Introduction to Fluid Mechanics

Description

Cover......Page 1 Title Page ......Page 3 Copyright......Page 4 Preface......Page 5 Contents......Page 8 Chapter 1 Problems......Page 13 Chapter 1 Introduction......Page 15 Note to Students......Page 16 Definition of a Fluid......Page 17 1.2 Basic Equations......Page 18 1.3 Methods of Analysis......Page 19 System and Control Volume......Page 20 Methods of Description......Page 21 Systems of Dimensions......Page 23 Systems of Units......Page 24 Dimensional Consistency and “Engineering” Equations ......Page 25 1.5 Analysis of Experimental Error......Page 27 References......Page 28 Chapter 2 Problems......Page 29 Chapter 2 Fundamental Concepts......Page 33 2.1 Fluid as a Continuum......Page 34 2.2 Velocity Field......Page 35 One-, Two-, and Three-Dimensional Flows......Page 36 Timelines, Pathlines, Streaklines, and Streamlines......Page 37 2.3 Stress Field......Page 41 2.4 Viscosity......Page 43 Newtonian Fluid......Page 44 Non-Newtonian Fluids......Page 46 2.5 Surface Tension......Page 47 2.6 Description and Classification of Fluid Motions......Page 48 Viscous and Inviscid Flows......Page 50 Compressible and Incompressible Flows......Page 52 Internal and External Flows......Page 53 2.7 Summary and Useful Equations......Page 54 References......Page 55 Chapter 3 Problems......Page 56 Chapter 3 Fluid Statics......Page 61 3.1 The Basic Equation of Fluid Statics......Page 62 3.2 The Standard Atmosphere......Page 65 Incompressible Liquids: Manometers......Page 66 Gases......Page 71 Hydrostatic Force on a Plane Submerged Surface......Page 73 Hydrostatic Force on a Curved Submerged Surface......Page 80 3.5 Buoyancy and Stability......Page 83 3.6 Fluids in Rigid-Body Motion......Page 86 3.7 Summary and Useful Equations......Page 91 References......Page 92 Chapter 4 Problems......Page 93 Chapter 4 Basic Equations in Integral Form for a Control Volume......Page 98 Conservation of Mass......Page 99 The First Law of Thermodynamics......Page 100 4.2 Relation of System Derivatives to the Control Volume Formulation......Page 101 Derivation......Page 102 Physical Interpretation......Page 104 4.3 Conservation of Mass......Page 105 Special Cases......Page 106 4.4 Momentum Equation for Inertial Control Volume......Page 110 Differential Control Volume Analysis......Page 121 Control Volume Moving with Constant Velocity......Page 125 4.5 Momentum Equation for Control Volume with Rectilinear Acceleration......Page 127 4.6 Momentum Equation for Control Volume with Arbitrary Acceleration......Page 133 Equation for Fixed Control Volume......Page 138 Equation for Rotating Control Volume......Page 142 4.8 The First and Second Laws of Thermodynamics......Page 146 Rate of Work Done by a Control Volume......Page 147 Control Volume Equation......Page 149 4.9 Summary and Useful Equations......Page 153 Chapter 5 Problems......Page 156 Chapter 5 Introduction to Differential Analysis of Fluid Motion......Page 158 Rectangular Coordinate System......Page 159 Cylindrical Coordinate System......Page 163 5.2 Stream Function for Two-Dimensional Incompressible Flow......Page 165 5.3 Motion of a Fluid Particle (Kinematics)......Page 167 Fluid Translation: Acceleration of a Fluid Particle in a Velocity Field......Page 168 Fluid Rotation......Page 174 Fluid Deformation......Page 177 Forces Acting on a Fluid Particle......Page 181 Newtonian Fluid: Navier–Stokes Equations......Page 182 5.5 Summary and Useful Equations......Page 190 References......Page 191 Chapter 6 Problems......Page 192 Chapter 6 Incompressible Inviscid Flow......Page 196 6.1 Momentum Equation for Frictionless