapolation beyond the resent would be sheer fly.
However. if history tll us anything, iis that engineers willbe applying
what they know 10 benefit society, researching what they dont know, nd
having à great time in he proces
1-3 » THE NO-SLIP CONDITION
Fluid flow is often confined by solid surfaces, and is important 10 under
‘stand how the presence of solid surfaces affects fluid flow. We know that
"water in a iver cannot flow through large rocks, and must go around them.
‘That i, the water velocity normal tothe rock surface must be zero, and
water approaching the surface normally comes to a complete stop athe sur
Face, What is not as obvious is that water approaching the rock any angle
“lso comes to a complete stop atthe rock surface, and thus he tangential
velocity of water atthe surface s alo 20
‘Consider the flow of a fluid in astaonary pipe or over a solid surface
that is nonporous (i. impermeable tothe fluid). All experimental observa-
tions indicate that a fluid in motion comes to a complete stop atthe surface
“The Wright bothers take
Flight at Kiny Hank.
ary tia Car Ps
‘Poca De DIE pe 2006)
FIGURE 1-13
‘Old and new wind turbine technologies
noah of Woodward, OK. The mode
turbines have vpo $ MW cape,
{heir work also explored the links between fluid mechanic, hermodynam-
ies and heat traste
‘The dawn ofthe twentieth century brought two monumental development.
Fin, in 1903, the self-taught Wright bothers (Wilbur. 1867-1912: Orville,
1871-1948) invented the airplane through application of theory and deter
mined experimentation. Ther primitive invention was complete and contained
“lt major aspects of modern aircraft (Fig. 1-12). The Navier-Stokes equa-
‘ions were of litle use upto this time because they wer o0 dificult sole.
In a pioneering paper in 1904, the German Ludwig Prandtl (1875-1953)
‘showed that id hws can be divided ino à aye nar he walls the bound-
fry layer where the fiction effecs are significant and an outer Layer where
Such effets are negligible and the simplified Euler and Bemoul equations
are applicable, His students. Teodor von Kármán (1881-1963), Paul Blasius
(1883-1970) Johann Nikuradse (1894-1979), and thes, ui on that theory
in both hydraulic and aerodynamic applications. (During World War Hl bah
‘ies benefited from the theory as Prandd remsined in Germany while his
best tent, the Hungarian-bern von Kärmän, worked in America]
‘The mid twentieth century could be considered a golden age of fluid
mechanics applications. Existing theories were adequate for the tasks at
hand, and fluid properties and parameters were well defined. These sup-
ported a huge expansion of the aeronautical, chemical. industrial, and
Water resources sectors; each of which pushed fluid mechanics in new
iections Fluid mechanic research and work i the ate twentieth century
were dominated by the development of the digital computer in America.
‘The ability o solve large complex problems, such as global climate mod-
cling or the optimization ofa turbine blade has provided a benefit to our
Society thatthe eighteenth-century developers of fluid mechanics could
ever have imagined (Fig. 1-13). The principles presented in the folowing
pages have been applied to flows ranging from à moment at the micro.
copie seal to 50 years of simulation for an entre river basin. ts truly
mind boggling
Where will fluid mechanics go in the twenty-first century and beyond?
Frankly, even limited extrapolation beyond the resent would be sheer fly.
However. if history tll us anything, iis that engineers willbe applying
what they know 10 benefit society, researching what they dont know, nd
having à great time in he proces
1-3 » THE NO-SLIP CONDITION
Fluid flow is often confined by solid surfaces, and is important 10 under
‘stand how the presence of solid surfaces affects fluid flow. We know that
"water in a iver cannot flow through large rocks, and must go around them.
‘That i, the water velocity normal tothe rock surface must be zero, and
water approaching the surface normally comes to a complete stop athe sur
Face, What is not as obvious is that water approaching the rock any angle
“lso comes to a complete stop atthe rock surface, and thus he tangential
velocity of water atthe surface s alo 20
‘Consider the flow of a fluid in astaonary pipe or over a solid surface
that is nonporous (i. impermeable tothe fluid). All experimental observa-
tions indicate that a fluid in motion comes to a complete stop atthe surface
and assumes a zero velocity relative 10 the surface, That i, afd in direct
Contact with a slid "sticks" to the surface, and there is no slip. This is
Known as the no-lip condition, The fluid property responsible for he no
slip condition and the development of the boundary layer is vs and is
discussed in Chap. 2.
“The photograph in Fig. 1-14 clearly shows the evolution ofa velocity gra
diet asa result ofthe fui sticking 10 the surface of a Blunt nose. The layer
{hat sticks 1 the surface slows the adjacent Maid ayer because of visos
forces between the fluid layers, which slows the next layer, and soon. À
consequence of the no-slip condition is that ll velocity profiles most have
Zero values with respect to the surface a the points of contact Between a
fluid and a solid surface (Fig. 1-15). Therefore, the no-tip condition is
responsible forthe development of the velocity profil, The flow region
adjacent tothe wal in which the viscous effects (and thus the velocity ra
‘ions are significant ¡called the boundary layer. Another consequence
{ofthe nosip condition is the surface drag, or skin friction drag, which is
the force a fluid exerts ona surface inthe flow direction
‘When a fluid is forced to flow over a curved surface, such as the back
de ofa cylinder the boundary layer may no longer remain atachcd to the
Surface and separates from the surface—a proces called flow separation
(Fig, 1-16). We emphasize hat the noslip condition applies everwhere
along the sure, even downsteam ofthe separation point, Flow separation
is disused in greater deal in Chap. 9,
A phenomenon Similar to the no-ip condition occurs in heut transe.
‘When two bodies a different temperatures are brought into contact, heat
transfer occurs such that both bodies assume the same temperature at the
points of contact Therefore, a lid and a solid surface have the Same fem
perature atthe points of contact, This is known as no-temperature jump
condition,
1-4 » CLASSIFICATION OF FLUID FLOWS
Easier we defined fluid mechanics as th science that deals withthe beh
ior of fluid a es or in motion, and he interaction of Aids with solids or
tothe fluids atthe boundaries. There is à wide variety of lid low prob
lems encountered in practice, and it is usually convenient to classify them
on the bass of some common characteristics to make it fssible 10 study
them in groups. There are many ways to classify fluid flow problems, and
here we present some general ca
FIGURE 1-14
‘The development ofa veloiy profile
ue tothe noi conditions uid
FIGURE 1-15.
A Mid flowing over stationary
surface comes 1 complete sop at
the surface because ofthe no
‘onion
Contact with a slid "sticks" to the surface, and there is no slip. This is
Known as the no-lip condition, The fluid property responsible for he no
slip condition and the development of the boundary layer is vs and is
discussed in Chap. 2.
“The photograph in Fig. 1-14 clearly shows the evolution ofa velocity gra
diet asa result ofthe fui sticking 10 the surface of a Blunt nose. The layer
{hat sticks 1 the surface slows the adjacent Maid ayer because of visos
forces between the fluid layers, which slows the next layer, and soon. À
consequence of the no-slip condition is that ll velocity profiles most have
Zero values with respect to the surface a the points of contact Between a
fluid and a solid surface (Fig. 1-15). Therefore, the no-tip condition is
responsible forthe development of the velocity profil, The flow region
adjacent tothe wal in which the viscous effects (and thus the velocity ra
‘ions are significant ¡called the boundary layer. Another consequence
{ofthe nosip condition is the surface drag, or skin friction drag, which is
the force a fluid exerts ona surface inthe flow direction
‘When a fluid is forced to flow over a curved surface, such as the back
de ofa cylinder the boundary layer may no longer remain atachcd to the
Surface and separates from the surface—a proces called flow separation
(Fig, 1-16). We emphasize hat the noslip condition applies everwhere
along the sure, even downsteam ofthe separation point, Flow separation
is disused in greater deal in Chap. 9,
A phenomenon Similar to the no-ip condition occurs in heut transe.
‘When two bodies a different temperatures are brought into contact, heat
transfer occurs such that both bodies assume the same temperature at the
points of contact Therefore, a lid and a solid surface have the Same fem
perature atthe points of contact, This is known as no-temperature jump
condition,
1-4 » CLASSIFICATION OF FLUID FLOWS
Easier we defined fluid mechanics as th science that deals withthe beh
ior of fluid a es or in motion, and he interaction of Aids with solids or
tothe fluids atthe boundaries. There is à wide variety of lid low prob
lems encountered in practice, and it is usually convenient to classify them
on the bass of some common characteristics to make it fssible 10 study
them in groups. There are many ways to classify fluid flow problems, and
here we present some general ca
FIGURE 1-14
‘The development ofa veloiy profile
ue tothe noi conditions uid
FIGURE 1-15.
A Mid flowing over stationary
surface comes 1 complete sop at
the surface because ofthe no
‘onion
FIGURE 1-17
The flow fan originally uniform
‘ud steam over a lat plate, and
the regions of vous flow (net to
the plate on bh sides) and inviscid
‘os (aay rom the plat)
FIGURE 1-18
External low over a ens al, and
the turbulent wake region being
Viscous versus Inviscid Regions of Flow
When two fluid layers move relative to each other, a friction force dew
‘ops between them and the slower layer ties o slow down the faster lier,
‘This internal resistance to Flow is quantified bythe Maid property scan,
which is a measure of intemal stickiness of the fui Viscosity is caused
by cohesive forces between the molecules in quid and by molecular col
sons in gases. There i no fluid with ero viscosity, and ths al id flows
involve viseous effets to some degree. Flows in which the fitional effects
are significant are called viscous flows, However, in many flows of practi
al interest here are regions (picaly regions not close to slid surfaces)
Where viscous forces are negligibly small compared to ineial or pressure
forces. Neglecting the viscous terms in such invscid flow regions greatly
simplifies the analysis without much los in accuracy.
The development of viscous and inviscid regions of flow as a result of
inserting a at plate paral into Fluid steam of unilorm velocity i shown
in Fig. 1-17, The Mid sticks tothe plate on bath sides because ofthe noi
condition, andthe thin boundary ayer in which the viscous effects ae i
ant near the plate surface isthe wscous flow regio. The region of flow on
both sides away from the plate and largely unaffected by the presence of the
late the invsch flow region
Internal versus External Flow
A fluid flow is classified as being internal or eternal, depending on whether
the Hd flows in a contined space or over a surface. The flow of an
‘unbounded Maid ever à surface such as a plate, wire, or a pipe is external
‘low, The flow in a pipe or dot is internal flow if the fui is bounded
by solid surfaces. Water flow ina pipe, for example, i intemal flow, and
airflow over a ball or over an exposed pipe during a windy day is extra
flow (Fig. 1-18). The flow of ges in a uct i ale open-channel flow 4
the duct only partly filed withthe lid and there À a Tree surface, The
Fous of water inves and irigation ich ae examples of sich Mow,
Internal flows are dominated by the influence of viscosity thoughout
the flow field In external flows the viscous effects are limited to boundary
layers near sold surfaces and o wake regions downstream of Boies.
Compressible versus Incompressible Flow
A flow is clasified as being compressible or incompressible, depending
où the level of variation of density during flow. Incompessibili is an
Appronimtion, in which the flow is said o be incompressible ifthe density
‘emai nearly constant throughout. Therefore the volume of every portion
‘of id remains unchanged over the course of is motion when the Flow is
approximsted ss incompressible,
"The denis of iquids are essentially constant, and thus the flow of tig
id typically incompressible, Therefore, liquids ae usually referred to as
incompressible substances. À pressure of 210 am, for example, causes the
density of quid water at L atm to change by just 1 percent. Gases on the
¿ber hand, are highly compressible. A pressure change of jus 001 am, for
‘example, causes a change of 1 percent inthe density of atmosphere ar,
The flow fan originally uniform
‘ud steam over a lat plate, and
the regions of vous flow (net to
the plate on bh sides) and inviscid
‘os (aay rom the plat)
FIGURE 1-18
External low over a ens al, and
the turbulent wake region being
Viscous versus Inviscid Regions of Flow
When two fluid layers move relative to each other, a friction force dew
‘ops between them and the slower layer ties o slow down the faster lier,
‘This internal resistance to Flow is quantified bythe Maid property scan,
which is a measure of intemal stickiness of the fui Viscosity is caused
by cohesive forces between the molecules in quid and by molecular col
sons in gases. There i no fluid with ero viscosity, and ths al id flows
involve viseous effets to some degree. Flows in which the fitional effects
are significant are called viscous flows, However, in many flows of practi
al interest here are regions (picaly regions not close to slid surfaces)
Where viscous forces are negligibly small compared to ineial or pressure
forces. Neglecting the viscous terms in such invscid flow regions greatly
simplifies the analysis without much los in accuracy.
The development of viscous and inviscid regions of flow as a result of
inserting a at plate paral into Fluid steam of unilorm velocity i shown
in Fig. 1-17, The Mid sticks tothe plate on bath sides because ofthe noi
condition, andthe thin boundary ayer in which the viscous effects ae i
ant near the plate surface isthe wscous flow regio. The region of flow on
both sides away from the plate and largely unaffected by the presence of the
late the invsch flow region
Internal versus External Flow
A fluid flow is classified as being internal or eternal, depending on whether
the Hd flows in a contined space or over a surface. The flow of an
‘unbounded Maid ever à surface such as a plate, wire, or a pipe is external
‘low, The flow in a pipe or dot is internal flow if the fui is bounded
by solid surfaces. Water flow ina pipe, for example, i intemal flow, and
airflow over a ball or over an exposed pipe during a windy day is extra
flow (Fig. 1-18). The flow of ges in a uct i ale open-channel flow 4
the duct only partly filed withthe lid and there À a Tree surface, The
Fous of water inves and irigation ich ae examples of sich Mow,
Internal flows are dominated by the influence of viscosity thoughout
the flow field In external flows the viscous effects are limited to boundary
layers near sold surfaces and o wake regions downstream of Boies.
