This book is exceptional in providing an up-to-date, but compact, introduction to the field of hydrodynamics and fluid dynamics that is both sufficiently comprehensive and easy to read. It covers all the elements of compressible and incompressible fluid dynamics, from the basic concepts through to the constituent equations and their applications. Fluid flows in different environments are thoroughly discussed, and specific aspects such as dissipation, turbulence, shock waves, and blast waves receive detailed attention. The book contains many exercises and draws attention to numerical solutions to specific problems. The book is ideal for undergraduate and graduate students and young researchers in physics, astrophysics, mathematics (pure and applied), and engineering. As this book is intended for a wide audience, the mathematical prerequisites are kept to a low level.
Author(s): Roberto A. Capuzzo Dolcetta
Series: UNITEXT for Physics
Edition: 1
Publisher: Springer Nature Switzerland
Year: 2023
Language: English
Pages: 136
City: Cham
Preface
Contents
Symbols
1 Fluids and Their Fundamental Aspects
1.1 Newtonian and Non-Newtonian Fluids
1.2 Plasma as Peculiar Fluid
1.3 The Continuum Hypothesis
1.4 The Lagrangian and Eulerian Descriptions of Fluids
1.4.1 From the Lagrangian to the Eulerian Description and Vice Versa
1.5 Stream Lines and Flux Tubes
1.6 Solved Exercises
1.7 Further Readings
2 The Basic Equations for Fluid Motion
2.1 The Continuity Equation
2.1.1 Lagrangian Form of Continuity Equation
2.2 The Motion Equation for Fluids
2.2.1 For Ideal Fluids
2.2.2 For Non-ideal Fluids
2.2.3 The Stream Function
2.3 The Energy Equation
2.3.1 Kinetic Energy of the Fluid
2.3.2 The Energy Equation for a Dissipative Fluid
2.4 Thermodynamics of Fluids and Equations of State
2.5 Turbulence
2.6 Stokes Law and Falling Sphere Viscometer
2.7 Solved Exercises
2.8 Further Readings
3 Fluid Flows in Different Environments
3.1 Fluids in Terrestrial and Astrophysical Contexts
3.2 Self-gravitating Fluids
3.2.1 Equilibrium of Self-gravitating Fluids
3.2.2 Gravitating Systems Out of Equilibrium
3.3 Jeans Theory of Gravitational Instability
3.4 The Role of Viscosity in Astrophysical Environments
3.5 Peculiarities of Astrophysical Equations of State
3.6 Solved Exercises
3.7 Further Readings
4 Discontinuities in Fluid Flows
4.1 Jump Conditions
4.2 Tangential Discontinuities
4.3 Shock Waves
4.3.1 Jumps in Terms of Mach Numbers
4.3.2 Weak Shocks
4.3.3 Physical Meaning of Shock Waves
4.4 Solved Exercises
4.5 Further Readings
5 Blast Waves
5.1 Propagation of a Blast Wave
5.2 A Similarity Solution
5.2.1 Determination of the Dimensionless Constant kγ
5.3 Supernova Explosions
5.4 Solved Exercises
5.5 Further Readings
6 Peculiar Fluid Dynamics
6.1 Relativistic Fluid Dynamics
6.1.1 The Energy–Momentum Tensor
6.1.2 Relativistic Equations of Fluid Motion
6.2 Superfluids
6.3 Further Readings
Appendix A Basic Vector Analysis and Calculus
A.1 The Formal Vector Operator
A.2 Coordinate Systems
A.2.1 Gradient, Divergence, Laplacian and Curl in Different Coordinate Systems
A.2.2 Continuity and Motion Equation in Spherical Polar and Cylindrical Coordinates
A.3 Some Useful Vector Formulas
A.3.1 Identities of Vector Algebra
A.3.2 Identities Involving
A.4 Basic Concepts and Theorems of Vector Calculus
A.5 Tensors
A.6 Further Readings
Appendix References
Index