Flow: Euler’s Equation......Page 197 Derivation Using Streamline Coordinates......Page 201 Derivation Using Rectangular Coordinates......Page 202 Static, Stagnation, and Dynamic Pressures......Page 203 Applications......Page 205 Cautions on Use of the Bernoulli Equation......Page 210 6.3 The Bernoulli Equation Interpreted as an Energy Equation......Page 211 6.4 Energy Grade Line and Hydraulic Grade Line......Page 215 6.5 Unsteady Bernoulli Equation: Integration of Euler’s Equation Along a Streamline......Page 217 Bernoulli Equation Applied to Irrotational Flow......Page 219 Velocity Potential......Page 220 Stream Function and Velocity Potential for Two-Dimensional, Irrotational, Incompressible Flow: Laplace’s Equation......Page 221 Elementary Plane Flows......Page 223 Superposition of Elementary Plane Flows......Page 225 6.7 Summary and Useful Equations......Page 234 References......Page 235 Chapter 7 Problems......Page 236 Chapter 7 Dimensional Analysis and Similitude......Page 239 7.1 Nondimensionalizing the Basic Differential Equations......Page 241 7.2 Buckingham Pi Theorem......Page 243 7.3 Significant Dimensionless Groups in Fluid Mechanics......Page 249 7.4 Flow Similarity and Model Studies......Page 251 Incomplete Similarity......Page 253 Scaling with Multiple Dependent Parameters......Page 258 Comments on Model Testing......Page 261 7.5 Summary and Useful Equations......Page 262 References......Page 263 Chapter 8 Problems......Page 264 Chapter 8 Internal Incompressible Viscous Flow......Page 268 Laminar versus Turbulent Flow......Page 269 The Entrance Region......Page 270 Both Plates Stationary......Page 271 Upper Plate Moving with Constant Speed, U ......Page 277 8.3 Fully Developed Laminar Flow in a Pipe......Page 282 Part B Flow in Pipes and Ducts......Page 286 8.4 Shear Stress Distribution in Fully Developed Pipe Flow......Page 287 8.5 Turbulent Velocity Profiles in Fully Developed Pipe Flow......Page 288 8.6 Energy Considerations in Pipe Flow......Page 292 Head Loss......Page 293 Major Losses: Friction Factor......Page 294 Minor Losses......Page 299 Noncircular Ducts......Page 303 8.8 Solution of Pipe Flow Problems......Page 304 Single-Path Systems......Page 305 Multiple-Path Systems......Page 317 8.9 Restriction Flow Meters for Internal Flows......Page 320 The Orifice Plate......Page 323 The Venturi......Page 327 The Laminar Flow Element......Page 328 Linear Flow Meters......Page 329 Traversing Methods......Page 330 8.10 Summary and Useful Equations......Page 331 References......Page 333 Chapter 9 Problems......Page 334 Chapter 9 External Incompressible Viscous Flow......Page 337 9.1 The Boundary Layer Concept......Page 339 9.2 Laminar Flat Plate Boundary Layer: Exact Solution......Page 343 9.3 Momentum Integral Equation......Page 346 9.4 Use of the Momentum Integral Equation for Flow with Zero Pressure Gradient......Page 350 Laminar Flow......Page 351 Turbulent Flow......Page 355 9.5 Pressure Gradients in Boundary Layer Flow......Page 358 9.6 Drag......Page 360 Pure Friction Drag: Flow over a Flat Plate Parallel to the Flow......Page 361 Friction and Pressure Drag: Flow over a Sphere and Cylinder......Page 364 Streamlining......Page 370 9.7 Lift......Page 372 9.8 Summary and Useful Equations......Page 384 References......Page 386 Chapter 10 Problems......Page 387 Chapter 10 Fluid Machinery......Page 391 Machines for Doing Work on a Fluid......Page 392 Machines for Extracting Work (Power) from a Fluid......Page 394 The Angular-Momentum Principle: The Euler Turbomachine Equation......Page 396 Velocity Diagrams......Page 398 Performance—Hydraulic Power......Page 400 