Nguồn ngoài
All Things Flow - Fluid Mechanics for the Natural Sciences
This book on fluid mechanics is concerned with phenomena that we have all been familiar with since childhood: flows you see in sinks and bathtubs, in rivers, and at the beach. Prerequisites include basic linear algebra, differential and integral calculus and Newton’s laws of motion. As we go along we discover the need for the more advanced tools of tensor analysis.
- Tác giả
- Bill Smyth
- Nhà xuất bản
- Oregon State University
- Nguồn
- LibreTexts
- Giấy phép
- CC BY-NC
- Ngôn ngữ
- EN
- Danh mục
- Khoa học cơ bản
Mục lục· 76 mục
- 01: Introduction
- 1.01: Preface
- 1.02: What is a fluid? The continuum hypothesis
- 02: Review of Elementary Linear Algebra
- 2.01: Scalars and vectors
- 2.02: Matrices
- 2.03: Systems of linear equations
- 2.04: Eigenvalues and eigenvectors
- 03: Cartesian Vectors and Tensors
- 3.01: Measuring space with Cartesian coordinates
- 3.02: Vectors and Scalars
- 3.03: Cartesian tensors
- 04: Tensor Calculus
- 4.01: Vector calculus operations
- 4.02: Flux and divergence
- 4.03: Vorticity and Circulation
- 05: Fluid Kinematics
- 5.01: Lagrangian and Eulerian descriptions
- 5.02: The Streamfunction
- 5.03: Rotation and strain- the relative motion of two nearby particles
- 5.04: Pancakes and noodles- the geometry of turbulence
- 06: Fluid Dynamics
- 6.01: Solution methods
- 6.02: Leibniz rule
- 6.03: Mass conservation
- 6.04: Momentum conservation
- 6.05: Energy conservation in a Newtonian fluid
- 6.06: The temperature (heat) equation
- 6.07: Equations of state
- 6.08: The advection-diffusion equation for a scalar concentration
- 6.09: Summary- the equations of motion
- 6.10: Solution methods
- 07: Vortices
- 7.01: Introduction
- 7.02: Vortex dynamics in a homogeneous, inviscid fluid
- 7.03: Viscous effects
- 7.04: Buoyancy effects- the baroclinic torque
- 08: Waves
- 8.01: Introduction
- 8.02: The Dispersion Relation
- 8.03: Superposition phenomena
- 8.04: Limiting cases
- 09: Nonlinear, Hydrostatic Flow Over Topography
- 9.01: Introduction
- 9.02: Hydraulic control
- 9.03: Hydraulic jumps and bores
- 9.04: Flood waves in a turbulent river
- 10: Postface
- 11: Exercises
- 12: Appendix A- Taylor Series Expansions
- 13: Appendix B- Torque and the Moment of Inertia
- 13.01: B.1- Torque
- 13.02: B.2- The moment of inertia tensor
- 14: Appendix C- Isotropic Tensors
- 14.01: C.1- Infintesimal Rotations
- 14.02: C.2- 1st-order isotropic tensors
- 14.03: C.3- 2nd-order isotropic tensors
- 14.04: C.4 3rd-Order Isotropic Tensors
- 14.05: C.5 4th-order isotropic tensors
- 15: Appendix D- The Leva-Cevita Alternating Tensor
- 15.01: D.1 A completely antisymmetric, three dimensional array
- 15.02: D.2 The ε-δ relation
- 15.03: D.3 Applications of (epsilon)
- 16: Appendix E- Vector Identities
- 17: Appendix F- The Cauchy Stress Tensor
- 17.01: F.1 Local Equilibrium
- 17.02: F.2 Stress on a tilted plane
- 17.03: F.3 Symmetry of the stress tensor
- 18: Appendix G- Boussinesq Approximation
- 18.01: G.1 The Navier-Stokes equation for nearly-uniform density
- 18.02: G.2 Alternative derivation
- 19: Appendix H- Bernoulli's Equation
- 20: Appendix I- Vector Operations in Curvilinear Coordinates
- 20.01: I.1 Cylindrical coordinates
- 20.02: I.2 Spherical coordinates
- 21: Appendix J- The Stokes Drift