Introduction To Fluid Mechanics - Toc

Contents

ABOUT THE AUTHORS

viii

PREFACE

ix

LIST OF SYMBOLS

xi

OF FLUID MECHANICS IHISTORY Fluid mechanics in everyday life

1.1 1.2 The beginning of fluid mechanics

P CHARACTERISTICS OF A FLUID 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8

Fluid Units and dimensions Density, specific gravity and specific volume Viscosity Surface tension Compressibility Characteristics of a perfect gas Problems

FLUID STATICS

3.1 3.2 3.3 3.4 3.5

Pressure Forces acting on the vessel of liquid Why does a ship float? Relatively stationary state Problems

1 1 1 6 6 6 8 9 13 16 17 18 20 20 30 33 35 37

FUNDAMENTALS OF FLOW

41

4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9

41 43 43 44 46 46 47 50 53

Streamline and stream tube Steady flow and unsteady flow Three-dimensional, two-dimensional and one-dimensional flow Laminar flow and turbulent flow Reynolds number Incompressible and compressible fluids Rotation and spinning of a liquid Circulation Problems

vi Contents

ONE-DIMENSIONALFLOW: mechanism for conservation of flow properties 5.1 Continuity equation 5.2 Conservation of energy 5.3 Conservation of momentum 5.4 Conservation of angular momentum 5.5 Problems

55 55 56 70 76 78

FLOW OF VISCOUS FLUID 6.1 Continuity equation 6.2 Navier-Stokes equation 6.3 Velocity distribution of laminar flow 6.4 Velocity distribution of turbulent flow 6.5 Boundary layer 6.6 Theory of lubrication 6.7 Problems

82 82 83 88 94 101 106 109

FLOW IN PIPES 7.1 Flow in the inlet region 7.2 Loss by pipe friction 7.3 Frictional loss on pipes other than circular pipes 7.4 Various losses in pipe lines 7.5 Pumping to higher levels 7.6 Problems

111 112 114 118 119 132 134

FLOW IN A WATER CHANNEL 8.1 Flow in an open channel with constant section and

136

8.2 8.3 8.4 8.5 8.6 8.7 8.8

flow velocity Best section shape of an open channel Specific energy Constant discharge Constant specific energy Constant water depth Hydraulic jump Problems

136 138 141 142 143 143 144 146

DRAG ANDLIFT 9.1 Flows around a body 9.2 Forces acting on a body 9.3 The drag of a body 9.4 The lift of a body 9.5 Cavitation 9.6 Problems

148 148 149 149 161 167 169

DIMENSIONAL ANALYSIS AND LAW OF SIMILARITY 10.1 Dimensional analysis 10.2 Buckingham’s 7c theorem 10.3 Application examples of dimensional analysis 10.4 Law of similarity 10.5 Problems

171 171 172 172 175 180

Contents vii

MEASUREMENT OF FLOW VELOCITY AND FLOW RATE

182

11.1 Measurement of flow velocity 11.2 Measurement of flow discharge 11.3 Problems

182 186 195

FLOW OF AN IDEAL FLUID

197 197

12.1 12.2 12.3 12.4 12.5 12.6 12.7

Euler’s equation of motion Velocity potential Stream function Complex potential Example of potential flow Conformal mapping Problems

198 200 20 1 203 212 216

FLOW OF A COMPRESSIBLE FLUID

218

13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8

218 22 1 223 224 226 230 235 236

Thermodynamical characteristics Sonic velocity Mach number Basic equations for one-dimensional compressible flow Isentropic flow Shock waves Fanno flow and Rayleigh flow Problems

UNSTEADY FLOW

238

14.1 14.2 14.3 14.4 14.5 14.6

238 240 242 243 244 247

Vibration of liquid column in U-tube Propagation of pressure in pipe line Transitional change in flow quantity in a pipe line Velocity of pressure wave in a pipe line Water hammer Problems

COMPUTATIONAL FLUID DYNAMICS

249

15.1 15.2 15.3 15.4

249 262 264 269

Finite difference method Finite volume method Finite element method Boundary element method

FLOW VISUALISATION

274

16.1 Classification of techniques 16.2 Experimental visualisation methods 16.3 Computer-aided visualisation methods

274 274 286

ANSWERS TO PROBLEMS

291

INDEX

299