Dimensional Analysis and Specific Speed......Page 401 Application of Euler Turbomachine Equation to Centrifugal Pumps......Page 406 Application of the Euler Equation to Axial Flow Pumps and Fans......Page 407 Performance Characteristics......Page 410 Similarity Rules......Page 415 Cavitation and Net Positive Suction Head......Page 419 Pump Selection: Applications to Fluid Systems......Page 422 Blowers and Fans......Page 428 10.4 Positive Displacement Pumps......Page 432 Hydraulic Turbine Theory......Page 435 Performance Characteristics for Hydraulic Turbines......Page 437 Propellers......Page 443 Wind Turbines......Page 448 Application of the Energy Equation to a Compressible Flow Machine......Page 454 Compressors......Page 455 10.8 Summary and Useful Equations......Page 458 References......Page 460 Chapter 11 Problems......Page 462 Chapter 11 Flow in Open Channels......Page 464 Simplifying Assumptions......Page 466 Channel Geometry......Page 468 Speed of Surface Waves and the Froude Number......Page 469 11.2 Energy Equation for Open-Channel Flows......Page 473 Specific Energy......Page 475 Critical Depth: Minimum Specific Energy......Page 476 Flow over a Bump......Page 481 11.4 The Hydraulic Jump......Page 485 Depth Increase Across a Hydraulic Jump......Page 488 Head Loss Across a Hydraulic Jump......Page 489 11.5 Steady Uniform Flow......Page 491 The Manning Equation for Uniform Flow......Page 493 Energy Equation for Uniform Flow......Page 498 Optimum Channel Cross Section......Page 500 11.6 Flow with Gradually Varying Depth......Page 501 Calculation of Surface Profiles......Page 502 Suppressed Rectangular Weir......Page 505 Triangular Weir......Page 506 Broad-Crested Weir......Page 507 11.8 Summary and Useful Equations......Page 508 References......Page 509 Chapter 12 Problems......Page 510 Chapter 12 Introduction to Compressible Flow......Page 512 12.1 Review of Thermodynamics......Page 513 Speed of Sound......Page 519 Types of Flow—The Mach Cone......Page 523 12.3 Reference State: Local Isentropic Stagnation Properties......Page 525 Local Isentropic Stagnation Properties for the Flow of an Ideal Gas......Page 526 12.5 Basic Equations for One-Dimensional Compressible Flow......Page 532 First Law of Thermodynamics......Page 533 Second Law of Thermodynamics......Page 534 12.6 Isentropic Flow of an Ideal Gas: Area Variation......Page 535 Subsonic Flow, M< 1......Page 537 Sonic Flow, M=1......Page 538 Reference Stagnation and Critical Conditions for Isentropic Flow of an Ideal Gas......Page 539 Isentropic Flow in a Converging Nozzle......Page 544 Isentropic Flow in a Converging-Diverging Nozzle......Page 548 Basic Equations for a Normal Shock......Page 553 Normal-Shock Flow Functions for One-Dimensional Flow of an Ideal Gas......Page 555 12.8 Supersonic Channel Flow with Shocks......Page 559 12.9 Summary and Useful Equations......Page 561 References......Page 563 A.1 Specific Gravity......Page 564 A.2 Surface Tension......Page 567 Effect of Temperature on Viscosity......Page 568 Effect of Pressure on Viscosity......Page 570 A.4 Lubricating Oils......Page 572 A.5 Properties of Common Gases, Air, and Water......Page 573 Appendix B Videos for Fluid Mechanics ......Page 576 C.2 Pump Selection......Page 578 C.3 Fan Selection......Page 579 D.1 Isentropic Flow......Page 589 D.2 Normal Shock......Page 590 E.3 Estimation of Uncertainty......Page 592 E.4 Applications to Data......Page 595 References......Page 597 The Need for CFD......Page 598 F.2 Finite Difference Approach to CFD......Page 599 Techniques of CFD......Page 602 References......Page 603 Index......Page 604 EULA......Page 610