CONTENT : Preface xiii Acknowledgements xv 1 Properties of Fluids 1 1.1 Definition of a Fluid 1 1.2 Density 1 1.3 Specific Weight 2 1.4 Pressure 2 1.5 Equations of State 2 1.6 Bulk Modulus 4 1.7 Viscosity 4 1.8 Surface Tension 8 1.9 Capillarity 10 1.10Vapour Pressure 12 Exercises 12 2 Fluid Statics 16 2.1 Introduction . 16 2.2 Pressure at a Point 16 2.3 Variation of Pressure within a Static Fluid 17 2.4 Pressure Variation in Compressible Fluids with Elevation 19 2.5 Force on Plane Areas Immersed in a Fluid 21 2.6 Forces on Curved Surfaces 26 2.7 Measurement of Pressure 30 2.8 Relative Motion 36 2.9 Floating Bodies 44 2.10Stability of Floating Bodies with Liquid Cargo 50 Exercises o50 3 Kinematics of Fluid Flow 57 3.1 Flow Variables and Classification '57 3.2 Continuum ' 58 3.3 Kinematics of Fluid Flow , 59 3.4 Stream Lines, Path Lines and Streak Lines 59 3.5 Construction of Path and Streak Lines 60 3.6 Equations for Stream and Path Lines 61 3.7 Stream Function 62 3.8 Elements of Particle Motion 64 3.9 Circulation 67 3.10Equation of Continuity 68 Exercises 73 4 Dynamics of Flow 75 4.1 Acceleration 75 4.2 Tangential and Normal Components of Accelerations 76 4.3 Forces 76 4.4 Equation of Motion along a Stream Line 77 4.5 Equation of Motion in the xy-Coordinates 79 4.6 Velocity Potential 81 4.7 Relation between Velocity Potential and Stream Function 82 4.8 Flow Nets 83 4.9 Laplace's Equation 85 Exercises 85 5 Examples of Irrotational Flow of Ideal Fluids 87 5.1 Uniform Flows 87 5.2 Plane Potential Flow in Polar Coordinates 89 5.3 Flow Around Corners 93 5.4 Combination of Two or More Flows 94 Exercises 102 6 Applications of Bernoulli's Theorem and Modifications 104 6.1 Introduction 104 6.2 Free Liquid Jet 104 6.3 Efflux from an Opening at the End of a Pipe 107 6.4 Venturimeter 109 6.5 Orifice Meter 111 6.6 Discharge from a Tank through Outlet Fittings 112 6.7 Large Vertical Orifice 114 6.8 Time of Emptying a Tank 115 6.9 Transfer Time from One Tank to Another 117 6.10Inflow and Outflow ' 118 6.11Weirs and Notches 120 Exercises 127 7 Force-Momentum Relationship 131 7.1 Introduction 131 7.2 Control Volume 131 7.3 Impact of Jet on a Flat Plate 135 7.4 Force on a Curved Vane 137 7.5 Pipe Bend 139 7.6 Rocket 140 7.7 Jet Propulsion 141 7.8 Loss of Energy in a Pipe Expansion 142 7.9 Angular Momentum 144 Exercises 149 8 Laminar Flow 155 Laminar Motion 155 8.1 Introduction 155 8.2 Shear Stresses 156 8.3 Navier-Stokes Equations 157 8.4 Navier-Stokes Equations in Cylindrical Coordinates 159 8.5 Exact Solutions of Navier-Stokes Equations 160 8.6 Flow between Horizontal Parallel Plates (Hagen-Poiseuille Flow) 160 8.7 Inclined Parallel Plates 163 8.8 CouetteFlow 164 8.9 Combined Hagen-Poiseuille and Couette Flows 166 8.10Flow along an Inclined Channel with a Free Surface 168 8.11Hagen-Poiseuille Flow in Cylindrical Tubes 169 8.12Laminar Flow in an Annulus 172 8.13Co-Axial Couette Flow 173 8.14Rotating Cylinders 173 8.15Non-Linear Exact Solutions 175 8.16Approximate Solution for Slow Motion Around a Sphere 175 Laminar Stability 177 8.17Introduction - 177 8.18Reynolds Number 177 8.19Stability Parameter 178 8.20Stability Curves 180 Laminar Boundary Layer 181 8.21Introduction ' 181 8.22Boundary-Layer Thickness 183 8.23Displacement, Momentum and Energy Thickness 183 8.24Boundary-Layer Equations 185 8.25Boundary Layer along a Flat Plate with Zero Pressure Gradient 187 8.26Boundary-Layer Integral Momentum Equation 188 8.27Transition to Turbulence 192 Exercises 196 9 Turbulent Flow 199 Reynolds Equation 199 9.1 Introduction 199 9.2 Reynolds Equations of Motion for Turbulent Flow 200 9.3 Characteristics of Turbulence 203 9.4 Role of Eddies in Fluid Motion 205 9.5 Classification of Turbulence 207 9.6 Phenomenological Theories 207 Turbulent Boundary Layer 210 9.7 Turbulent Boundary Layer