A Brief Introduction To Fluid Mechanics

Cover......Page 1
Title Page......Page 7
Copyright......Page 8
About the Authors......Page 9
Preface......Page 13
CONTENTS......Page 23
1 INTRODUCTION......Page 29
1.2 Dimensions, Dimensional Homogeneity, and Units......Page 31
1.2.1 Systems of Units......Page 34
1.4.1 Density......Page 37
1.4.3 Specific Gravity......Page 38
1.5 Ideal Gas Law......Page 39
1.6 Viscosity......Page 40
1.7.1 Bulk Modulus......Page 45
1.7.2 Compression and Expansion of Gases......Page 46
1.7.3 Speed of Sound......Page 47
1.9 Surface Tension......Page 49
1.10 A Brief Look Back in History......Page 52
1.11 Chapter Summary and Study Guide......Page 55
Problems......Page 56
2 FLUID STATICS......Page 60
2.1 Pressure at a Point......Page 61
2.2 Basic Equation for Pressure Field......Page 62
2.3.1 Incompressible Fluid......Page 64
2.3.2 Compressible Fluid......Page 66
2.5 Measurement of Pressure......Page 67
2.6.1 Piezometer Tube......Page 70
2.6.2 U-Tube Manometer......Page 71
2.6.3 Inclined-Tube Manometer......Page 74
2.8 Hydrostatic Force on a Plane Surface......Page 75
2.9 Pressure Prism......Page 80
2.10 Hydrostatic Force on a Curved Surface......Page 82
2.11.1 Archimedes’ Principle......Page 85
2.11.2 Stability......Page 87
2.13 Chapter Summary and Study Guide......Page 88
References......Page 89
Problems......Page 90
3 ELEMENTARY FLUID DYNAMICS—THE BERNOULLI EQUATION......Page 96
3.1 Newton’s Second Law......Page 97
3.2 F = ma Along a Streamline......Page 98
3.3 F = ma Normal to a Streamline......Page 102
3.4 Physical Interpretation......Page 103
3.5 Static, Stagnation, Dynamic, and Total Pressure......Page 106
3.6.1 Free Jets......Page 109
3.6.2 Confined Flows......Page 110
3.6.3 Flowrate Measurement......Page 117
3.7 The Energy Line and the Hydraulic Grade Line......Page 120
3.8 Restrictions on the Use of the Bernoulli Equation......Page 122
3.9 Chapter Summary and Study Guide......Page 123
Review Problems......Page 124
Problems......Page 125
4 FLUID KINEMATICS......Page 130
4.1 The Velocity Field......Page 131
4.1.2 One-, Two-, and Three-Dimensional Flows......Page 133
4.1.3 Steady and Unsteady Flows......Page 134
4.1.4 Streamlines, Streaklines, and Pathlines......Page 135
4.2.1 The Material Derivative......Page 138
4.2.2 Unsteady Effects......Page 140
4.2.3 Convective Effects......Page 141
4.2.4 Streamline Coordinates......Page 142
4.3 Control Volume and System Representations......Page 143
4.4.1 Derivation of the Reynolds Transport Theorem......Page 144
4.5 Chapter Summary and Study Guide......Page 148
Problems......Page 149
5 FINITE CONTROL VOLUME ANALYSIS......Page 153
5.1.1 Derivation of the Continuity Equation......Page 154
5.1.2 Fixed, Nondeforming Control Volume......Page 155
5.1.3 Moving, Nondeforming Control Volume......Page 159
5.2.1 Derivation of the Linear Momentum Equation......Page 161
5.2.2 Application of the Linear Momentum Equation......Page 162
5.2.3 Derivation of the Moment-of-Momentum Equation......Page 172
5.2.4 Application of the Moment-of-Momentum Equation......Page 173
5.3.1 Derivation of the Energy Equation......Page 180
5.3.2 Application of the Energy Equation......Page 182
5.3.3 Comparison of the Energy Equation with the Bernoulli Equation......Page 185
5.3.4 Application of the Energy Equation to Nonuniform Flows......Page 190
5.4 Chapter Summary and Study Guide......Page 192
Problems......Page 194
6 DIFFERENTIAL ANALYSIS OF FLUID FLOW......Page 203
6.1.1 Velocity and Acceleration Fields Revisited......Page 204
6.1.2 Linear Motion and Deformation......Page 205
6.1.3 Angular Motion and Deformation......Page 207
6.2.1 Differential Form of Continuity Equation......Page 210
6.2.2 Cylindrical Polar Coordinates......Page 212
6.2.3 The Stream Function......Page 213
6.3 Conservation of Linear Momentum......Page 216
6.3.1 Description of Forces Acting on Differential Element......Page 217
6.3.2 Equations of Motion......Page 219
6.4.1 Euler’s Equations of Motion......Page 220
6.4.2 The Bernoulli Equation......Page 221
6.4.3 Irrotational Flow......Page 223
6.4.5 The Velocity Potential......Page 224
6.5 Some Basic, Plane Potential Flows......Page 227
6.5.2 Source and Sink......Page 229
6.5.3 Vortex......Page 231
6.5.4 Doublet......Page 235
6.6.1 Source in a Uniform Stream—Half-Body......Page 237
6.6.2 Flow around a Circular Cylinder......Page 240
6.8.1 Stress–Deformation Relationships......Page 247
6.8.2 The Navier–Stokes Equations......Page 248
