Fundamentals of fluid mechanics

Cover......Page 1
Title Page......Page 5
Copyright......Page 6
About the Authors......Page 7
Preface......Page 9
Featured in this Book......Page 14
Contents......Page 17
Inside Front Cover......Page 23
Learning Objectives......Page 25
1.1 Some Characteristics of Fluids......Page 27
1.2 Dimensions, Dimensional Homogeneity, and Units......Page 28
1.2.1 Systems of Units......Page 31
1.4.1 Density......Page 35
1.5 Ideal Gas Law......Page 36
1.6 Viscosity......Page 38
1.7.1 Bulk Modulus......Page 44
1.7.2 Compression and Expansion of Gases......Page 45
1.7.3 Speed of Sound......Page 46
1.8 Vapor Pressure......Page 47
1.9 Surface Tension......Page 48
1.10 A Brief Look Back in History......Page 51
1.11 Chapter Summary and Study Guide......Page 53
References......Page 54
Problems......Page 55
2.1 Pressure at a Point......Page 64
2.2 Basic Equation for Pressure Field......Page 66
2.3 Pressure Variation in a Fluid at Rest......Page 67
2.3.1 Incompressible Fluid......Page 68
2.3.2 Compressible Fluid......Page 71
2.4 Standard Atmosphere......Page 73
2.5 Measurement of Pressure......Page 74
2.6.1 Piezometer Tube......Page 76
2.6.2 U-Tube Manometer......Page 77
2.6.3 Inclined-Tube Manometer......Page 80
2.7 Mechanical and Electronic Pressure-Measuring Devices......Page 81
2.8 Hydrostatic Force on a Plane Surface......Page 83
2.9 Pressure Prism......Page 89
2.10 Hydrostatic Force on a Curved Surface......Page 92
2.11.1 Archimedes’ Principle......Page 94
2.11.2 Stability......Page 97
2.12 Pressure Variation in a Fluid with Rigid-Body Motion......Page 98
2.12.1 Linear Motion......Page 99
2.12.2 Rigid-Body Rotation......Page 101
2.13 Chapter Summary and Study Guide......Page 103
Review Problems......Page 104
Problems......Page 105
3.1 Newton’s Second Law......Page 125
3.2 F = ma along a Streamline......Page 128
3.3 F = ma Normal to a Streamline......Page 132
3.4 Physical Interpretation......Page 134
3.5 Static, Stagnation, Dynamic, and Total Pressure......Page 137
3.6 Examples of Use of the Bernoulli Equation......Page 141
3.6.1 Free Jets......Page 142
3.6.2 Confined Flows......Page 144
3.6.3 Flowrate Measurement......Page 150
3.7 The Energy Line and the Hydraulic Grade Line......Page 155
3.8.1 Compressibility Effects......Page 158
3.8.2 Unsteady Effects......Page 160
3.8.3 Rotational Effects......Page 162
3.9 Chapter Summary and Study Guide......Page 163
Problems......Page 165
4.1 The Velocity Field......Page 181
4.1.1 Eulerian and Lagrangian Flow Descriptions......Page 184
4.1.2 One-, Two-, and Three-Dimensional Flows......Page 185
4.1.4 Streamlines, Streaklines, and Pathlines......Page 186
4.2.1 The Material Derivative......Page 190
4.2.3 Convective Effects......Page 193
4.2.4 Streamline Coordinates......Page 197
4.3 Control Volume and System Representations......Page 199
4.4 The Reynolds Transport Theorem......Page 200
4.4.1 Derivation of the Reynolds Transport Theorem......Page 202
4.4.3 Relationship to Material Derivative......Page 207
4.4.5 Unsteady Effects......Page 208
4.4.6 Moving Control Volumes......Page 210
4.4.7 Selection of a Control Volume......Page 211
4.5 Chapter Summary and Study Guide......Page 212
Conceptual Questions......Page 213
Problems......Page 214
Learning Objectives......Page 223
5.1.1 Derivation of the Continuity Equation......Page 224
5.1.2 Fixed, Nondeforming Control Volume......Page 226
5.1.3 Moving, Nondeforming Control Volume......Page 232
5.1.4 Deforming Control Volume......Page 234
5.2.1 Derivation of the Linear Momentum Equation......Page 237
5.2.2 Application of the Linear Momentum Equation......Page 238
5.2.3 Derivation of the Moment-of-Momentum Equation......Page 252
5.2.4 Application of the Moment-of-Momentum Equation......Page 253
5.3.1 Derivation of the Energy Equation......Page 260
5.3.2 Application of the Energy Equation......Page 263