Compressible versus Incompressible Flow
A flow is clasified as being compressible or incompressible, depending
où the level of variation of density during flow. Incompessibili is an
Appronimtion, in which the flow is said o be incompressible ifthe density
‘emai nearly constant throughout. Therefore the volume of every portion
‘of id remains unchanged over the course of is motion when the Flow is
approximsted ss incompressible,
"The denis of iquids are essentially constant, and thus the flow of tig
id typically incompressible, Therefore, liquids ae usually referred to as
incompressible substances. À pressure of 210 am, for example, causes the
density of quid water at L atm to change by just 1 percent. Gases on the
¿ber hand, are highly compressible. A pressure change of jus 001 am, for
‘example, causes a change of 1 percent inthe density of atmosphere ar,
When analyzing rockets, spacecraft and other systems that involve high
speed ges flows (Fig. 1-19), the flow sped is often exprese in terms of
the dimensionless Mach number defined as
Speed of low
where cis the speed of sound whose vale is 346 m/s in ai at room tempera:
ture at sea level A flow i called sonic when Ma = 1, subsonic when Ma < L
Supersonic when Ma > 1. and hypersonic when Ma >> 1. Dimensionless
parameters are discussed in detail in Chap. 7. Compressible Flow is discussed
in dealin Chop. 12
Liquid flows are incompressible to a high lve of accuracy, but the level
of variation of density in gas flows and the consequent level of approx
‘mation made when modeling gas flows as incompressible depends on the
Mach number. Gas flows can often be approximated as incompressible if the
density changes are under about $ percent, which is usually the case when
Ma < 03. Therefor, the compressibility effecs of ar at room tempera:
ture canbe neglected at speeds under about 100 mí. Compressibily effects
Should never be neglected for supersonic flows, however, since compress:
ible flow phenomena like shock waves occur (Fig. 1-19)
‘Small density changes of liquid corresponding to large pressure changes
can all have important consequences. The Iriting "water hammer” in à
‘water pip, for example, I caused by the vibrations of the pipe generated by
the reflection of pressure waves following the sudden closing ofthe valves
Laminar versus Turbulent Flow
Some flows are smooth and onlery while others ae rather chaotic. The
highly ordered fluid motion characterized by smooth ayes of li is called
laminar. The word laminar comes from the movement of adjacent fluid
particles together in “laminae.” The flow of high viscosiy Maids such as
fils au low velocities typically lamina. The highly disordered fluid mation
that typically occurs a high velocities ands characterized by velocity fluc
tuations i called turbulent (Fig. 1-20). The flow of low-viscosity Fluids
such as air at high velocities is typically turbulent. À flow that alternates
between being laminar and turbulent scaled transitional. The experiments
conducted by Osborne Reynolds in the 1880s resulted inthe establishment
fof the dimensionless Reynolds number, Re, as the key parameter fr the
determination of the Flow regime in pipes (Chap. 8)
Natural (or Unforced) versus Forced Flow
A fluid flow is said to be natural or forced, depending on how the fluid
‘motion i inated. In forced flow, a fui is forced to low over a surface
‘or in a pipe by external means such as a pump or a fan. In natural flows,
"uid motion is due to natural means such as the buoyancy effect, which
‘manifests itself as the rise of warmer and tus lighter fluid and the fall of
cooler (and thus dense) uid (Fig. 1-21), In solar hot-water systems, for
example, the thermosiphoning effets commonly used to replace pumps by
Placing the water tank sufficiently above the sla collectors,
FIGURE 1-19
Schlieren image ofthe spherical shook
vane produced by abusing ballon
athe Pen Sate Gas Dynamics Lab,
‘Several secondary shocks are seen in
he ai surrounding the ballon.
FIGURE 1-20
Laminar transition, nd turbulent
lows over lat plate
speed ges flows (Fig. 1-19), the flow sped is often exprese in terms of
the dimensionless Mach number defined as
Speed of low
where cis the speed of sound whose vale is 346 m/s in ai at room tempera:
ture at sea level A flow i called sonic when Ma = 1, subsonic when Ma < L
Supersonic when Ma > 1. and hypersonic when Ma >> 1. Dimensionless
parameters are discussed in detail in Chap. 7. Compressible Flow is discussed
in dealin Chop. 12
Liquid flows are incompressible to a high lve of accuracy, but the level
of variation of density in gas flows and the consequent level of approx
‘mation made when modeling gas flows as incompressible depends on the
Mach number. Gas flows can often be approximated as incompressible if the
density changes are under about $ percent, which is usually the case when
Ma < 03. Therefor, the compressibility effecs of ar at room tempera:
ture canbe neglected at speeds under about 100 mí. Compressibily effects
Should never be neglected for supersonic flows, however, since compress:
ible flow phenomena like shock waves occur (Fig. 1-19)
‘Small density changes of liquid corresponding to large pressure changes
can all have important consequences. The Iriting "water hammer” in à
‘water pip, for example, I caused by the vibrations of the pipe generated by
the reflection of pressure waves following the sudden closing ofthe valves
Laminar versus Turbulent Flow
Some flows are smooth and onlery while others ae rather chaotic. The
highly ordered fluid motion characterized by smooth ayes of li is called
laminar. The word laminar comes from the movement of adjacent fluid
particles together in “laminae.” The flow of high viscosiy Maids such as
fils au low velocities typically lamina. The highly disordered fluid mation
that typically occurs a high velocities ands characterized by velocity fluc
tuations i called turbulent (Fig. 1-20). The flow of low-viscosity Fluids
such as air at high velocities is typically turbulent. À flow that alternates
between being laminar and turbulent scaled transitional. The experiments
conducted by Osborne Reynolds in the 1880s resulted inthe establishment
fof the dimensionless Reynolds number, Re, as the key parameter fr the
determination of the Flow regime in pipes (Chap. 8)
Natural (or Unforced) versus Forced Flow
A fluid flow is said to be natural or forced, depending on how the fluid
‘motion i inated. In forced flow, a fui is forced to low over a surface
‘or in a pipe by external means such as a pump or a fan. In natural flows,
"uid motion is due to natural means such as the buoyancy effect, which
‘manifests itself as the rise of warmer and tus lighter fluid and the fall of
cooler (and thus dense) uid (Fig. 1-21), In solar hot-water systems, for
example, the thermosiphoning effets commonly used to replace pumps by
Placing the water tank sufficiently above the sla collectors,
FIGURE 1-19
Schlieren image ofthe spherical shook
vane produced by abusing ballon
athe Pen Sate Gas Dynamics Lab,
‘Several secondary shocks are seen in
he ai surrounding the ballon.
FIGURE 1-20
Laminar transition, nd turbulent
lows over lat plate
FIGURE 1-24
In the seinen image ofa git in a
Swimming sit the mc of lige.
amer ar adjacent her body
Bioode animals are surounde by
thermal plumes of rising warm ae,
FIGURE 1-22
Comparison ola) instantaneous
snapshot of an unsteady flow, and
(Dong exposure pear ofthe
Same los
Steady versus Unsteady Flow
‘The terms steady and uniform ae used frequently in engineering, and thus
it important to have a clear understanding of their meanings The term
steady implies no change of properties, velocity temperature, ec. ata point
With me, The opposite of sicady is unsteady. The term uniform implies no
Change wth location over a specified region These meanings are consent
with their everyday use (steady girliiend, uniform distribution. e.
‘The terms ana and ation! are often usd interchangeably, ut these
rms are no synonyns. In uid mechanics, wneud he most genera tem
that applies o any low that isnot steady, bt rasen is pia wed fer
(developing flows. When a rocket engine is fied up, for example ihre ae ta
Sie effects (the pressure bls upinsiethe rocket engine, the flow accelerates,
«tc uni be engine sel down and operates stay. The tem period refers
the kind of unsteady low in Which the low eels about a steady mean.
Many devices such as turbines, comessrs, Biles, condensers, and heat
exchangers operate fr lng periods of me under the same confins, and they
are clasfed as send fm devices. (Note thatthe low ld near he rotating
blades of a turbomachine is of couse unsteady, but we consider the overall
Flow field rater han the details some loeaies when we class devices)
During steal low, the fluid properties can change fem point to pont within
a device, but at any na pin they remain constant Merlo the volume,
the mass, and the ttl energy content of a steady-ow device or flow satin
remain constat in scady operation. À simple analogy is shown in Fig. 1-22.
Steady-flow conditions can be closely approximated by devices that are
intended for continuous operation such as turbines, pumps, oiler, onen
ers, and heat exchangers of power plans or religerion systems. Some
yee devices such as reciprocating engines or compressor, do nat sa
isfy the eady-flow conditions since the flow atthe inlets and the exits Es
Pulsstng and notseady. However, the fluid properties vary with time in a
In the seinen image ofa git in a
Swimming sit the mc of lige.
amer ar adjacent her body
Bioode animals are surounde by
thermal plumes of rising warm ae,
FIGURE 1-22
Comparison ola) instantaneous
snapshot of an unsteady flow, and
(Dong exposure pear ofthe
Same los
Steady versus Unsteady Flow
‘The terms steady and uniform ae used frequently in engineering, and thus
it important to have a clear understanding of their meanings The term
steady implies no change of properties, velocity temperature, ec. ata point
With me, The opposite of sicady is unsteady. The term uniform implies no
Change wth location over a specified region These meanings are consent
with their everyday use (steady girliiend, uniform distribution. e.
‘The terms ana and ation! are often usd interchangeably, ut these
rms are no synonyns. In uid mechanics, wneud he most genera tem
that applies o any low that isnot steady, bt rasen is pia wed fer
(developing flows. When a rocket engine is fied up, for example ihre ae ta
Sie effects (the pressure bls upinsiethe rocket engine, the flow accelerates,
«tc uni be engine sel down and operates stay. The tem period refers
the kind of unsteady low in Which the low eels about a steady mean.
Many devices such as turbines, comessrs, Biles, condensers, and heat
exchangers operate fr lng periods of me under the same confins, and they
are clasfed as send fm devices. (Note thatthe low ld near he rotating
blades of a turbomachine is of couse unsteady, but we consider the overall
Flow field rater han the details some loeaies when we class devices)
During steal low, the fluid properties can change fem point to pont within
a device, but at any na pin they remain constant Merlo the volume,
the mass, and the ttl energy content of a steady-ow device or flow satin
remain constat in scady operation. À simple analogy is shown in Fig. 1-22.
Steady-flow conditions can be closely approximated by devices that are
intended for continuous operation such as turbines, pumps, oiler, onen
ers, and heat exchangers of power plans or religerion systems. Some
yee devices such as reciprocating engines or compressor, do nat sa
isfy the eady-flow conditions since the flow atthe inlets and the exits Es
Pulsstng and notseady. However, the fluid properties vary with time in a
periodic manner, and the flow trough these devices can sil be analyzed as
3 steay-flw process by using time-averaged values for the properties
Some fascinating vsizations of fui flow ae provided in the book An
Albarn of Fluid Motion by. Milton Van Dyke (1982). A nie illtraion of
an une flow field is shown in Fig. 1-23, taken from Van Dyke's book,
Figure 1-28ais an insantncoss snaps rom high peed modo picture e
reveals age, alemating, swing turbulent eddies that ae she into the perl
‘ally oxcilltin wake fromthe blunt base ofthe objet. The unvcady wake pro
dus wanes that move upsteam alemtchy ver the top and tom surface of
the efi in an unsteady fasion Figure 1-235 shows the same flow fied, bu
the film is expose fr à longer time so that the image time averaged over 12
cycle. The resling time-averaged Now fel appears “steady” sine the des
‘ofthe undendy oscillations have been losin the lng exposure.
‘One of the most important jobs of an engince sto determine wheter it is
uff study only he time-meraged “Steady flow features of a problem.
‘or wheter a mare detailed study ofthe unsteady Features is eid the en
eer were interested only inthe overall properties ofthe how field (such as the
ime average drug coefficient, the mean velit, and presu Fl) ime
averaged deserpio Ike that of Fig. 1-23, time weriged experimental mea
Surement, oran analytical or numerical calculan ofthe time-averaged flow
field would be suficien, However. if the engineer were ierstd in dais
about the unsteady flow fil, such as floues batons, unscady pres
Sure Msetwations, the sound vanes emit fom the ubulent ees o the
Shock veas, a ime-veraged description of the ow feld would be inf.
"Most ofthe analytical and computational examples provided inthis text
hook deal with steady or time-aeraged flows, although we occasionally
point out some relevant unseady-flow features as well when appropriate
One-, Two-, and Three-Dimensional Flows
A flou field is best characterized by is velocity distribu, and us flow
is said to be one, tuo», oF tee dimensional ifthe flow velocity varies in
one. two, or thee primary dimensions, respectively. A typical Tid flow
invohes tree dimensional geomety, and the velocity may vary in all hee
dimensions, rendering the flow treo «dimensional [Vx 2) in rectangular
or Vir 0,5) in cyhndrcal coordinates. However, the variation of velocity in
‘certain ection canbe smal lative to the variation in eter direcion and
fen be ignored with negligible ero. In such eases, the flow can be modeled
(onveniently as being one o two dimensional, which is casir (0 analyze
Consider steady flow of a fluid entering from a lage tank into a circular
pipe. The fluid velocity everywhere on the pipe surface is zero because
91 the no-lip condition, and the How is two-dimensional in the entrance
region ofthe pipe since the velocity changes in both the 7- and directions,
ut nt in the Gizetion. The velocity profil develops fully and remains
unchanged after some distance from the inlet (about 10 pipe diameter in
turbulent flow, and typically farther than that in laminar pipe flow. asin
Fig. 1-24), and the flow io ths region is said to be fully developed. The
fully developed flow in a circular pipe is one-dimensional since the velocity
‘varies inthe adil rection but not in the angular 0 or axial direction.
as shown in Fig. 1-24, Thats, the velocity profil is the same a any axial
“location, and iis symmetric about the axis ofthe pipe
FIGURE 1-23
(Ouai wake ofa lat has
rit Mach number 0.6. Photo (a)
isan instantaneous image, while
Photo () sa long-oxposare
(me weraged) imag.
rm Dent
3 steay-flw process by using time-averaged values for the properties
Some fascinating vsizations of fui flow ae provided in the book An
Albarn of Fluid Motion by. Milton Van Dyke (1982). A nie illtraion of
an une flow field is shown in Fig. 1-23, taken from Van Dyke's book,
Figure 1-28ais an insantncoss snaps rom high peed modo picture e
reveals age, alemating, swing turbulent eddies that ae she into the perl
‘ally oxcilltin wake fromthe blunt base ofthe objet. The unvcady wake pro
dus wanes that move upsteam alemtchy ver the top and tom surface of
the efi in an unsteady fasion Figure 1-235 shows the same flow fied, bu
the film is expose fr à longer time so that the image time averaged over 12
cycle. The resling time-averaged Now fel appears “steady” sine the des
‘ofthe undendy oscillations have been losin the lng exposure.