along a Flat Plate 210 9.8 Momentum Equation 213 9.9 Turbulent Flow in Pipes 214 9.10Mean Velocity and Maximum Velocity 218 9.11Pipe Resistance Factor 219 9.12Explicit Formula for Pipe Resistance Factor 220 Exercises 226 Appendix 227 10Flow in Pipes 229 Steady Flow o 229 10.1Losses in Pipes 229 10.2Losses in Pipe Fittings 231 10.3Equivalent Length 231 10.4Hydraulic and Energy Grade Lines 233 10.5Problems in Pipe Flows (Pipes in Series) 234 10.6Parallel Pipes '237 10.7Branch Pipes 238 10.8Pipe Networks 240 Unsteady Flow in Pipes 243 10.9Establishment of Flow 243 10.10 Water Hammer ' 245 10.11 Basic Equations of Water Hammer 247 10.12 Oscillations of Liquid Column in a U-Tube 252 10.13 Surge Tanks 254 10.14 Basic Equations of Mass Oscillations in a Simple Surge Tank 255 10.15 Instantaneous Closure or Opening of Valve Neglecting Tunnel Boundary Resistance 256 10.16 Linear Closure of Valve 258 10.17 Instantaneous Closure of Valve Considering Tunnel Resistance 259 10.18 Numerical Integration 260 10.19 Types of Surge Tanks 262 Exercises 263 11Forces on Submerged Bodies 267 11.1 Introduction 267 11.2 Boundary Layer Separation 267 11.3 Laminar Wake Behind a Cylinder 270 11.4 Drag on Immersed Bodies 272 11.5 Lift Force 277 11.6 Induced Drag 282 Exercises 286 12Open Channels 288 12.1 Introduction 288 12.2 Velocity Distribution 289 12.3 Pressure Coefficient 291 12.4 Energy Equation 293 12.5 Specific Energy 295 12.6 Specific Energy Diagram 296 12.7 Discharge Diagram ' 298 12.8 Application of Specific Energy and Discharge Diagrams 299 12.9 Critical Depth in Non-rectangular Channels 301 12.10 Critical Depth and Wave Celerity 303 12.11 Critical Flow and Control of Flow 303 12.12 Momentum Equation 304 12.13 Specific Force Curve - 305 12.14 Flow Conditions at Piers 307 12.15 Uniform Flow 308 12.16 Uniform Flow Formulae 309 12.17 Manning's Formula 310 12.18 Computation of Equivalent Manning's n for Composite Roughness 311 12.19 Computation of Uniform Flow 312 12.20 Economical Cross-Section 313 12.21 Gradually Varied Flow 315 12.22 Classification of Flow Profiles 316 12.23 Characteristics of Flow Profiles 317 12.24 Flow Profile Analysis 324 12.25 Integration of the Dynamic Equation 327 12.26 Rapidly Varied Flow 334 12.27 Hydraulic Jump 334 12.28 The Oblique Jump 339 12.29 Channel Transitions 340 12.30 Stilling Basins 345 12.31 Canal Bends 345 12.32 Unsteady Flow in Open Channels 348 12.33 Negative Surge 352 Exercises 354 Appendix 1 358 Appendix 2 360 Appendix 3 361 Appendix 4 362 13Compressible Flow 363 13.1Introduction 363 13.2Speed of Sound 364 33.3Mach Number 366 13.4One-Dimensional Flow (Basic Equations) 366 13.5Area-Velocity Relation in One-Dimensional Isentropic Flow 369 13.6Mass-Flow Rate 371 13.7Normal Shock Wave 372 13.8Fanno and Rayleigh Lines 375 13.9Flow of a Perfect Gas in a Duct of Constant Area with Heat Transfer 376 13.10 Oblique Shock Waves 379 13.11 Behaviour of Nozzle Flow as a Function of Back Pressure 381 13.12 Flow through a Truncated Nozzle 384 13.13 Compressible Flow in a Pipe with Friction 385 13.14 Isothermal Flow 388 Exercises 390 Appendix 392 14Dimensional Analysis and Similitude 397 Dimensional Analysis 397 14.1Introduction397 14.2Fundamental Dimensions 397 14.3Physical Quantity and Dimensions 398 14.4Dimensional Homogeneity 399 14.5Summation of Quantities 401 14.6Product of Quantities 401 14.7Non-Dimensional Parameters 402 14.8jr-Theorem 404 14.9Significance of the JT-Theorem 405 14.10 Dimensional Analysis: Choice of Variables 406 14.11 Criticisms of the Dimensional Analysis 407 14.12 Detennination of Dimensionless Parameters 407 14.13 Method of Repeating Variables 409 14.14 Further Examples in Dimensional Analysis 410 14.1Model Similitude 414 14.15 Physical Models 414 14.16 Scale Models in Submerged Flows 415 Exercises 421 Solutions 424 Index 434