6.9 Some Simple Solutions for Laminar, Viscous, Incompressible Fluids......Page 249
6.9.1 Steady, Laminar Flow between Fixed Parallel Plates......Page 250
6.9.2 Couette Flow......Page 252
6.9.3 Steady, Laminar Flow in Circular Tubes......Page 255
6.10 Other Aspects of Differential Analysis......Page 257
6.11 Chapter Summary and Study Guide......Page 258
Problems......Page 260
7 SIMILITUDE, DIMENSIONAL ANALYSIS, AND MODELING......Page 266
7.1 Dimensional Analysis......Page 267
7.2 Buckingham Pi Theorem......Page 268
7.3 Determination of Pi Terms......Page 269
7.4 Some Additional Comments about Dimensional Analysis......Page 274
7.4.3 Uniqueness of Pi Terms......Page 275
7.5 Determination of Pi Terms by Inspection......Page 276
7.6 Common Dimensionless Groups in Fluid Mechanics......Page 277
7.7 Correlation of Experimental Data......Page 278
7.7.1 Problems with One Pi Term......Page 279
7.7.2 Problems with Two or More Pi Terms......Page 280
7.8.1 Theory of Models......Page 282
7.8.2 Model Scales......Page 286
7.8.3 Distorted Models......Page 287
7.9.1 Flow through Closed Conduits......Page 288
7.9.2 Flow around Immersed Bodies......Page 290
7.9.3 Flow with a Free Surface......Page 292
7.10 Chapter Summary and Study Guide......Page 295
References......Page 296
Problems......Page 297
8 VISCOUS FLOW IN PIPES......Page 302
8.1.1 Laminar or Turbulent Flow......Page 303
8.1.2 Entrance Region and Fully Developed Flow......Page 305
8.2.1 From F = ma Applied Directly to a Fluid Element......Page 306
8.3 Fully Developed Turbulent Flow......Page 310
8.3.1 Transition from Laminar to Turbulent Flow......Page 311
8.3.2 Turbulent Shear Stress......Page 312
8.4 Dimensional Analysis of Pipe Flow......Page 313
8.4.1 Major Losses......Page 314
8.4.2 Minor Losses......Page 318
8.4.3 Noncircular Conduits......Page 326
8.5 Pipe Flow Examples......Page 327
8.5.1 Single Pipes......Page 328
8.5.2 Multiple Pipe Systems......Page 335
8.6 Pipe Flowrate Measurement......Page 337
8.7 Chapter Summary and Study Guide......Page 341
References......Page 342
Problems......Page 343
9 FLOW OVER IMMERSED BODIES......Page 349
9.1.1 Lift and Drag Concepts......Page 350
9.1.2 Characteristics of Flow Past and Object......Page 353
9.2.1 Boundary Layer Structure and Thickness on a Flat Plate......Page 356
9.2.2 Prandtl/Blasius Boundary Layer Solution......Page 358
9.2.3 Momentum Integral Boundary Layer Equation for a Flat Plate......Page 360
9.2.4 Transition from Laminar to Turbulent Flow......Page 362
9.2.5 Turbulent Boundary Layer Flow......Page 364
9.2.6 Effects of Pressure Gradient......Page 366
9.3 Drag......Page 369
9.3.2 Pressure Drag......Page 370
9.3.3 Drag Coefficient Data and Examples......Page 371
9.4.1 Surface Pressure Distribution......Page 385
9.4.2 Circulation......Page 389
9.5 Chapter Summary and Study Guide......Page 391
Problems......Page 392
10.1 General Characteristics of Open-Channel Flow......Page 398
10.2 Surface Waves......Page 399
10.2.1 Wave Speed......Page 400
10.3 Energy Considerations......Page 402
10.3.1 Specific Energy......Page 403
10.4.2 The Chezy and Manning Equations......Page 406
10.4.3 Uniform Depth Examples......Page 409
10.5 Gradually Varied Flow......Page 413
10.6.1 The Hydraulic Jump......Page 414
10.6.2 Sharp-Crested Weirs......Page 418
10.6.3 Broad-Crested Weirs......Page 421
10.6.4 Underflow Gates......Page 423
10.7 Chapter Summary and Study Guide......Page 425
Problems......Page 426
11 TURBOMACHINES......Page 431
11.2 Basic Energy Considerations......Page 432
11.3 Basic Angular Momentum Considerations......Page 436
11.4.1 Theoretical Considerations......Page 438
11.4.2 Pump Performance Characteristics......Page 442
11.4.3 System Characteristics and Pump Selection......Page 444
11.5 Dimensionless Parameters and Similarity Laws......Page 447
11.5.1 Specific Speed......Page 450
11.6 Axial-Flow and Mixed-Flow Pumps......Page 451
11.7 Turbines......Page 454
11.7.1 Impulse Turbines......Page 455
11.7.2 Reaction Turbines......Page 461
11.8 Compressible Flow Turbomachines......Page 464
11.9 Chapter Summary and Study Guide......Page 465
References......Page 466
Problems......Page 467
A: COMPUTATIONAL FLUID DYNAMICS AND FLOWLAB......Page 471
B: PHYSICAL PROPERTIES OF FLUIDS......Page 486
C: PROPERTIES OF THE U.S. STANDARD ATMOSPHERE......Page 491
D: REYNOLDS TRANSPORT THEOREM......Page 493
E: COMPREHENSIVE TABLE OF CONVERSION FACTORS......Page 498
ONLINE APPENDIX LIST......Page 502
ANSWERS......Page 503
INDEX......Page 509
INDEX OF FLUIDS PHENOMENA VIDEOS......Page 518