‘One of the most important jobs of an engince sto determine wheter it is
uff study only he time-meraged “Steady flow features of a problem.
‘or wheter a mare detailed study ofthe unsteady Features is eid the en
eer were interested only inthe overall properties ofthe how field (such as the
ime average drug coefficient, the mean velit, and presu Fl) ime
averaged deserpio Ike that of Fig. 1-23, time weriged experimental mea
Surement, oran analytical or numerical calculan ofthe time-averaged flow
field would be suficien, However. if the engineer were ierstd in dais
about the unsteady flow fil, such as floues batons, unscady pres
Sure Msetwations, the sound vanes emit fom the ubulent ees o the
Shock veas, a ime-veraged description of the ow feld would be inf.
"Most ofthe analytical and computational examples provided inthis text
hook deal with steady or time-aeraged flows, although we occasionally
point out some relevant unseady-flow features as well when appropriate
One-, Two-, and Three-Dimensional Flows
A flou field is best characterized by is velocity distribu, and us flow
is said to be one, tuo», oF tee dimensional ifthe flow velocity varies in
one. two, or thee primary dimensions, respectively. A typical Tid flow
invohes tree dimensional geomety, and the velocity may vary in all hee
dimensions, rendering the flow treo «dimensional [Vx 2) in rectangular
or Vir 0,5) in cyhndrcal coordinates. However, the variation of velocity in
‘certain ection canbe smal lative to the variation in eter direcion and
fen be ignored with negligible ero. In such eases, the flow can be modeled
(onveniently as being one o two dimensional, which is casir (0 analyze
Consider steady flow of a fluid entering from a lage tank into a circular
pipe. The fluid velocity everywhere on the pipe surface is zero because
91 the no-lip condition, and the How is two-dimensional in the entrance
region ofthe pipe since the velocity changes in both the 7- and directions,
ut nt in the Gizetion. The velocity profil develops fully and remains
unchanged after some distance from the inlet (about 10 pipe diameter in
turbulent flow, and typically farther than that in laminar pipe flow. asin
Fig. 1-24), and the flow io ths region is said to be fully developed. The
fully developed flow in a circular pipe is one-dimensional since the velocity
‘varies inthe adil rection but not in the angular 0 or axial direction.
as shown in Fig. 1-24, Thats, the velocity profil is the same a any axial
“location, and iis symmetric about the axis ofthe pipe
FIGURE 1-23
(Ouai wake ofa lat has
rit Mach number 0.6. Photo (a)
isan instantaneous image, while
Photo () sa long-oxposare
(me weraged) imag.
rm Dent
FIGURE1-24
‘The development ofthe velocity
profile in ire pipe. V= Mr 2)
nd his he low is two dimensional
Inthe entrance regio, and becomes
‘one-dimensional Jounsteam when
the velocity profile fly develops
and remains unchanged the flow
recon, ven,
FIGURE 1-25
Flow over a car antennas
appeoximatly to dimensional
‘except ear he op and item
ET gs
HA
(=a
—
ricune 1-26
Asigmmetric flow over bullet
passe a
=
=
[Note that the dimensionality of the flow also depends on the choice of
(online system and is orientation. The pipe flow discussed for example, is
‘one-dimensional in cylindrical coordinates, but two-dimensional in Cartesian
coondinates—illustating the importance of choosing the most appropriate
Soondinte system, Also note hat eve in his simple flow, the velocity cannot
be uniform across he eros section ofthe pipe Because of the no sip condi
‘ion, However, at well sounded entrance tthe pipe the velocity profile muy
‘be approximated as being nearly uniform aros the pipe, sine the velocity is
cary constant a al radi excep very lose the pipe wall.
"A flow may be approximated as ovo-dimensanal when the aspect ratio is
large and the flow docs ot change appreciably along the longer dimension, For
example, the low of air ver acu antenna can be considered two. dimensional
‘except near its nds sine the antennas length is much greater than ls diam
‘ter and ih flow biting he antenna i fly uniform (Fi. 1-25)
EXAMPLE -1 Axisymmetrie Flow over a Bullet
Conder bl peca tough al ir ung sh einer in wich he m
tales peo conan Demi i he ng sow orth ballet m
hig ts gt san, wo ere dies (ig 1.20
SOLUTION tis to determin wht slow oer a bull on mo, |
“Assumptions The ar 0 sit wins and the alti sing
“Anette The al psss an ais of syne and there an a)
‘nc body. The sel pare of he bulk prall this asa we
‘pest the fie ange be muta smi at he a uch
‘ows ae sl he axis The ve this case varies witha di.
tance Zand ral stance. Dt oo with angle 2, Therefor, he time erage
Sito over te halle no mena
Discusion “Whe be tine argo aile is asymm th amenos
tif is not arate in Fig 1-2. In Cartesian coeds, Now wo
Peredo, Fah may las abo sá
Uniform versus Nonuniform Flow
nie flow implies dat ll Mui properties, such as velocity, pressure. tem
perature, et, donot vary with posa. A wind tunnel est section, or exam
De, is designed such that the air flow is as uniform as possible. Even then,
however, the flow does not remain uniform as we approach the wind tun
rel wall, due tothe o-slip condition andthe presence of a boundary layer,
‘The development ofthe velocity
profile in ire pipe. V= Mr 2)
nd his he low is two dimensional
Inthe entrance regio, and becomes
‘one-dimensional Jounsteam when
the velocity profile fly develops
and remains unchanged the flow
recon, ven,
FIGURE 1-25
Flow over a car antennas
appeoximatly to dimensional
‘except ear he op and item
ET gs
HA
(=a
—
ricune 1-26
Asigmmetric flow over bullet
passe a
=
=
[Note that the dimensionality of the flow also depends on the choice of
(online system and is orientation. The pipe flow discussed for example, is
‘one-dimensional in cylindrical coordinates, but two-dimensional in Cartesian
coondinates—illustating the importance of choosing the most appropriate
Soondinte system, Also note hat eve in his simple flow, the velocity cannot
be uniform across he eros section ofthe pipe Because of the no sip condi
‘ion, However, at well sounded entrance tthe pipe the velocity profile muy
‘be approximated as being nearly uniform aros the pipe, sine the velocity is
cary constant a al radi excep very lose the pipe wall.
"A flow may be approximated as ovo-dimensanal when the aspect ratio is
large and the flow docs ot change appreciably along the longer dimension, For
example, the low of air ver acu antenna can be considered two. dimensional
‘except near its nds sine the antennas length is much greater than ls diam
‘ter and ih flow biting he antenna i fly uniform (Fi. 1-25)
EXAMPLE -1 Axisymmetrie Flow over a Bullet
Conder bl peca tough al ir ung sh einer in wich he m
tales peo conan Demi i he ng sow orth ballet m
hig ts gt san, wo ere dies (ig 1.20
SOLUTION tis to determin wht slow oer a bull on mo, |
“Assumptions The ar 0 sit wins and the alti sing
“Anette The al psss an ais of syne and there an a)
‘nc body. The sel pare of he bulk prall this asa we
‘pest the fie ange be muta smi at he a uch
‘ows ae sl he axis The ve this case varies witha di.
tance Zand ral stance. Dt oo with angle 2, Therefor, he time erage
Sito over te halle no mena
Discusion “Whe be tine argo aile is asymm th amenos
tif is not arate in Fig 1-2. In Cartesian coeds, Now wo
Peredo, Fah may las abo sá
Uniform versus Nonuniform Flow
nie flow implies dat ll Mui properties, such as velocity, pressure. tem
perature, et, donot vary with posa. A wind tunnel est section, or exam
De, is designed such that the air flow is as uniform as possible. Even then,
however, the flow does not remain uniform as we approach the wind tun
rel wall, due tothe o-slip condition andthe presence of a boundary layer,
as mentioned previously. The flow just downstream of a wellounded pipe
entance (Fig. 1-24) is nearly uniform, again except fora very thin bound:
ary layer near the wall. In engineering practice tis common to approximate
the flow in ducts and pipes and at inlets and outs as unilorm even when
{tis ot, for simpliciy in alulaons, For example, the Tull developed pine
‘ow velocity profile of Fig. 1-24 i cently no uniform, bat for calculation
purposes we Sometimes approximate it asthe uniform profil a the ar lett
Of the pipe, which has the same average velocity. Although this makes the
Saleulatons ea, it also introduces some eres that require correction fa:
Lors: these are discussed in Chaps. $ and 6 for Kinetic energy and momentum,
respectively,
1-5 + SYSTEM AND CONTROL VOLUME
A system is defined asa quantity of mater ora region in space chosen for
study. The mass or region outside the system is calle the surroundings,
‘The cal or imaginary surface that separates the system from surround.
ings is called the boundary (Fig. 1-27). The boundary ofa system can be
{fired or movable. Note that the boundary isthe contact surface shared by
‘both the system andthe surroundings. Mathematically speaking the bound:
ty has zero thickness, and thus i can neither contain any mass nor CUS
any volume in space.
‘Systems may be considered to be closed or open, depending on whether
fined mass or a volume in space is chosen for study. A closed system
{also known as a control mass or simply a system when the context makes
it clear) consis of a fixed amount of muss, and no mass can cross its
‘boundary. But energy in the form of heat or work, can cross the boundary,
and the volume ofa closed system does not have to be fixed. I, asa special
fase even energy is not allowed to cross the boundary, that system i called
an isolated system.
‘Consider th pision-cplnder device shown in Fig. 1-28, Let us say that
we would lke o find out what happens to the enclosed gas when itis
heated, Since we ae focusing our stemion on the gas, is our system, The
inner surfaces ofthe piston and the cylinder form the boundary, and since
‘no mass is crossing this Boundary, itis a closed system. Notice that energy
may cross the boundary, and par of the boundary (he inner surface o the
piston in this case) may move. Everything outside the gas, including the
Piston and the cylinder, is the suroundings.
"An open system, or a control volume, as it is often called, i a selected
region in space usually enlose a device that involves muss low such as
4 Compressor, turbine, of nozzle. Flow through these devices is best tu:
fed by selecting the region within the device as the contol volume. Both
mass and energy can cross the boundary (the contol surface) of a control
volume.
‘A large number of engineering problems involve mass flow in and out
of an open system and, therefore are modele as con volumes, A water
eater, à car eaitor, a tubin, and a compresor all involve mass Flow
and should be analyzed as contol volumes (open systems) instead of as
control masses (closed systems). In general, any arbitrary region in space
San be selected as control volume, There are no concrete rules fr the
FIGURE +-27
System, suroundings, and Boundary:
FIGURE 1-28
AA che sytem with a moving
boundan:
entance (Fig. 1-24) is nearly uniform, again except fora very thin bound:
ary layer near the wall. In engineering practice tis common to approximate
the flow in ducts and pipes and at inlets and outs as unilorm even when
{tis ot, for simpliciy in alulaons, For example, the Tull developed pine
‘ow velocity profile of Fig. 1-24 i cently no uniform, bat for calculation
purposes we Sometimes approximate it asthe uniform profil a the ar lett
Of the pipe, which has the same average velocity. Although this makes the
Saleulatons ea, it also introduces some eres that require correction fa:
Lors: these are discussed in Chaps. $ and 6 for Kinetic energy and momentum,
respectively,
1-5 + SYSTEM AND CONTROL VOLUME
A system is defined asa quantity of mater ora region in space chosen for
study. The mass or region outside the system is calle the surroundings,
‘The cal or imaginary surface that separates the system from surround.
ings is called the boundary (Fig. 1-27). The boundary ofa system can be
{fired or movable. Note that the boundary isthe contact surface shared by
‘both the system andthe surroundings. Mathematically speaking the bound:
ty has zero thickness, and thus i can neither contain any mass nor CUS
any volume in space.
‘Systems may be considered to be closed or open, depending on whether
fined mass or a volume in space is chosen for study. A closed system
{also known as a control mass or simply a system when the context makes
it clear) consis of a fixed amount of muss, and no mass can cross its
‘boundary. But energy in the form of heat or work, can cross the boundary,
and the volume ofa closed system does not have to be fixed. I, asa special
fase even energy is not allowed to cross the boundary, that system i called
an isolated system.
‘Consider th pision-cplnder device shown in Fig. 1-28, Let us say that
we would lke o find out what happens to the enclosed gas when itis
heated, Since we ae focusing our stemion on the gas, is our system, The
inner surfaces ofthe piston and the cylinder form the boundary, and since
‘no mass is crossing this Boundary, itis a closed system. Notice that energy
may cross the boundary, and par of the boundary (he inner surface o the
piston in this case) may move. Everything outside the gas, including the
Piston and the cylinder, is the suroundings.
"An open system, or a control volume, as it is often called, i a selected
region in space usually enlose a device that involves muss low such as
4 Compressor, turbine, of nozzle. Flow through these devices is best tu:
fed by selecting the region within the device as the contol volume. Both
mass and energy can cross the boundary (the contol surface) of a control
volume.
‘A large number of engineering problems involve mass flow in and out
of an open system and, therefore are modele as con volumes, A water
eater, à car eaitor, a tubin, and a compresor all involve mass Flow
and should be analyzed as contol volumes (open systems) instead of as
control masses (closed systems). In general, any arbitrary region in space
San be selected as control volume, There are no concrete rules fr the
FIGURE +-27
System, suroundings, and Boundary:
FIGURE 1-28
AA che sytem with a moving
boundan:
FIGURE 1-29
A contol volume may involve
Fined, moving, eal and inary
boundaries.
election of cont! volumes, but a wise choice certainly makes the analysis
much easier If we were to analyze the flow of air through a nozzle, for
example, a good choice fr he control volume would be the region within
the nozzie. or perhaps surrounding the entire noz
"A contol volume can be fixed in size and shape, a i the case of a no2-
‘le, ort may invole a moving boundary, as shown in Fig. 1-29, Most con
‘wal volumes, however, have fied boundaries and thus do not involve any
moving boundaries. A consol volume may als ivolve heat and work inter
actions just asa closed sytem, in addition to mass interaction.
