fluid_mechanics

xviii
Contents
4
FLUID KINEMATICS 147
Learning Objectives 147
4.1 The Velocity Field 147
4.1.1 Eulerian and Lagrangian Flow
Descriptions 150
4.1.2 One-, Two-, and Three-
Dimensional Flows 151
4.1.3 Steady and Unsteady Flows 152
4.1.4 Streamlines, Streaklines,
and Pathlines 152
4.2 The Acceleration Field 156
4.2.1 The Material Derivative 156
4.2.2 Unsteady Effects 159
4.2.3 Convective Effects 159
4.2.4 Streamline Coordinates 163
4.3 Control Volume and System Representations 165
4.4 The Reynolds Transport Theorem 166
4.4.1 Derivation of the Reynolds
Transport Theorem 168
4.4.2 Physical Interpretation 173
4.4.3 Relationship to Material Derivative 173
4.4.4 Steady Effects 174
4.4.5 Unsteady Effects 174
4.4.6 Moving Control Volumes 176
4.4.7 Selection of a Control Volume 177
4.5 Chapter Summary and Study Guide 178
References 179
Review Problems 179
Problems 179
5
FINITE CONTROL VOLUME
ANALYSIS 187
Learning Objectives 187
5.1 Conservation of Mass—The
Continuity Equation 188
5.1.1 Derivation of the Continuity
Equation 188
5.1.2 Fixed, Nondeforming Control
Volume 190
5.1.3 Moving, Nondeforming
Control Volume 196
5.1.4 Deforming Control Volume 198
5.2 Newton’s Second Law—The Linear
Momentum and Moment-of-
Momentum Equations 200
5.2.1 Derivation of the Linear
Momentum Equation 200
5.2.2 Application of the Linear
Momentum Equation 201
5.2.3 Derivation of the Moment-of-
Momentum Equation 215
5.2.4 Application of the Moment-of-
Momentum Equation 216
5.3 First Law of Thermodynamics—The
Energy Equation 223
5.3.1 Derivation of the Energy Equation 223
5.3.2 Application of the Energy
Equation 225
5.3.3 Comparison of the Energy
Equation with the Bernoulli
Equation 229
5.3.4 Application of the Energy
Equation to Nonuniform Flows 235
5.3.5 Combination of the Energy
Equation and the Moment-of-
Momentum Equation 238
5.4 Second Law of Thermodynamics—
Irreversible Flow 239
5.4.1 Semi-infinitesimal Control
Volume Statement of the
Energy Equation 239
5.4.2 Semi-infinitesimal Control
Volume Statement of the
Second Law of Thermodynamics 240
5.4.3 Combination of the Equations
of the First and Second
Laws of Thermodynamics 241
5.4.4 Application of the Loss Form
of the Energy Equation 242
5.5 Chapter Summary and Study Guide 244
References 245
Review Problems 245
Problems 245
6
DIFFERENTIAL ANALYSIS OF
FLUID FLOW 263
Learning Objectives 263
6.1 Fluid Element Kinematics 264
6.1.1 Velocity and Acceleration
Fields Revisited 265
6.1.2 Linear Motion and Deformation 265
6.1.3 Angular Motion and Deformation 266
6.2 Conservation of Mass 269
6.2.1 Differential Form of
Continuity Equation 269
6.2.2 Cylindrical Polar Coordinates 272
6.2.3 The Stream Function 272
6.3 Conservation of Linear Momentum 275
6.3.1 Description of Forces Acting
on the Differential Element 276
6.3.2 Equations of Motion 278
6.4 Inviscid Flow 279
6.4.1 Euler’s Equations of Motion 279
6.4.2 The Bernoulli Equation 279