5.3.3 Comparison of the Energy Equation with the Bernoulli Equation......Page 267
5.3.4 Application of the Energy Equation to Nonuniform Flows......Page 273
5.3.5 Combination of the Energy Equation and the Moment-of-Momentum Equation......Page 276
5.5 Chapter Summary and Study Guide......Page 277
References......Page 278
Problems......Page 279
Learning Objectives......Page 300
6.1 Fluid Element Kinematics......Page 301
6.1.2 Linear Motion and Deformation......Page 302
6.1.3 Angular Motion and Deformation......Page 303
6.2.1 Differential Form of Continuity Equation......Page 306
6.2.3 The Stream Function......Page 309
6.3 Conservation of Linear Momentum......Page 312
6.3.1 Description of Forces Acting on the Differential Element......Page 313
6.3.2 Equations of Motion......Page 315
6.4.2 The Bernoulli Equation......Page 316
6.4.3 Irrotational Flow......Page 318
6.4.5 The Velocity Potential......Page 320
6.5 Some Basic, Plane Potential Flows......Page 323
6.5.1 Uniform Flow......Page 324
6.5.2 Source and Sink......Page 325
6.5.3 Vortex......Page 327
6.5.4 Doublet......Page 330
6.6.1 Source in a Uniform Stream—Half-Body......Page 332
6.6.2 Rankine Ovals......Page 335
6.6.3 Flow around a Circular Cylinder......Page 337
6.7 Other Aspects of Potential Flow Analysis......Page 342
6.8.1 Stress-Deformation Relationships......Page 343
6.8.2 The Navier–Stokes Equations......Page 344
6.9 Some Simple Solutions for Viscous, Incompressible Fluids......Page 345
6.9.1 Steady, Laminar Flow between Fixed Parallel Plates......Page 346
6.9.2 Couette Flow......Page 348
6.9.3 Steady, Laminar Flow in Circular Tubes......Page 350
6.9.4 Steady, Axial, Laminar Flow in an Annulus......Page 353
6.10.1 Numerical Methods......Page 355
6.11 Chapter Summary and Study Guide......Page 356
References......Page 357
Problems......Page 358
Learning Objectives......Page 370
7.1 Dimensional Analysis......Page 371
7.2 Buckingham Pi Theorem......Page 373
7.3 Determination of Pi Terms......Page 374
7.4.1 Selection of Variables......Page 379
7.4.2 Determination of Reference Dimensions......Page 380
7.4.3 Uniqueness of Pi Terms......Page 382
7.5 Determination of Pi Terms by Inspection......Page 383
7.6 Common Dimensionless Groups in Fluid Mechanics......Page 384
7.7 Correlation of Experimental Data......Page 388
7.7.1 Problems with One Pi Term......Page 389
7.7.2 Problems with Two or More Pi Terms......Page 390
7.8.1 Theory of Models......Page 392
7.8.3 Practical Aspects of Using Models......Page 396
7.9.1 Flow through Closed Conduits......Page 398
7.9.2 Flow around Immersed Bodies......Page 401
7.9.3 Flow with a Free Surface......Page 405
7.10 Similitude Based on Governing Differential Equations......Page 408
7.11 Chapter Summary and Study Guide......Page 411
Review Problems......Page 412
Problems......Page 413
Learning Objectives......Page 424
8.1 General Characteristics of Pipe Flow......Page 425
8.1.1 Laminar or Turbulent Flow......Page 426
8.1.2 Entrance Region and Fully Developed Flow......Page 429
8.1.3 Pressure and Shear Stress......Page 430
8.2.1 From F = ma Applied Directly to a Fluid Element......Page 431
8.2.2 From the Navier–Stokes Equations......Page 435
8.2.3 From Dimensional Analysis......Page 437
8.2.4 Energy Considerations......Page 438
8.3.1 Transition from Laminar to Turbulent Flow......Page 440
8.3.2 Turbulent Shear Stress......Page 442
8.3.3 Turbulent Velocity Profile......Page 446
8.4 Dimensional Analysis of Pipe Flow......Page 450
8.4.1 Major Losses......Page 451
8.4.2 Minor Losses......Page 456
8.4.3 Noncircular Conduits......Page 466
8.5.1 Single Pipes......Page 469
8.5.2 Multiple Pipe Systems......Page 479
8.6.1 Pipe Flowrate Meters......Page 483
8.6.2 Volume Flowmeters......Page 488
8.7 Chapter Summary and Study Guide......Page 489
References......Page 491
Problems......Page 492
Learning Objectives......Page 504