1-6 » IMPORTANCE OF DIMENSIONS
AND UNITS
Any physical quantity can be characterized by dimensions, The magnitudes
signed to the dimensions are called units, Some basic dimensions such
38 muss m, length L ime 1, and temperature T are selected as primary or
fundamental dimensions, while others such as velocity Y, enemy E, and
volume V are expressed in terms of the primary dimensions and ar called
secondary dimensions or derived dimensions,
"A number of unit systems have been developed over the years. Despite
strong effors in the scientific and engineering community to unify the
‘world with a single unit system, two sets of unis are still in common use
toda: the English system, which is also known asthe United States Cus:
romary System (USCS), and the metic SI (rom Le Système International
Unis), which is also known as the International System. The Sh is a
Simple and logical system based on à decimal relationship beeen the ari
ous units, and ii being used for scientific and engineering work in most of
the indusilized nations, including England. The English system, however,
has no apparent systematic numerical base, and various units in this system
are related o each ether rather arbitrarily (12 in = Tf 1 mile = $280 fi,
Aa = 1 gal ete), which makes it confusing and diflul o lean, The
United States is the only industrialized country that has not ye full con.
verted tothe mewie system,
“The systematic efforts to develop a univenally acceptable system of
nit dates back to 1790 when the French National Assembly charged the
French Academy of Sciences to come up with such a uni system, An early
version ofthe metric system was soon developed in France, but tdi ot
find universal acceptance until 1875 when The Metric Convention Treaty
‘was prepared and signed by 17 nations, including the United Sates. In this
international tray, meter and gram were established as the metre unis
for length and muss, respectively, and a General Conference of Weights
and Measures (CGPM) was established that was 10 meet every six years.
In 1960, the CGPM produced the SI, which vas based on six fundamental
quam, and their units were adopted in 1954 atthe Tenth General Con:
Terence of Weights and Measures; meter (m) fr length, kilogram (kg) for
mass second (s) for ime, ampere (A) or electric current, degree Kelvin °K)
for temperature, and candela (cd) for luminous intensity (ameunt of li
In 1971. the CGPM added a seventh fundamental quantity and unit: mole
{mob for the amount of matter
A contol volume may involve
Fined, moving, eal and inary
boundaries.
election of cont! volumes, but a wise choice certainly makes the analysis
much easier If we were to analyze the flow of air through a nozzle, for
example, a good choice fr he control volume would be the region within
the nozzie. or perhaps surrounding the entire noz
"A contol volume can be fixed in size and shape, a i the case of a no2-
‘le, ort may invole a moving boundary, as shown in Fig. 1-29, Most con
‘wal volumes, however, have fied boundaries and thus do not involve any
moving boundaries. A consol volume may als ivolve heat and work inter
actions just asa closed sytem, in addition to mass interaction.
1-6 » IMPORTANCE OF DIMENSIONS
AND UNITS
Any physical quantity can be characterized by dimensions, The magnitudes
signed to the dimensions are called units, Some basic dimensions such
38 muss m, length L ime 1, and temperature T are selected as primary or
fundamental dimensions, while others such as velocity Y, enemy E, and
volume V are expressed in terms of the primary dimensions and ar called
secondary dimensions or derived dimensions,
"A number of unit systems have been developed over the years. Despite
strong effors in the scientific and engineering community to unify the
‘world with a single unit system, two sets of unis are still in common use
toda: the English system, which is also known asthe United States Cus:
romary System (USCS), and the metic SI (rom Le Système International
Unis), which is also known as the International System. The Sh is a
Simple and logical system based on à decimal relationship beeen the ari
ous units, and ii being used for scientific and engineering work in most of
the indusilized nations, including England. The English system, however,
has no apparent systematic numerical base, and various units in this system
are related o each ether rather arbitrarily (12 in = Tf 1 mile = $280 fi,
Aa = 1 gal ete), which makes it confusing and diflul o lean, The
United States is the only industrialized country that has not ye full con.
verted tothe mewie system,
“The systematic efforts to develop a univenally acceptable system of
nit dates back to 1790 when the French National Assembly charged the
French Academy of Sciences to come up with such a uni system, An early
version ofthe metric system was soon developed in France, but tdi ot
find universal acceptance until 1875 when The Metric Convention Treaty
‘was prepared and signed by 17 nations, including the United Sates. In this
international tray, meter and gram were established as the metre unis
for length and muss, respectively, and a General Conference of Weights
and Measures (CGPM) was established that was 10 meet every six years.
In 1960, the CGPM produced the SI, which vas based on six fundamental
quam, and their units were adopted in 1954 atthe Tenth General Con:
Terence of Weights and Measures; meter (m) fr length, kilogram (kg) for
mass second (s) for ime, ampere (A) or electric current, degree Kelvin °K)
for temperature, and candela (cd) for luminous intensity (ameunt of li
In 1971. the CGPM added a seventh fundamental quantity and unit: mole
{mob for the amount of matter
Based on the notational scheme introduced in 1967, the degree sym.
bol was officially dropped from the absolute temperature un, and all
unit names were to be written without capitalization even if they were
derived from proper names (Table 1-1). However. the abbreviation of a
nit was to de capitalized if he unit was derived from a proper name.
For example, the SI uni of force, which is named after Sir Isaac Newton
(1617-1723), is newton (not Newton), and it is abbreviated as N. Also,
the fll name of a unit may be plualizd, but its abbreviation cannot, For
example, the length of an object can be $ m or S meters. not $ ms or 5
‘meter Finally, no period is to be used in unit abbreviations unless they
appear atthe end of a sentence, For example, the proper abbreviation of
meter is m (not m).
“The recent move toward the meti system in the United States seems to
have started in 1968 when Congres, in response 10 what was happening
in the rest of the world, passed a Metric Study Act. Congress cominued
to promote voluntary Switch tothe mri sytem by passing the Marc
Conversion Act in 1975. A trade bill assed by Congress in 1988 set a
September 1992 deadline for all federal agencies to convert o the marc
system, However, the deadlines were relased later with no clear plans for
the futur,
"As poined out, the SIs based on a decimal relationship between unis, The
prefixes used topes he mulipls a various uns ar ted in Table 1-2.
‘They ae standar or al nis, ad the student encourage to memorize some
cof thom because of their widespread use (Fig 1-30)
Some SI and English Units
In SI. the unis of mass, length, and time are the kilogram (ke) meter (m)
and second () respectively. The respective units in the English system arc
the pound-mass (Ibm), foot (fi, and second (). The pound symbol Ib is
actually the abbreviation of libra, which was the ancient Roman unit of
‘weight The English retained this symbol even after he end ofthe Roman
occupation of Britain in 410, The mass and length unks inthe two systems
ar elated to each other by
In the English system, force i often considered to be one of the pi
dimensions and is assigned a nonderived uni. This i à source of co
Sion and eror that necessitates the use of a dimensional constant (.) in
many formulas. To avoid this nuisance, we consider force tobe a secondary
dimension whose units derived from Newton's second law, ke.
For
Mas) (Accra)
or Fam oy
In SL the force units the newton (N), and is define a the fore required
to accelerate a mass of 1 kg a a rate of } més. In the English sytem. the
force un the pound.force (Ib) and is defined as the force required to
Ugh man)
Mas grams)
Tine second)
Tente chi
Bene ares (A)
Amount ofp call)
Amon of mater mo (oh,
FIGURE 1-30
‘The Suit refines are use in ll
branches of engineering
bol was officially dropped from the absolute temperature un, and all
unit names were to be written without capitalization even if they were
derived from proper names (Table 1-1). However. the abbreviation of a
nit was to de capitalized if he unit was derived from a proper name.
For example, the SI uni of force, which is named after Sir Isaac Newton
(1617-1723), is newton (not Newton), and it is abbreviated as N. Also,
the fll name of a unit may be plualizd, but its abbreviation cannot, For
example, the length of an object can be $ m or S meters. not $ ms or 5
‘meter Finally, no period is to be used in unit abbreviations unless they
appear atthe end of a sentence, For example, the proper abbreviation of
meter is m (not m).
“The recent move toward the meti system in the United States seems to
have started in 1968 when Congres, in response 10 what was happening
in the rest of the world, passed a Metric Study Act. Congress cominued
to promote voluntary Switch tothe mri sytem by passing the Marc
Conversion Act in 1975. A trade bill assed by Congress in 1988 set a
September 1992 deadline for all federal agencies to convert o the marc
system, However, the deadlines were relased later with no clear plans for
the futur,
"As poined out, the SIs based on a decimal relationship between unis, The
prefixes used topes he mulipls a various uns ar ted in Table 1-2.
‘They ae standar or al nis, ad the student encourage to memorize some
cof thom because of their widespread use (Fig 1-30)
Some SI and English Units
In SI. the unis of mass, length, and time are the kilogram (ke) meter (m)
and second () respectively. The respective units in the English system arc
the pound-mass (Ibm), foot (fi, and second (). The pound symbol Ib is
actually the abbreviation of libra, which was the ancient Roman unit of
‘weight The English retained this symbol even after he end ofthe Roman
occupation of Britain in 410, The mass and length unks inthe two systems
ar elated to each other by
In the English system, force i often considered to be one of the pi
dimensions and is assigned a nonderived uni. This i à source of co
Sion and eror that necessitates the use of a dimensional constant (.) in
many formulas. To avoid this nuisance, we consider force tobe a secondary
dimension whose units derived from Newton's second law, ke.
For
Mas) (Accra)
or Fam oy
In SL the force units the newton (N), and is define a the fore required
to accelerate a mass of 1 kg a a rate of } més. In the English sytem. the
force un the pound.force (Ib) and is defined as the force required to
Ugh man)
Mas grams)
Tine second)
Tente chi
Bene ares (A)
Amount ofp call)
Amon of mater mo (oh,
FIGURE 1-30
‘The Suit refines are use in ll
branches of engineering
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"Olen kyllá, rakas täti; Piersin táytyy taas mitata minut. En voinut
olla juoksematta sisälle nähdäkseni vanhan mittani, kun kuljin
Kirjastohuoneen ohitse, ja luulen — olen siitä varmakin, — ettei se
enää ulotu paljoa korkeammalle silmiáni."
“Ja vaikka epäilemättä o/et hoikempi, näytät terveeltä. Tietysti olet
terve?"
“ivan terve, táysin terve, täti."
"Neiti Exeter on varmaan pitányt sinusta hyván huolen." Ja sitten
— ihmeitten ihme! — lady Alfreton lisási ihan kuin luonnollisena
jatkona: "Minun táytynee káydá neiti Exeterin luona lausumassa
hánelle tunnustukseni."
Han oli káynyt niin monien ihmisten luona siitá ajasta, kun hänet
viimeksi tapasimme, että yksi vierailu enemmän tai váhemmán ei
paljoa merkinnyt, eiká neiti Exeter ollut enemmán hánen oman
säätypiirinsä ulkopuolella kuin monet muut olivat olleet.
Hänen poikansa ehdottama koe oli, kuten olemme rouvalta
itseltään kuulleet, onnistunut erinomaisesti. Han oli huomannut, ettá
kohteliaisuus, ystävällisyys ja naapurilisuus eivät ehdottomasti
tietäneet tartuntaa tai edes alituista kanssakäymistä. Váhitellen
hänen silmánsá olivat avautuneet näkemään sen tosiasian, että oli
mahdollista olla huomaavainen, jopa viettää aivan hauska puolitunti
yksinkertaisten kansanihmisten parissa, jotka tiesivät vähän tai eivat
mitään siitä maailmasta, missä han eli, mutta joiden oma maailma
kuitenkin oli sellainen, ettei han voinut sitá halveksia. Alkoipa han
heistá oppiakin.
olla juoksematta sisälle nähdäkseni vanhan mittani, kun kuljin
Kirjastohuoneen ohitse, ja luulen — olen siitä varmakin, — ettei se
enää ulotu paljoa korkeammalle silmiáni."
“Ja vaikka epäilemättä o/et hoikempi, näytät terveeltä. Tietysti olet
terve?"
“ivan terve, táysin terve, täti."
"Neiti Exeter on varmaan pitányt sinusta hyván huolen." Ja sitten
— ihmeitten ihme! — lady Alfreton lisási ihan kuin luonnollisena
jatkona: "Minun táytynee káydá neiti Exeterin luona lausumassa
hánelle tunnustukseni."
Han oli káynyt niin monien ihmisten luona siitá ajasta, kun hänet
viimeksi tapasimme, että yksi vierailu enemmän tai váhemmán ei
paljoa merkinnyt, eiká neiti Exeter ollut enemmán hánen oman
säätypiirinsä ulkopuolella kuin monet muut olivat olleet.
Hänen poikansa ehdottama koe oli, kuten olemme rouvalta
itseltään kuulleet, onnistunut erinomaisesti. Han oli huomannut, ettá
kohteliaisuus, ystävällisyys ja naapurilisuus eivät ehdottomasti
tietäneet tartuntaa tai edes alituista kanssakäymistä. Váhitellen
hänen silmánsá olivat avautuneet näkemään sen tosiasian, että oli
mahdollista olla huomaavainen, jopa viettää aivan hauska puolitunti
yksinkertaisten kansanihmisten parissa, jotka tiesivät vähän tai eivat
mitään siitä maailmasta, missä han eli, mutta joiden oma maailma
kuitenkin oli sellainen, ettei han voinut sitá halveksia. Alkoipa han
heistá oppiakin.
"Poloinen rouva Smith oli táállá tänään ja han on todella varsin
hauska puheissaan ja varsin kaino ja vaatimaton esintymisessään —
vaikka on ihan ihmeellistä, mitá han on tehnyt, — niin ihmeellistä,
ettá muut saavat vallan hávetá", oli ylháinen rouva eráássá
tilaisuudessa vakuuttanut; "enkä suinkaan enää koskaan edes
ajattelekaan hántá sivistymättömäksi. Kah, ihan unohdin hänen
pienet omituisuutensa hánen täällä ollessaan — eiká sellaisista saisi
niin kovin paljoa välittääkään. Mind pyysin häntä Käymään toistekin,
pyysin niinkin; mind todellakin pidän hánen käynneistään."
Eräänä paivana han taas oli lausunut: "Rakas Piers, jos olisin
tuntenut sen sääliteltävän, kauhean miespoloisen aikaisemman
elámántarinan, jonka tänne tuonnoin toit, en suinkaan olisi
käyttäytynyt hántá kohtaan niinkuin káyttáydyin. Olen nyt aivan
suuttunut itseeni. Tiedátkó sen? Oletko kuullut siitá? Vai et?
