3
Contents
Preface... 5
Acknowledgements... 7
1. Introduction and Basic Terminology... 9
1.1. Introduction... 9
1.2. Methodology of Fluid Mechanics... 10
1.3. The No-Slip Condition... 13
1.4. Classification of Fluid Flows... 14
1.5. Flow Instability... 23
1.6. Other Helpful Terminology... 25
2. Properties of Fluids... 27
2.1. Definition of Property... 27
2.2. Common Properties of Fluids... 27
2.3. Viscosity... 30
2.4. Surface Tension and Capillary Effect... 42
3. Hydrostatics... 51
3.1. Pressure... 51
3.2. Pressure Measurement... 59
3.3. Hydrostatic Forces on Submerged Plane Surfaces... 66
3.4. Hydrostatic Forces on Submerged Curved Surfaces... 75
3.5. Archimedes Principle – Buoyancy... 79
3.6. Stability of Floating Bodies... 83
4. Fluid Kinematics... 86
4.1. Lagrangian and Eulerian Description of Fluid Flow... 86
4.2. Reynolds Transport Theorem... 90
4.3. Velocity Field and Acceleration Field... 95
4.4. Material Derivative... 96
4.5. Flow Visualization... 101
4.6. Vorticity and Rotationality... 111
4.7. Kinematics of Selected Types of Flow... 113
5. Mass Conservation Principle... 119
5.1. The Integral Form of Mass Conservation... 120
5.2. The Differential Form of Mass Conservation – the Continuity Equation... 127
5.3. The Stream Function... 135
6. Energy Conservation – Bernoulli Equation... 148
6.1. Derivation of Bernoulli Equation... 148
6.2. Applications of Bernoulli Equation... 158
6.3. Bernoulli Equation in Meteorology and Oceanography... 164
6.4. Conservation of Mechanical Energy... 166
7. Conservation of Linear and Angular Momentum... 175
7.1. Conservation of Momentum for a System (Lagrangian Approach)... 175
7.2. The Linear Momentum Equation for a Control Volume . (Eulerian Approach)... 178
7.3. The Angular Momentum Equation... 189
8. The Navier–Stokes Equation... 200
8.1. The Derivation Methodology for the Navier–Stokes Equation... 200
8.2. Simplification of the Navier–Stokes Equation for Specific Cases... 203
8.3. Application of the Navier–Stokes Equation to Calculate Pressure Field... 204
8.4. Exact Solutions of the Navier–Stokes Equation... 206
8.5. Approximate Solutions of the Navier–Stokes Equation... 220
8.6. Summary of Navier–Stokes Equation Approximations... 243
Bibliography... 245