9.1 General External Flow Characteristics......Page 505
9.1.1 Lift and Drag Concepts......Page 506
9.1.2 Characteristics of Flow Past an Object......Page 509
9.2.1 Boundary Layer Structure and Thickness on a Flat Plate......Page 513
9.2.2 Prandtl/Blasius Boundary Layer Solution......Page 517
9.2.3 Momentum Integral Boundary Layer Equation for a Flat Plate......Page 521
9.2.4 Transition from Laminar to Turbulent Flow......Page 526
9.2.5 Turbulent Boundary Layer Flow......Page 528
9.2.6 Effects of Pressure Gradient......Page 531
9.2.7 Momentum Integral Boundary Layer Equation with Nonzero Pressure Gradient......Page 535
9.3 Drag......Page 536
9.3.1 Friction Drag......Page 537
9.3.2 Pressure Drag......Page 538
9.3.3 Drag Coefficient Data and Examples......Page 540
9.4.1 Surface Pressure Distribution......Page 552
9.4.2 Circulation......Page 561
9.5 Chapter Summary and Study Guide......Page 565
References......Page 566
Conceptual Questions......Page 567
Problems......Page 568
Learning Objectives......Page 578
10.1 General Characteristics of Open-Channel Flow......Page 579
10.2.1 Wave Speed......Page 580
10.2.2 Froude Number Effects......Page 583
10.3 Energy Considerations......Page 585
10.3.1 Specific Energy......Page 586
10.3.2 Channel Depth Variations......Page 589
10.4.1 Uniform Flow Approximations......Page 590
10.4.2 The Chezy and Manning Equations......Page 591
10.4.3 Uniform Depth Examples......Page 594
10.5 Gradually Varied Flow......Page 599
10.6 Rapidly Varied Flow......Page 600
10.6.1 The Hydraulic Jump......Page 601
10.6.2 Sharp-Crested Weirs......Page 606
10.6.3 Broad-Crested Weirs......Page 609
10.6.4 Underflow Gates......Page 611
10.7 Chapter Summary and Study Guide......Page 613
References......Page 614
Problems......Page 615
Learning Objectives......Page 625
11.1 Ideal Gas Relationships......Page 626
11.2 Mach Number and Speed of Sound......Page 631
11.3 Categories of Compressible Flow......Page 634
11.4 Isentropic Flow of an Ideal Gas......Page 638
11.4.1 Effect of Variations in Flow Cross-Sectional Area......Page 639
11.4.2 Converging–Diverging Duct Flow......Page 641
11.5.1 Adiabatic Constant Area Duct Flow with Friction (Fanno Flow)......Page 655
11.5.2 Frictionless Constant Area Duct Flow with Heat Transfer (Rayleigh Flow)......Page 666
11.5.3 Normal Shock Waves......Page 672
11.6 Analogy between Compressible and Open-Channel Flows......Page 679
11.7 Two-Dimensional Compressible Flow......Page 681
11.8 Chapter Summary and Study Guide......Page 682
References......Page 685
Problems......Page 686
Learning Objectives......Page 691
12.1 Introduction......Page 692
12.2 Basic Energy Considerations......Page 693
12.3 Basic Angular Momentum Considerations......Page 697
12.4 The Centrifugal Pump......Page 699
12.4.1 Theoretical Considerations......Page 700
12.4.2 Pump Performance Characteristics......Page 704
12.4.3 Net Positive Suction Head (NPSH)......Page 706
12.4.4 System Characteristics and Pump Selection......Page 708
12.5 Dimensionless Parameters and Similarity Laws......Page 712
12.5.1 Special Pump Scaling Laws......Page 714
12.5.2 Specific Speed......Page 715
12.5.3 Suction Specific Speed......Page 716
12.6 Axial-Flow and Mixed-Flow Pumps......Page 717
12.8 Turbines......Page 719
12.8.1 Impulse Turbines......Page 720
12.8.2 Reaction Turbines......Page 728
12.9 Compressible Flow Turbomachines......Page 731
12.9.1 Compressors......Page 732
12.9.2 Compressible Flow Turbines......Page 735
12.10 Chapter Summary and Study Guide......Page 737
Conceptual Questions......Page 739
Problems......Page 740
A Computational Fluid Dynamics......Page 749
B Physical Properties of Fluids......Page 761
C Properties of the U.S. Standard Atmosphere......Page 766
D Compressible Flow Graphs for an Ideal Gas (k =1.4)......Page 768
Answers......Page 773
Index......Page 779
Video Index......Page 789
Inside Back Cover......Page 795