Annahan, kun sitten kerron sinulle." Senjälkeen oli seurannut
yksityiskohtia, ja lopuksi oli rouva lausunut: “Jos siis joskus haluat
Käskeä hänet jálleen tánne, Piers, tahdon tehdä parhaani
poistaakseni sanojeni aikaisemman vaikutuksen; ja vaikken
ymmärräkään kaikkea, mitä han sanoo, sillá tiedäthän, ettá hänen
murteensa ja puhetapansa on miltei mahdotonta, tahdon hymyillä ja
virkkaa jotakin, mitá hyvänsä, rauhoittaakseni ja rohkaistakseni
häntä."
Piersin lause: "Kukaan ei kykene sihen paremmin kuin sinä,
eni", oli ollut pienenä lisápalkkiona tästä.
Mutta totta puhuen lady Alfreton ei olisi kaivannut mitään muuta
palkkiota kuin omat onnellisemmat tunteensa. Jokainen pieni
ponnistus oli kantanut omat hedelmänsä; ja hänen puolisonsa ja
poikansa hyváksyminen Julietin huvitetun myéntymisen kera oli vain
hauska puheissaan ja varsin kaino ja vaatimaton esintymisessään —
vaikka on ihan ihmeellistä, mitá han on tehnyt, — niin ihmeellistä,
ettá muut saavat vallan hávetá", oli ylháinen rouva eráássá
tilaisuudessa vakuuttanut; "enkä suinkaan enää koskaan edes
ajattelekaan hántá sivistymättömäksi. Kah, ihan unohdin hänen
pienet omituisuutensa hánen täällä ollessaan — eiká sellaisista saisi
niin kovin paljoa välittääkään. Mind pyysin häntä Käymään toistekin,
pyysin niinkin; mind todellakin pidän hánen käynneistään."
Eräänä paivana han taas oli lausunut: "Rakas Piers, jos olisin
tuntenut sen sääliteltävän, kauhean miespoloisen aikaisemman
elámántarinan, jonka tänne tuonnoin toit, en suinkaan olisi
käyttäytynyt hántá kohtaan niinkuin káyttáydyin. Olen nyt aivan
suuttunut itseeni. Tiedátkó sen? Oletko kuullut siitá? Vai et?
Annahan, kun sitten kerron sinulle." Senjälkeen oli seurannut
yksityiskohtia, ja lopuksi oli rouva lausunut: “Jos siis joskus haluat
Käskeä hänet jálleen tánne, Piers, tahdon tehdä parhaani
poistaakseni sanojeni aikaisemman vaikutuksen; ja vaikken
ymmärräkään kaikkea, mitä han sanoo, sillá tiedäthän, ettá hänen
murteensa ja puhetapansa on miltei mahdotonta, tahdon hymyillä ja
virkkaa jotakin, mitá hyvänsä, rauhoittaakseni ja rohkaistakseni
häntä."
Piersin lause: "Kukaan ei kykene sihen paremmin kuin sinä,
eni", oli ollut pienenä lisápalkkiona tästä.
Mutta totta puhuen lady Alfreton ei olisi kaivannut mitään muuta
palkkiota kuin omat onnellisemmat tunteensa. Jokainen pieni
ponnistus oli kantanut omat hedelmänsä; ja hänen puolisonsa ja
poikansa hyváksyminen Julietin huvitetun myéntymisen kera oli vain
tasoittanut hánen tiensá hiukan sileámmáksi kuin se ehká muutoin
olisi ollut. Hánen alettuaan kerran astua tata polkua hi ei enáá
hevillá olisi saatu siitä poikkeamaan.
Sir Thomas oli kummastuneena kohottanut kulmakarvojansa,
mutta oli muutoksen johdosta myöskin mielihyvástá hykerrellyt
käsiänsä. Hankin oli luvannut tulla maalais-herrasmieheksi, jollaiseksi
hänen poikansa oli muuttumassa. Vielá ei ollut liian myöhään: se
tekisi erinomaisen hyvää seká hänen terveydelleen että hánen
maineelleen.
Jouluna Towers tuskin tunnettiin entisekseen, kun ilta illan perään
ajopelejá vieri edestakaisin; ja Elman sanojen mukaan oli ollut
milloin mitákin “ihania, ihania" juhlia ja kestityksiä sekä rikkaille ettá
kóyhille, jopa onnettomille "keskiluokkalaisillekin", jotka alussa olivat
olleet hánen tátinsá erityisená kammona, mutta joista han sittemmin
erikoisesti huolehti. Julietkin oli huomannut, ettei naapurillisuus
sittenkáán ollut mit huonoa huvia ja etteivat ihmiset senvuoksi
käyneet "röyhkeiksi, tungetteleviksi ja hánnysteleviksi", kuten han ja
hánen áitinsá ennen olivat luulleet.
"Tietysti meidän joskus täytyi suoristaa ryhtiámme, náyttáá hiukan
Jáykiltá ja villeité", tunnusti han uskotuilleen myöhemmin, “mutta
ylimalkaan onnistuimme mielestámme ihmeellisen hyvin. Ja minun
täytyy myöntää, ettá jos maalla tahtoo asua, ei ole viisasta esiintyá
tylysti, niinkuin meidán tapamme ennen oli."
Tuskin tarvitsee mainita, että niiden joukossa, jotka tástá olivat
enimmin hyötyneet, oli rouva Mansell tyttárineen. Heistá oli tullut
perheen ystäviä; ja Towers oli todella osoittautunut heille niin
vieraanvaraiseksi ja mieluiseksi, että he lopuksi olivat suostuneet
vastaanottamaan sir Thomasin tarjoaman mökin, joka hánellá oli
olisi ollut. Hánen alettuaan kerran astua tata polkua hi ei enáá
hevillá olisi saatu siitä poikkeamaan.
Sir Thomas oli kummastuneena kohottanut kulmakarvojansa,
mutta oli muutoksen johdosta myöskin mielihyvástá hykerrellyt
käsiänsä. Hankin oli luvannut tulla maalais-herrasmieheksi, jollaiseksi
hänen poikansa oli muuttumassa. Vielá ei ollut liian myöhään: se
tekisi erinomaisen hyvää seká hänen terveydelleen että hánen
maineelleen.
Jouluna Towers tuskin tunnettiin entisekseen, kun ilta illan perään
ajopelejá vieri edestakaisin; ja Elman sanojen mukaan oli ollut
milloin mitákin “ihania, ihania" juhlia ja kestityksiä sekä rikkaille ettá
kóyhille, jopa onnettomille "keskiluokkalaisillekin", jotka alussa olivat
olleet hánen tátinsá erityisená kammona, mutta joista han sittemmin
erikoisesti huolehti. Julietkin oli huomannut, ettei naapurillisuus
sittenkáán ollut mit huonoa huvia ja etteivat ihmiset senvuoksi
käyneet "röyhkeiksi, tungetteleviksi ja hánnysteleviksi", kuten han ja
hánen áitinsá ennen olivat luulleet.
"Tietysti meidän joskus täytyi suoristaa ryhtiámme, náyttáá hiukan
Jáykiltá ja villeité", tunnusti han uskotuilleen myöhemmin, “mutta
ylimalkaan onnistuimme mielestámme ihmeellisen hyvin. Ja minun
täytyy myöntää, ettá jos maalla tahtoo asua, ei ole viisasta esiintyá
tylysti, niinkuin meidán tapamme ennen oli."
Tuskin tarvitsee mainita, että niiden joukossa, jotka tástá olivat
enimmin hyötyneet, oli rouva Mansell tyttárineen. Heistá oli tullut
perheen ystäviä; ja Towers oli todella osoittautunut heille niin
vieraanvaraiseksi ja mieluiseksi, että he lopuksi olivat suostuneet
vastaanottamaan sir Thomasin tarjoaman mökin, joka hánellá oli
vuokrattavana Iyhyen matkan páássá kartanostaan. Eikä kukaan ollut
tästä järjestelystä enemmän mielissáán kuin lady Alfreton, joka
hartaasti huolehti siita, että mökki sisustuksineen olisi kaikin puolin
siro ja täydellinen — aivan sellainen kuin hän olisi itselleen halunnut.
Nyt hänestä tuntui perin yksinkertaiselta sanoa: "Minun täytynee
käydä neiti Exeterin luona."
Neiti Exeter istui seuraavana iltapäivänä etummaisessa
vastaanottohuoneessa vierastaan odottamassa. Hänelle oli ilmoitettu
hánen osakseen aiotusta kunniasta, ja Elma oli támán viestin
viedessáán hiukan arastellut. Tyttö oli omana vakaumuksenaan
lisännyt, että vierailu tehtäisiin viivyttelematta.
‘Tama vihjaus oli rittänyt. Kaikki oli nyt valmiina, ja kaikki oli
ulkopuolisesti tyyntä, vaikka lempeán kaitsijan povessa epäilemättä
oli paljonkin levottomuutta.
Mitáhán tuo omituinen ja odottamaton toimenpide merkitsi?
Aikoiko Elman holhooja ehdottaa jotakin muutosta, jotakin
sovittelua? Koettiko sir Thomas keksiá jotakin keinoa pannakseen
táytántóón sen, mitá neiti Exeter jo jonkun aikaa oli peljännyt hänen
omaisineen haluavan, nimittáin riistáá hänen rakkaan oppilaansa
pysyväisesti hänen hoivastaan? Vuoden päästä hánellá oli siihen
valta, mutta nyt — ja neiti Exeter pudisti päätänsä, ja hánen
huulensa sulkeutuivat tiukkaan. El, ei; mieluummin mitá muuta
tahansa! Mitá hyvánsá muuta vaadittaisiin tai pyydettaisiin, mitä
tahansa han saattoi hyvállá omallatunnolla tehdä, sühen han oli
valmis; mutta luovuttaa hänelle uskottu pyhá aarre toisille,
ennemmin taipua elävien vaatimuksiin kuin kunnioittaa vainajain
toivomuksia? Ei koskaan!
tästä järjestelystä enemmän mielissáán kuin lady Alfreton, joka
hartaasti huolehti siita, että mökki sisustuksineen olisi kaikin puolin
siro ja täydellinen — aivan sellainen kuin hän olisi itselleen halunnut.
Nyt hänestä tuntui perin yksinkertaiselta sanoa: "Minun täytynee
käydä neiti Exeterin luona."
Neiti Exeter istui seuraavana iltapäivänä etummaisessa
vastaanottohuoneessa vierastaan odottamassa. Hänelle oli ilmoitettu
hánen osakseen aiotusta kunniasta, ja Elma oli támán viestin
viedessáán hiukan arastellut. Tyttö oli omana vakaumuksenaan
lisännyt, että vierailu tehtäisiin viivyttelematta.
‘Tama vihjaus oli rittänyt. Kaikki oli nyt valmiina, ja kaikki oli
ulkopuolisesti tyyntä, vaikka lempeán kaitsijan povessa epäilemättä
oli paljonkin levottomuutta.
Mitáhán tuo omituinen ja odottamaton toimenpide merkitsi?
Aikoiko Elman holhooja ehdottaa jotakin muutosta, jotakin
sovittelua? Koettiko sir Thomas keksiá jotakin keinoa pannakseen
táytántóón sen, mitá neiti Exeter jo jonkun aikaa oli peljännyt hänen
omaisineen haluavan, nimittáin riistáá hänen rakkaan oppilaansa
pysyväisesti hänen hoivastaan? Vuoden päästä hánellá oli siihen
valta, mutta nyt — ja neiti Exeter pudisti päätänsä, ja hánen
huulensa sulkeutuivat tiukkaan. El, ei; mieluummin mitá muuta
tahansa! Mitá hyvánsá muuta vaadittaisiin tai pyydettaisiin, mitä
tahansa han saattoi hyvállá omallatunnolla tehdä, sühen han oli
valmis; mutta luovuttaa hänelle uskottu pyhá aarre toisille,
ennemmin taipua elävien vaatimuksiin kuin kunnioittaa vainajain
toivomuksia? Ei koskaan!
— Tapahtuuhan se sittenkin kyllin pian, kyllin pian, — huokasi han
ajatellen nopeasti Kitäviä kuukausia. — Suloinen Elmani, pitkää
aikaa et saa enáá viettáá tyyntä, hiljaista elämääsi ja rauhallisesti
harjoittaa opintojasi. Maailma vaatii sinut. Oi lemmikkini! — ja
kyyneleet kumpusivat uskollisen olennon silmiin. — Oi, Elmani,
kunpa osaisit elää maailmassa silti tulematta maailmalliseksi! Mutta
onko se mahdollista? — Silla kunnon neiti Exeter oli tállá haavaa
hiukan epäuskoinen ja alakuloinen, ja ken voi häntä moittia?
Seuraavassa silmánrápáyksessá ovi lensi auki, lady Alfreton astui
sisälle, ja pieni johtajatar, jálleen sotahaarniskassa, meni hántá
vastaan. Hánen sävynsä tosiaan hieman kummastutti vierasta, joka,
ollen keveäluontoinen, oli niin täydellisesti unohtanut kuin jos ei olisi
koskaan ollut olemassakaan mitään syytá, miksi he kaksi eivat nyt
olisi mitá parhaimmissa väleissä. Mutta neiti Exeter sai vuorostaan
aihetta kummastua, ennenkuin haastattelu oli päättynyt.
Ei vihjaustakaan mistään uudesta ehdotuksesta. Ei vilttaustakaan
mihinkään muutokseen. Sanalla sanoen, ei mitään muuta kuin
hauskaa ystävällisyyttä, ylistystä, sieviä kehuskeluja opettajattarelle,
ja kaikki tuo esitettynä niin herttaisesti kuin ainoastaan lady Alfreton
taisi.
— Hyväinen aika! — huudahti lauhtunut ja katuvainen neiti Exeter
jástyáán jálleen yksikseen. — Hyväinen aika! Elma on varmaan
oikeassa, ja yhtá varmasti mina olen tuominnut váárin tuota
hurmaavaa rouvaa. Elma on minua viisaampi. Hänen on opetettava
minua, eikä minun häntä, eráissá suhteissa.
Hyváluontoisen Mertounin herttuattaren auliissa ja iloisessa
myötävaikutuksessa lady Alfretonilla oli myöskin alituista tukea ja
puolustusta uudelle asiaintilalle.
ajatellen nopeasti Kitäviä kuukausia. — Suloinen Elmani, pitkää
aikaa et saa enáá viettáá tyyntä, hiljaista elämääsi ja rauhallisesti
harjoittaa opintojasi. Maailma vaatii sinut. Oi lemmikkini! — ja
kyyneleet kumpusivat uskollisen olennon silmiin. — Oi, Elmani,
kunpa osaisit elää maailmassa silti tulematta maailmalliseksi! Mutta
onko se mahdollista? — Silla kunnon neiti Exeter oli tállá haavaa
hiukan epäuskoinen ja alakuloinen, ja ken voi häntä moittia?
Seuraavassa silmánrápáyksessá ovi lensi auki, lady Alfreton astui
sisälle, ja pieni johtajatar, jálleen sotahaarniskassa, meni hántá
vastaan. Hánen sävynsä tosiaan hieman kummastutti vierasta, joka,
ollen keveäluontoinen, oli niin täydellisesti unohtanut kuin jos ei olisi
koskaan ollut olemassakaan mitään syytá, miksi he kaksi eivat nyt
olisi mitá parhaimmissa väleissä. Mutta neiti Exeter sai vuorostaan
aihetta kummastua, ennenkuin haastattelu oli päättynyt.
Ei vihjaustakaan mistään uudesta ehdotuksesta. Ei vilttaustakaan
mihinkään muutokseen. Sanalla sanoen, ei mitään muuta kuin
hauskaa ystävällisyyttä, ylistystä, sieviä kehuskeluja opettajattarelle,
ja kaikki tuo esitettynä niin herttaisesti kuin ainoastaan lady Alfreton
taisi.
— Hyväinen aika! — huudahti lauhtunut ja katuvainen neiti Exeter
jástyáán jálleen yksikseen. — Hyväinen aika! Elma on varmaan
oikeassa, ja yhtá varmasti mina olen tuominnut váárin tuota
hurmaavaa rouvaa. Elma on minua viisaampi. Hänen on opetettava
minua, eikä minun häntä, eráissá suhteissa.
Hyváluontoisen Mertounin herttuattaren auliissa ja iloisessa
myötävaikutuksessa lady Alfretonilla oli myöskin alituista tukea ja
puolustusta uudelle asiaintilalle.
"Mitä herttuatar tekee, sitá voin minäkin tehdá", oli hánen tapansa
päättäväisesti vastata Julietin silloin tállóin huomautellessa, ettei
Park Lane ollut Towers ja ettá se, mika varsin hyvin meni mukiin B:n
kreivikunnassa, tuskin sopi Lontoossa.
Lady Alfreton ei lisännyt — kenties ehkä ei tiennyt, — ettá, mitá
herttuatar teki, johtui yhdeksássá tapauksessa kymmenestá hánen
omassa perheessään tapahtuneesta vallan siirrosta, toisin sanoen,
että mihin Mabel johti, sinne Mabelin äiti seurasi — ja me tiedámme,
kuka oli kaiken johtajana.
— Se on Elman, yksinomaan Elman vaikutusta! — päätteli eras,
joka myóskin tiesi.
Mutta Piers ei sina kesänä sallinut itselleen tilaisuutta usein tavata
Elmaa. Hän lähti pitkälle ulkomaanmatkalle heti kaupunkiin muuton
jälkeen; ja jos sopii vilkaista viattoman sydámen kuulakkaan
syvyyteen, voimme aavistella, ettá hánen nuoren serkkunsa mielestá
kaikki oli menettänyt puolet kirkkaudestaan, kun hän oli poissa.
Elman joutohetket Park Lanen talossa eivat siitá pitáen koskaan
kuluneet yhtá hupaisasti — varsinkaan eivät tarjonneet läheskään
samaa tenhoa kuin muutamina ensi vikkoina tuon onnellisen
pääsiäisajan jälkeen. Han kaipasi aina jotakin. Hetket olivat
kadottaneet viehätyksensä, ihana kirkkaus oli niistá kaikonnut.
Erááná päivänä lady Alfreton sanoi äkkiä: "Kah, Elma! Olen saanut
kirjeen Piersiltá. Han láhettáá sinulle sydámellisiá terveisiá. Se ei ole
laisinkaan Piersin tapaista; mutta sina olit aina hánen suosikkinsa."
Sitten han käännellen kirjettä kädessään alkoi lukea höpistä ensin
hiljaa ja vihdoin äänekkäämmin: "Rakastava poikasi Piers Alfreton.
päättäväisesti vastata Julietin silloin tállóin huomautellessa, ettei
Park Lane ollut Towers ja ettá se, mika varsin hyvin meni mukiin B:n
kreivikunnassa, tuskin sopi Lontoossa.
Lady Alfreton ei lisännyt — kenties ehkä ei tiennyt, — ettá, mitá
herttuatar teki, johtui yhdeksássá tapauksessa kymmenestá hánen
omassa perheessään tapahtuneesta vallan siirrosta, toisin sanoen,
että mihin Mabel johti, sinne Mabelin äiti seurasi — ja me tiedámme,
kuka oli kaiken johtajana.
— Se on Elman, yksinomaan Elman vaikutusta! — päätteli eras,
joka myóskin tiesi.
Mutta Piers ei sina kesänä sallinut itselleen tilaisuutta usein tavata
Elmaa. Hän lähti pitkälle ulkomaanmatkalle heti kaupunkiin muuton
jälkeen; ja jos sopii vilkaista viattoman sydámen kuulakkaan
syvyyteen, voimme aavistella, ettá hánen nuoren serkkunsa mielestá
kaikki oli menettänyt puolet kirkkaudestaan, kun hän oli poissa.
Elman joutohetket Park Lanen talossa eivat siitá pitáen koskaan
kuluneet yhtá hupaisasti — varsinkaan eivät tarjonneet läheskään
samaa tenhoa kuin muutamina ensi vikkoina tuon onnellisen
pääsiäisajan jälkeen. Han kaipasi aina jotakin. Hetket olivat
kadottaneet viehätyksensä, ihana kirkkaus oli niistá kaikonnut.
Erááná päivänä lady Alfreton sanoi äkkiä: "Kah, Elma! Olen saanut
kirjeen Piersiltá. Han láhettáá sinulle sydámellisiá terveisiá. Se ei ole
laisinkaan Piersin tapaista; mutta sina olit aina hánen suosikkinsa."
Sitten han käännellen kirjettä kädessään alkoi lukea höpistä ensin
hiljaa ja vihdoin äänekkäämmin: "Rakastava poikasi Piers Alfreton.
Sano sydámellisiá terveisiä Elmalle." Sitten osoittaen lausetta:
"Tuossa näet! Tuossa se on! 'Sano sydámellisiá terveisiä Elmalle".
Jálkeenpáin puhuja mietiskeli itsekseen tähän tapaan:
— Lieneekóhán se punehdus mitään merkinnyt? Toivoisin niin —
kaikesta sydámestáni sitä toivoisin. Mutta ainahan Elma punastuu.
Han punastuu ujostellessaan ja punastuu innostuessaan. Mutta
sentáán... En voi muistella nähneeni mitéän aivan samanlaista
punehdusta tata ennen.
"Tuossa näet! Tuossa se on! 'Sano sydámellisiá terveisiä Elmalle".
Jálkeenpáin puhuja mietiskeli itsekseen tähän tapaan:
— Lieneekóhán se punehdus mitään merkinnyt? Toivoisin niin —
kaikesta sydámestáni sitä toivoisin. Mutta ainahan Elma punastuu.
Han punastuu ujostellessaan ja punastuu innostuessaan. Mutta
sentáán... En voi muistella nähneeni mitéän aivan samanlaista
punehdusta tata ennen.
iva, linnut visertelivät riemukkaasti ja kukkaset
puhkesivat huhtikuun heleänä aamuna; mutta kulmatalosta
Haverstockin máellá kuului itkua ja valitusta.
Oli páásidisloman edelinen paiva — paiva, jolloin tavallisesti
hiljaisen tyytyvaisyyden ja säädyllisen hilpeyden tunteet tayttivat
koko laitoksen. Mutta ken saattoi tänään olla iloinen? Elma teki
lähtöä. Elmaa ei enáá koskaan nähtäisi innokkaine, jokaista tulijaa
tervehtivine kasvoineen lupa-ajan päätyttyä — häntä, joka aina
ensimáisená oli heitá vastaan ilmestynyt.
Elma ei koskaan enää olisi siellá tuota välttämätöntä hetkeá
sulostuttamassa ja jokaista uutta tulokasta laitokseen tervehtimässä.
Elma, jolla oli niin rohkaisevat, puoleensa vetávát silmát, niin taitava,
vihdyttelevä kieli ja jonka esprit-de-corps oli niin innokasta (tama
hánen yhteishenkensá oli vaikuttanut jokaiseen jäseneen talossa
vanhimmasta nuorimpaan), — Elma oli jattava heidät iäksi. Tosin oli
muitakin hänen ikäisiään, hänen aikalaisiaan, muiden muassa náillá
sivuilla jo ennen mainitut pitká Henrietta ja tyyni ja vakava Margaret,
puhkesivat huhtikuun heleänä aamuna; mutta kulmatalosta
Haverstockin máellá kuului itkua ja valitusta.
Oli páásidisloman edelinen paiva — paiva, jolloin tavallisesti
hiljaisen tyytyvaisyyden ja säädyllisen hilpeyden tunteet tayttivat
koko laitoksen. Mutta ken saattoi tänään olla iloinen? Elma teki
lähtöä. Elmaa ei enáá koskaan nähtäisi innokkaine, jokaista tulijaa
tervehtivine kasvoineen lupa-ajan päätyttyä — häntä, joka aina
ensimáisená oli heitá vastaan ilmestynyt.
Elma ei koskaan enää olisi siellá tuota välttämätöntä hetkeá
sulostuttamassa ja jokaista uutta tulokasta laitokseen tervehtimässä.
Elma, jolla oli niin rohkaisevat, puoleensa vetávát silmát, niin taitava,
vihdyttelevä kieli ja jonka esprit-de-corps oli niin innokasta (tama
hánen yhteishenkensá oli vaikuttanut jokaiseen jäseneen talossa
vanhimmasta nuorimpaan), — Elma oli jattava heidät iäksi. Tosin oli
muitakin hänen ikäisiään, hänen aikalaisiaan, muiden muassa náillá
sivuilla jo ennen mainitut pitká Henrietta ja tyyni ja vakava Margaret,
jo ennen lähtenyt, ja toisia oli tullut heidán sijaansa; ja olikin aika —
niin, he eivát voineet olla myónt että Elma Alfretoninkin, joka
nyt oli, kuten ne toisetkin olivat olleet, naiseksi kypsymässä, oli jo
aika leijailla ylóspáin korkeampiin, avarampiin ilmapiireihin. Mutta
sittenkin — Elma! Ken voi korvata Elman — pienen yhdyskunnan
joustavan, lehahtelevan, likkeellepanevan hengen, sen oman
kirkkaan, erikoisen tähtösen?
"Neiti Exeteristá se tuntuu kauhean katkeralta", kuiskasi eräs tyttö
henkeänsä pidätellen toiselle. "Han ei virka mitáán — mutta han
kärsii. Se näet tuntuu hänestä melkein kuin täytyisi luopua omasta
lapsestaan; eikä saa luovuttaa häntä edes lapsen oikeille
vanhemmille."
‘Ainakin yhdessá suhteessa kay olo meille valkeammaksi", vastasi
toinen surumielisesti. "Ei ole enáá ketään viihdyttelemässä neiti
Exeteriä hänen synkkiná päivinään ja palauttamassa hánet hilpeälle
tuulelle, kuten Elma aina osasi tehdä. Elma voi aina hánet lepytellä.
Ajattelen mielihaikealla, miltá taalla tuntunee, kun Elma on mennyt."
Niin ajatteli moni muukin.
Tuo kunnon neiti Exeter, jota kaikki hänen oppilaansa kunnioittivat
ja josta useimmat jossakin määrin pitivátkin, ei kenties ollut
erikoisen taitava voittamaan heidán myötätuntoansa. Kuten olemme
nahneet, han saattoi eräissä tiloissa taipua, jopa heltyá liiaksikin, —
mutta tavallisesti hän arvokkaan koulunjohtajattaren asemassa
hairahtui liian jyrkán periaatteellisuuden varsin yleiseen ansaan.
Hánen periaatteensa mukaan tuli ja táytyikin määrätyn sarjan
huolellisesti táytettyjá velvollisuuksia, joiden vaihteluna olivat
määrätyt huvitukset ja virkistykset, ehdottomasti tyydyttää jokaisen
niin, he eivát voineet olla myónt että Elma Alfretoninkin, joka
nyt oli, kuten ne toisetkin olivat olleet, naiseksi kypsymässä, oli jo
aika leijailla ylóspáin korkeampiin, avarampiin ilmapiireihin. Mutta
sittenkin — Elma! Ken voi korvata Elman — pienen yhdyskunnan
joustavan, lehahtelevan, likkeellepanevan hengen, sen oman
kirkkaan, erikoisen tähtösen?
"Neiti Exeteristá se tuntuu kauhean katkeralta", kuiskasi eräs tyttö
henkeänsä pidätellen toiselle. "Han ei virka mitáán — mutta han
kärsii. Se näet tuntuu hänestä melkein kuin täytyisi luopua omasta
lapsestaan; eikä saa luovuttaa häntä edes lapsen oikeille
vanhemmille."
‘Ainakin yhdessá suhteessa kay olo meille valkeammaksi", vastasi
toinen surumielisesti. "Ei ole enáá ketään viihdyttelemässä neiti
Exeteriä hänen synkkiná päivinään ja palauttamassa hánet hilpeälle
tuulelle, kuten Elma aina osasi tehdä. Elma voi aina hánet lepytellä.
Ajattelen mielihaikealla, miltá taalla tuntunee, kun Elma on mennyt."
Niin ajatteli moni muukin.
Tuo kunnon neiti Exeter, jota kaikki hänen oppilaansa kunnioittivat
ja josta useimmat jossakin määrin pitivátkin, ei kenties ollut
erikoisen taitava voittamaan heidán myötätuntoansa. Kuten olemme
nahneet, han saattoi eräissä tiloissa taipua, jopa heltyá liiaksikin, —
mutta tavallisesti hän arvokkaan koulunjohtajattaren asemassa
hairahtui liian jyrkán periaatteellisuuden varsin yleiseen ansaan.
Hánen periaatteensa mukaan tuli ja táytyikin määrätyn sarjan
huolellisesti táytettyjá velvollisuuksia, joiden vaihteluna olivat
määrätyt huvitukset ja virkistykset, ehdottomasti tyydyttää jokaisen
cikeamielisen, järkevän, vastuunalaisen ihmisen vaistoja ja
vaatimuksia.
Mutta kasvuiássá olevia tyttöjä (álkáá säikähtykö Atalantan kauniit
lukijattaret!) voidaan tuskin luokittaa járkeviin, vastuunalaisiin
ihmisolentoihin; ja meillá lienee lupa vihjaista, ettá oivallinen neiti
Exeter ei liene kylliksi ottanut huomioon nuorten ailahtelevaisuutta.
Tássá tuli Elma hyvään tarpeeseen. Ei kukaan kuolevainen voinut
vastustaa Elmaa, saati sitten neiti Exeter — varsinkaan silloin, kun
Elma oli laupeuden asioilla. On náet ensiksikin muistettava, ettei
Elma koskaan anonut mitáán itselleen; han ei koskaan puhunut
omasta puolestaan. Ja sitten kuvastui nuoren lähetin silmássá
sellaista kaihoa, ilmeessä sellaista arkaa levottomuutta ja samalla
eräänlaista luottamusta, ettá kuuntelijan sydän tuskin olisi voinut olla
sulamatta, vaikka se olisi ollut kivestá. Ja vielá — mutta miksi
luetella? Neiti Exeter oli sittenkin vain ihminen inhimillisin
heikkouksin ja myóskin inhimillisesti tietoinen siitá. Ja tuo heikkous
ilmeni hánen suhteessaan hánen orpoon turvattiinsa, joka ei enäi
olisi hänen. Eron paiva saapui, kuten olemme maininneet, ja
tahdomme vetää verhon sen yli.
"Tosiaankin luulen, ettá muutat meille haikein mielin", väitti Elman
täti samana iltana, "niin tosiaan, Elma", ja hánen äänessään oli
vivahdus nuhdetta. "Ja kuitenkin sir Thomas saapui kaksi p
ennen pääsiäistä, sen sijaan etta olisi tullut páásidisen jálkeen,
toimittaakseen sinut suoraan tänne. Ja... ja mina olen hommannut
huoneesikin aivan valmiiksi."
“Oi, se on ihana, täti! Ah, täti, se on sievin, hauskin, armain pikku
suoja! Enkö teille sanonut, etten ollut eläessäni nähnyt mitään sen
vertaista?"
vaatimuksia.
Mutta kasvuiássá olevia tyttöjä (álkáá säikähtykö Atalantan kauniit
lukijattaret!) voidaan tuskin luokittaa járkeviin, vastuunalaisiin
ihmisolentoihin; ja meillá lienee lupa vihjaista, ettá oivallinen neiti
Exeter ei liene kylliksi ottanut huomioon nuorten ailahtelevaisuutta.
Tássá tuli Elma hyvään tarpeeseen. Ei kukaan kuolevainen voinut
vastustaa Elmaa, saati sitten neiti Exeter — varsinkaan silloin, kun
Elma oli laupeuden asioilla. On náet ensiksikin muistettava, ettei
Elma koskaan anonut mitáán itselleen; han ei koskaan puhunut
omasta puolestaan. Ja sitten kuvastui nuoren lähetin silmássá
sellaista kaihoa, ilmeessä sellaista arkaa levottomuutta ja samalla
eräänlaista luottamusta, ettá kuuntelijan sydän tuskin olisi voinut olla
sulamatta, vaikka se olisi ollut kivestá. Ja vielá — mutta miksi
luetella? Neiti Exeter oli sittenkin vain ihminen inhimillisin
heikkouksin ja myóskin inhimillisesti tietoinen siitá. Ja tuo heikkous
ilmeni hánen suhteessaan hánen orpoon turvattiinsa, joka ei enäi
olisi hänen. Eron paiva saapui, kuten olemme maininneet, ja
tahdomme vetää verhon sen yli.
"Tosiaankin luulen, ettá muutat meille haikein mielin", väitti Elman
täti samana iltana, "niin tosiaan, Elma", ja hánen äänessään oli
vivahdus nuhdetta. "Ja kuitenkin sir Thomas saapui kaksi p
ennen pääsiäistä, sen sijaan etta olisi tullut páásidisen jálkeen,
toimittaakseen sinut suoraan tänne. Ja... ja mina olen hommannut
huoneesikin aivan valmiiksi."
“Oi, se on ihana, täti! Ah, täti, se on sievin, hauskin, armain pikku
suoja! Enkö teille sanonut, etten ollut eläessäni nähnyt mitään sen
vertaista?"
"Kyllä, rakas lapsi, kyllä. Oh, en mind tarkoittanut sanoa, että olet
küttämätön, Elma; sinä vain et mielestäni näyttänyt ihan niin
onnelliselta, ihan niin hurmaantuneelta kuin olin odottanut olevasi
päästessäsi pois tuosta väsyttävästä koulusta ja tietäessäsi, että
tästälähin kotisi on vakituisesti meidän luonamme."
"Olen onnellinen, sanomattoman onnellinen tietäessäni, ett kotini
on oleva teidän luonanne", vastasi Elma hiljaisella äänellä. "Rakastan
teitá kaikkia hyvin paljon ja, voi, kuinka ystävällisiä te minulle aina
olettel"
"Rakas lapsi! Enhän sitá tarkoittanut. Kah, Elma, tuntuu kuin olisin
kalastellut imartelevia kehuskeluja! Hyväinen aika! Minähän
ainoastaan ihmettelin, ettet näyttänyt iloisemmalta, hilpeámmálta,
hyvá lapsi."
len juuri eronnut useista ystávistá", virkkoi Elma, "ja jotkut
olivat minulle rakkaita ystäviä, tät."
"Nii-in, tietysti, armas tyttöseni." Lady Alfreton liikahti
hermostuneesti nojatuolissaan.
"He olivat ikävissään nähdessään minun láhteván. Sanoessamme
toisillemme hyvästi monet... itkivät."
"Kaiketi ne pitivät sinusta."
"Neiti Exeter ei itkenyt."
"Eikö?
"Mutta hánen silmänsä punottivat ja olivat turvoksissa. Tati, se
rakas, ystävällinen, oivallinen neiti Exeter rakasti minua enemmän
küttämätön, Elma; sinä vain et mielestäni näyttänyt ihan niin
onnelliselta, ihan niin hurmaantuneelta kuin olin odottanut olevasi
päästessäsi pois tuosta väsyttävästä koulusta ja tietäessäsi, että
tästälähin kotisi on vakituisesti meidän luonamme."
"Olen onnellinen, sanomattoman onnellinen tietäessäni, ett kotini
on oleva teidän luonanne", vastasi Elma hiljaisella äänellä. "Rakastan
teitá kaikkia hyvin paljon ja, voi, kuinka ystävällisiä te minulle aina
olettel"
"Rakas lapsi! Enhän sitá tarkoittanut. Kah, Elma, tuntuu kuin olisin
kalastellut imartelevia kehuskeluja! Hyväinen aika! Minähän
ainoastaan ihmettelin, ettet näyttänyt iloisemmalta, hilpeámmálta,
hyvá lapsi."
len juuri eronnut useista ystávistá", virkkoi Elma, "ja jotkut
olivat minulle rakkaita ystäviä, tät."
"Nii-in, tietysti, armas tyttöseni." Lady Alfreton liikahti
hermostuneesti nojatuolissaan.
"He olivat ikävissään nähdessään minun láhteván. Sanoessamme
toisillemme hyvästi monet... itkivät."
"Kaiketi ne pitivät sinusta."
"Neiti Exeter ei itkenyt."
"Eikö?
"Mutta hánen silmänsä punottivat ja olivat turvoksissa. Tati, se
rakas, ystävällinen, oivallinen neiti Exeter rakasti minua enemmän
kuin kukaan muu heistä; ja mina luulen, ettá han tunsi uhraavansa
minut ainiaaksi." —
Muutamia päiviä aikaisemmin lady Alfreton oli esittányt
ajatuksiaan tähän tapaan:
"Olen valmis myöntämään, ettá Elma on hyvin kasvatettu ja ettá
hänen lahjojansa on siiná suhteessa kehitetty niin paljon kuin on
ollut mahdollista. Mutta pelkát lukutiedot eivät yksin riitá; ja vaikkei
minulla ole hitustakaan muistutettavaa neiti Exeteriá vastaan, joka
on todellakin miellyttävä, järkevä nainen, olen kuitenkin ylimalkaan
koulukasvatusta vastaan, enka... enka voi olla toivomatta, että nuori
sukulaisemme vastedes välttää Haverstock Hillin alinomaista
mainitsemista, kuten han tähän asti on sitá maininnut."
“ita tulee tyttökouluihin yleensä, lady Alfreton, olen táysin samaa
vastasi se naishenkilö, jolle yllámainitut sanat
järkevä maalaisnaapuri, eras niité Towersin
lähettyvillä asuvia, joiden seuraa Piers oli aidilleen suositellut. "En
kylläkään pidá nuorten neitien tavallisista kasvatuslaitoksista; sillá
kun on joukko tyttäriä, kuten minulla, niin lukutuntien járjestáminen
kotona on mielestäni kaikissa suhteissa edullisempaa. Mutta on
— puolisonne veljentytár esimerkiksi, — joiden olosuhteet
tekevát koulunkáynnin aivan välttämättömäksi. Heidán laisilleen,
kuten Elman täällà ollessa hánen kuvailuistaan mielestáni hyvin
tajusin, neiti Exeterin opisto on varmaan varsin oivallinen."
"Oh, kyllá; epäilemättä. Oivallinen joka suhteessa." (Nyttemmin
lady
Alfreton poikkeuksetta uljaasti puolusti hänen kouluansa kouluna.)
"Mutta luulen kuitenkin kásittávánne, rakas rouva Wotherham, ettei
minut ainiaaksi." —
Muutamia päiviä aikaisemmin lady Alfreton oli esittányt
ajatuksiaan tähän tapaan:
"Olen valmis myöntämään, ettá Elma on hyvin kasvatettu ja ettá
hänen lahjojansa on siiná suhteessa kehitetty niin paljon kuin on
ollut mahdollista. Mutta pelkát lukutiedot eivät yksin riitá; ja vaikkei
minulla ole hitustakaan muistutettavaa neiti Exeteriá vastaan, joka
on todellakin miellyttävä, järkevä nainen, olen kuitenkin ylimalkaan
koulukasvatusta vastaan, enka... enka voi olla toivomatta, että nuori
sukulaisemme vastedes välttää Haverstock Hillin alinomaista
mainitsemista, kuten han tähän asti on sitá maininnut."
“ita tulee tyttökouluihin yleensä, lady Alfreton, olen táysin samaa
vastasi se naishenkilö, jolle yllámainitut sanat
järkevä maalaisnaapuri, eras niité Towersin
lähettyvillä asuvia, joiden seuraa Piers oli aidilleen suositellut. "En
kylläkään pidá nuorten neitien tavallisista kasvatuslaitoksista; sillá
kun on joukko tyttäriä, kuten minulla, niin lukutuntien járjestáminen
kotona on mielestäni kaikissa suhteissa edullisempaa. Mutta on
— puolisonne veljentytár esimerkiksi, — joiden olosuhteet
tekevát koulunkáynnin aivan välttämättömäksi. Heidán laisilleen,
kuten Elman täällà ollessa hánen kuvailuistaan mielestáni hyvin
tajusin, neiti Exeterin opisto on varmaan varsin oivallinen."
"Oh, kyllá; epäilemättä. Oivallinen joka suhteessa." (Nyttemmin
lady
Alfreton poikkeuksetta uljaasti puolusti hänen kouluansa kouluna.)
"Mutta luulen kuitenkin kásittávánne, rakas rouva Wotherham, ettei
Elmalla voi olla mitään tarvetta — mitään syytä, — viel pääsiäisen
Jálkeen yllápitáá suhteitaan siellä
Mutta tässä nyt Elma pää tätinsä helmassa kuiskaili, kuinka neiti
Exeter hántá rakasti ja kuinka tama oli aavistanut ikuista eroa.
Tietysti Elman táti antoi peráán. Pienoinen sana oikealla hetkella
painaa vaa'assa enemmán kuin tuhannen muulloin.
Neiti Exeter olisi tervetullut Park Lanelle, milloin hántá vain halutti;
Elma saisi käydä Haverstock Hillin kulmatalossa niin usein kuin
tahtoi. Ja lady Alfreton itse tunsi saavansa runsaan palkan
molemmista myénnytyksistään nähdessään tuon mitä
aurinkoisimman luonteen aartehistosta páivápaisteen nyt hiipiván
herkkänä esille.
Mitäpä muita toivomuksia Elmalla tosiaankaan enáá saattoi olla?
Neiti
Exeter oli ollut koetuskivená.
Jos täti olisi jáányt kylmäksi ja járkkymáttómáksi silloin, kun neiti
Exeteristá tuli puhe, olisi ollut helppo nähdä, mika kohtalo odotti
kaikkia senlaatuisia pyyntöjä. Jos táti taas olisi parhaimmassa,
ystävällisimmässä mielentilassaan — ja sitá tati oli ollut, ja siis oli
kaikki hyvin.
Istuessaan siiná suloisessa huhtikuun hämärässä hellásti hyväillen
jalokivillá koristettua katt, johon oli tarttunut, ahmiessaan ulkoa
lóyhyileváá nuorten, veresten lehvien tuoksua ja rakkaasti
silmáillessáán huoneen tutunomaisia, kaunita esineitá Elma
mietiskeli ja pohti tuhansia ihmisrakkaita ja jalomielisié suunnitelmia.
Hánen oma itsensä ei niissá koskaan ollut etualalla. Mutta jos niiden
Jálkeen yllápitáá suhteitaan siellä
Mutta tässä nyt Elma pää tätinsä helmassa kuiskaili, kuinka neiti
Exeter hántá rakasti ja kuinka tama oli aavistanut ikuista eroa.
Tietysti Elman táti antoi peráán. Pienoinen sana oikealla hetkella
painaa vaa'assa enemmán kuin tuhannen muulloin.
Neiti Exeter olisi tervetullut Park Lanelle, milloin hántá vain halutti;
Elma saisi käydä Haverstock Hillin kulmatalossa niin usein kuin
tahtoi. Ja lady Alfreton itse tunsi saavansa runsaan palkan
molemmista myénnytyksistään nähdessään tuon mitä
aurinkoisimman luonteen aartehistosta páivápaisteen nyt hiipiván
herkkänä esille.
Mitäpä muita toivomuksia Elmalla tosiaankaan enáá saattoi olla?
Neiti
Exeter oli ollut koetuskivená.
Jos täti olisi jáányt kylmäksi ja járkkymáttómáksi silloin, kun neiti
Exeteristá tuli puhe, olisi ollut helppo nähdä, mika kohtalo odotti
kaikkia senlaatuisia pyyntöjä. Jos táti taas olisi parhaimmassa,
ystävällisimmässä mielentilassaan — ja sitá tati oli ollut, ja siis oli
kaikki hyvin.
Istuessaan siiná suloisessa huhtikuun hämärässä hellásti hyväillen
jalokivillá koristettua katt, johon oli tarttunut, ahmiessaan ulkoa
lóyhyileváá nuorten, veresten lehvien tuoksua ja rakkaasti
silmáillessáán huoneen tutunomaisia, kaunita esineitá Elma
mietiskeli ja pohti tuhansia ihmisrakkaita ja jalomielisié suunnitelmia.
Hánen oma itsensä ei niissá koskaan ollut etualalla. Mutta jos niiden
válistá välähti kultakuitu, mika tuskin hánen omankaan silmánsá
eroittamana kuitenkin kirkastutti näkyä ja siten teki sen
armaammaksi, ken voi häntä moittia?
Eikö meidän tulisi ajatella poissaolevia? Sopiiko meidán unohtaa
ne, jotka meitá rakastavat, vain siksi, etteivät tállá hetkellä ole
silmiemme edessá?
Elma lápikávi táydellisen Lontoon seurustelukauden ennenkuin
Piers tuli kotiin.
Viipyikö han ulkomailla kesäkuun loppuun vartavasten antaakseen
tytólle aikaa tähän, sitá han ei koskaan sanonut; mutta totta on, että
hánen ensimáinen kysymyksensá hánen palattuansa kuului: "Entá
Elma, onko han muuttumaton? Onko maailma pilannut hánet vai ei?
Nythán han on sitá koettanut? Sanokaa, minkä vaikutuksen se on
häneen tehnyt."
Näytti melkein siltá kuin lady Alfreton olisi vaistomaisesti havainnut
sen tunteen, mika tämän nopean kysymyksen aiheutti. Hänen
vastauksensa oli yhtá ripeá ja asiallinen —.
"Piers, maailma ei ole hántá pilannut, koska se ei voinut hántá
pilata. Miná olen heikko nais-rukka ja minun táytyy tunnustaa, että
olen saanut uutta elámánhalua nähdessäni sitá ihailua ja
huomaavaisuutta, jolla tuota lapsi-kultaa on tervehditty kaikkialla,
mihin ikáná han on mennyt. Han on ollut kevätkauden ihailluimpia
kaunottaria, ja kaikki hänen osakseen tullut imartelu ja
kunnianosoitukset eivät ole koskeneet háneen sen enempáá kuin jos
ne olisivat olleet aiotut toiselle. Minua kohtaan han on mit armain ja
velvollisuudentuntoisin tyttó; han seuraa minua kaikkialle, on aina
valmiina, aina aulis ja hyvällä páállá. Han kirjoittaa kutsukorttini ja
eroittamana kuitenkin kirkastutti näkyä ja siten teki sen
armaammaksi, ken voi häntä moittia?
Eikö meidän tulisi ajatella poissaolevia? Sopiiko meidán unohtaa
ne, jotka meitá rakastavat, vain siksi, etteivät tállá hetkellä ole
silmiemme edessá?
Elma lápikávi táydellisen Lontoon seurustelukauden ennenkuin
Piers tuli kotiin.
Viipyikö han ulkomailla kesäkuun loppuun vartavasten antaakseen
tytólle aikaa tähän, sitá han ei koskaan sanonut; mutta totta on, että
hánen ensimáinen kysymyksensá hánen palattuansa kuului: "Entá
Elma, onko han muuttumaton? Onko maailma pilannut hánet vai ei?
Nythán han on sitá koettanut? Sanokaa, minkä vaikutuksen se on
häneen tehnyt."
Näytti melkein siltá kuin lady Alfreton olisi vaistomaisesti havainnut
sen tunteen, mika tämän nopean kysymyksen aiheutti. Hänen
vastauksensa oli yhtá ripeá ja asiallinen —.
"Piers, maailma ei ole hántá pilannut, koska se ei voinut hántá
pilata. Miná olen heikko nais-rukka ja minun táytyy tunnustaa, että
olen saanut uutta elámánhalua nähdessäni sitá ihailua ja
huomaavaisuutta, jolla tuota lapsi-kultaa on tervehditty kaikkialla,
mihin ikáná han on mennyt. Han on ollut kevätkauden ihailluimpia
kaunottaria, ja kaikki hänen osakseen tullut imartelu ja
kunnianosoitukset eivät ole koskeneet háneen sen enempáá kuin jos
ne olisivat olleet aiotut toiselle. Minua kohtaan han on mit armain ja
velvollisuudentuntoisin tyttó; han seuraa minua kaikkialle, on aina
valmiina, aina aulis ja hyvällä páállá. Han kirjoittaa kutsukorttini ja
kirjeeni. Mina olen nykyisin viheliäinen, veltto olento; han kay sir
Thomasin mukana eduskunnassa ja ratsastelee Julietin kanssa, — en
Kásitá, kuinka háneltá rittää aikaa kaikkeen tuohon ja muuhun
viela."
"Mitä se muu on?" kysyi han.
"Oh, rakas Piers, siná tuskin tuntisit meitá enää. Mind itse
kyllákáán en tee varsin paljoa, mutta Juliet puuhailee Elman mukana
ihan kaikessa. Sisarellasi on sitá enemmán joutoaikaa, koska han
nykyisin ei todellakaan válitá niin paljoa seuraelämästä — tiedäthän,
että han on ollut seuraelámássá mukana jo monet kaudet; ja han
sanoo káyvánsá vanhaksi, hupsu tyttó! Olkoon sen asian laita kuinka
hyvänsä, han ainakin näyttää nuoremmalta ja reippaammalta ja on
monin verroin viehkeämpi entisestáán, nyt kun Elma on keksinyt
hánelle hommaa. Han puuhailee kaikenlaatuisten ihmisten kanssa,
saat uskoa. Ei ¡han kóyhien kanssa; tytót vakuuttavat minulle, että
on toisia, jotka semmoiseen työhön sopivat paremmin kuin he — ja
minun táytyy tunnustaa, että olenkin siitá iloinen. Mutta heillá näkyy
olevan loppumattomiin omituisia ihmisiá hoivattavina ja sellaisia,
joille osoittavat ystávyyttá ja hankkivat iloa. Muistat maininneeni
sinulle Elman taipumuksesta puolivillaisiin? Ka niin, puolirotuisia han
vielákin kaivaa esille, hááráilee niiden kanssa, puhuu nüstä paljon ja
saa lopuksi Julietin ja Mabelinkin asiaan innostumaan. Eipá niin, ettei
Mabel itsekin olisi kyllin taitava niité löytämään", jatkoi puhuja
nauraen.
"On tosiaan huvittavaa, Piers, vallan huvittavaa nähdä, millá tavoin
poloista Mertounin herttuatarta pyóritellán sinne tänne,
edestakaisin, tuon hánen suuren, omavaltaisen tyttárensá käskystä.
Mind pidän Mabelista; han on herttainen tyttó ja Elman paras ystävä,
Thomasin mukana eduskunnassa ja ratsastelee Julietin kanssa, — en
Kásitá, kuinka háneltá rittää aikaa kaikkeen tuohon ja muuhun
viela."
"Mitä se muu on?" kysyi han.
"Oh, rakas Piers, siná tuskin tuntisit meitá enää. Mind itse
kyllákáán en tee varsin paljoa, mutta Juliet puuhailee Elman mukana
ihan kaikessa. Sisarellasi on sitá enemmán joutoaikaa, koska han
nykyisin ei todellakaan válitá niin paljoa seuraelämästä — tiedäthän,
että han on ollut seuraelámássá mukana jo monet kaudet; ja han
sanoo káyvánsá vanhaksi, hupsu tyttó! Olkoon sen asian laita kuinka
hyvänsä, han ainakin näyttää nuoremmalta ja reippaammalta ja on
monin verroin viehkeämpi entisestáán, nyt kun Elma on keksinyt
hánelle hommaa. Han puuhailee kaikenlaatuisten ihmisten kanssa,
saat uskoa. Ei ¡han kóyhien kanssa; tytót vakuuttavat minulle, että
on toisia, jotka semmoiseen työhön sopivat paremmin kuin he — ja
minun táytyy tunnustaa, että olenkin siitá iloinen. Mutta heillá näkyy
olevan loppumattomiin omituisia ihmisiá hoivattavina ja sellaisia,
joille osoittavat ystávyyttá ja hankkivat iloa. Muistat maininneeni
sinulle Elman taipumuksesta puolivillaisiin? Ka niin, puolirotuisia han
vielákin kaivaa esille, hááráilee niiden kanssa, puhuu nüstä paljon ja
saa lopuksi Julietin ja Mabelinkin asiaan innostumaan. Eipá niin, ettei
Mabel itsekin olisi kyllin taitava niité löytämään", jatkoi puhuja
nauraen.
"On tosiaan huvittavaa, Piers, vallan huvittavaa nähdä, millá tavoin
poloista Mertounin herttuatarta pyóritellán sinne tänne,
edestakaisin, tuon hánen suuren, omavaltaisen tyttárensá käskystä.
Mind pidän Mabelista; han on herttainen tyttó ja Elman paras ystävä,
mutta häneltä puuttuvat kokonaan Elman rakkaat,
viehi pikku eleet. Aina vain: ‘Aiti, sinun on tehtävä náin' tai
‘Aiti, sinun on tehtava noin'. On kyllá totta, että herttuatar itse on
siihen alkuaan syypää. Mutta se ei suinkaan ole kaunista, se ei ole
hauskaa kuunnella. Elma sensijaan..."
Mutta ei ollut tarvis Piersille kuvailla Elmaa.
Han odotti vain varsin Iyhyen ajan, ja sitten han erááná tyynenä
iltana istuessaan Towersissa tytón kanssa kahdenkesken ison
kaariakkunan ääressä, kuten ennen, virkkoi:
"Elma, muistatko, mitä julkeuksia sinulle kerran tässä paikassa
lausuin?"
Elman sydän alkoi lyéda. Piers oli siellá täällä sanonut jotakin
julkeata, vaikkei siinä paikassa eiká mainitun ajankohdan jälkeen,
kuten kásittánette; ja Elma kai arvasi, niinkuin tyttó aina arvaa, ettá
oli tulossa enemmän sellaista, koska puhe alkoi moisella
kysymyksellä.
"En tiedä, rakastatko minua", jatkoi puhuja vielä pehmeämmällä ja
hiljaisemmalla äänellä, "mutta minusta itsestáni tuntuu, etten
milloinkaan voisi rakastaa ketään muuta tyttóá kuin sinua. Se alkoi jo
kauan sitten, paljoa aikaisemmin kuin tiesinkään. Sind olit silloin vain
lapsi — siitá on nyt kulunut kaksi vuotta, — mutta vaikka olitkin
lapsi, en voinut olla sinua tarkkaamatta ja ihmettelemättä. Pelkásin,
luulemma... niin, myönnän sen, olin melkein varmakin, ettei sitä
kestäisi; en luullut lupaavan umpun puhkeavan oikeaan kukkaansa.
Nähtyäni mina nyt uskon. Siná olet täyttänyt kaiken ja enemmánkin
kuin mitá ennustin täällä viimeksi yhdessä ollessamme. Olet
voittanut vanhempani, johdattanut sisartani, vaikuttanut muihin
viehi pikku eleet. Aina vain: ‘Aiti, sinun on tehtävä náin' tai
‘Aiti, sinun on tehtava noin'. On kyllá totta, että herttuatar itse on
siihen alkuaan syypää. Mutta se ei suinkaan ole kaunista, se ei ole
hauskaa kuunnella. Elma sensijaan..."
Mutta ei ollut tarvis Piersille kuvailla Elmaa.
Han odotti vain varsin Iyhyen ajan, ja sitten han erááná tyynenä
iltana istuessaan Towersissa tytón kanssa kahdenkesken ison
kaariakkunan ääressä, kuten ennen, virkkoi:
"Elma, muistatko, mitä julkeuksia sinulle kerran tässä paikassa
lausuin?"
Elman sydän alkoi lyéda. Piers oli siellá täällä sanonut jotakin
julkeata, vaikkei siinä paikassa eiká mainitun ajankohdan jälkeen,
kuten kásittánette; ja Elma kai arvasi, niinkuin tyttó aina arvaa, ettá
oli tulossa enemmän sellaista, koska puhe alkoi moisella
kysymyksellä.
"En tiedä, rakastatko minua", jatkoi puhuja vielä pehmeämmällä ja
hiljaisemmalla äänellä, "mutta minusta itsestáni tuntuu, etten
milloinkaan voisi rakastaa ketään muuta tyttóá kuin sinua. Se alkoi jo
kauan sitten, paljoa aikaisemmin kuin tiesinkään. Sind olit silloin vain
lapsi — siitá on nyt kulunut kaksi vuotta, — mutta vaikka olitkin
lapsi, en voinut olla sinua tarkkaamatta ja ihmettelemättä. Pelkásin,
luulemma... niin, myönnän sen, olin melkein varmakin, ettei sitä
kestäisi; en luullut lupaavan umpun puhkeavan oikeaan kukkaansa.
Nähtyäni mina nyt uskon. Siná olet täyttänyt kaiken ja enemmánkin
kuin mitá ennustin täällä viimeksi yhdessä ollessamme. Olet
voittanut vanhempani, johdattanut sisartani, vaikuttanut muihin
perhekuntiin, kaunistanut omamme... Ja nyt, Elma, — mitä teet nyt
minulle?"
Tyttó kääntyi puolittain häntä kohti.
"Olen sinun, jos minusta huolit", kuiskasi nuori mies. "Sinun... tee
minusta mitá tahdot. Kunhan vain otat minut..."
Ja kuinka saattoi tyttö olla häntä ottamatta?
minulle?"
Tyttó kääntyi puolittain häntä kohti.
"Olen sinun, jos minusta huolit", kuiskasi nuori mies. "Sinun... tee
minusta mitá tahdot. Kunhan vain otat minut..."
Ja kuinka saattoi tyttö olla häntä ottamatta?
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