Phu Xuan University Library
|
PXU E-LIB
Sign in
All Things Flow - Fluid Mechanics for the Natural Sciences

External

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.

Civil EngineeringEngineering
Author
Bill Smyth
Publisher
Oregon State University
Source
LibreTexts
License
CC BY-NC
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 76 sections
  1. 01: Introduction
  2. 1.01: Preface
  3. 1.02: What is a fluid? The continuum hypothesis
  4. 02: Review of Elementary Linear Algebra
  5. 2.01: Scalars and vectors
  6. 2.02: Matrices
  7. 2.03: Systems of linear equations
  8. 2.04: Eigenvalues and eigenvectors
  9. 03: Cartesian Vectors and Tensors
  10. 3.01: Measuring space with Cartesian coordinates
  11. 3.02: Vectors and Scalars
  12. 3.03: Cartesian tensors
  13. 04: Tensor Calculus
  14. 4.01: Vector calculus operations
  15. 4.02: Flux and divergence
  16. 4.03: Vorticity and Circulation
  17. 05: Fluid Kinematics
  18. 5.01: Lagrangian and Eulerian descriptions
  19. 5.02: The Streamfunction
  20. 5.03: Rotation and strain- the relative motion of two nearby particles
  21. 5.04: Pancakes and noodles- the geometry of turbulence
  22. 06: Fluid Dynamics
  23. 6.01: Solution methods
  24. 6.02: Leibniz rule
  25. 6.03: Mass conservation
  26. 6.04: Momentum conservation
  27. 6.05: Energy conservation in a Newtonian fluid
  28. 6.06: The temperature (heat) equation
  29. 6.07: Equations of state
  30. 6.08: The advection-diffusion equation for a scalar concentration
  31. 6.09: Summary- the equations of motion
  32. 6.10: Solution methods
  33. 07: Vortices
  34. 7.01: Introduction
  35. 7.02: Vortex dynamics in a homogeneous, inviscid fluid
  36. 7.03: Viscous effects
  37. 7.04: Buoyancy effects- the baroclinic torque
  38. 08: Waves
  39. 8.01: Introduction
  40. 8.02: The Dispersion Relation
  41. 8.03: Superposition phenomena
  42. 8.04: Limiting cases
  43. 09: Nonlinear, Hydrostatic Flow Over Topography
  44. 9.01: Introduction
  45. 9.02: Hydraulic control
  46. 9.03: Hydraulic jumps and bores
  47. 9.04: Flood waves in a turbulent river
  48. 10: Postface
  49. 11: Exercises
  50. 12: Appendix A- Taylor Series Expansions
  51. 13: Appendix B- Torque and the Moment of Inertia
  52. 13.01: B.1- Torque
  53. 13.02: B.2- The moment of inertia tensor
  54. 14: Appendix C- Isotropic Tensors
  55. 14.01: C.1- Infintesimal Rotations
  56. 14.02: C.2- 1st-order isotropic tensors
  57. 14.03: C.3- 2nd-order isotropic tensors
  58. 14.04: C.4 3rd-Order Isotropic Tensors
  59. 14.05: C.5 4th-order isotropic tensors
  60. 15: Appendix D- The Leva-Cevita Alternating Tensor
  61. 15.01: D.1 A completely antisymmetric, three dimensional array
  62. 15.02: D.2 The ε-δ relation
  63. 15.03: D.3 Applications of (epsilon)
  64. 16: Appendix E- Vector Identities
  65. 17: Appendix F- The Cauchy Stress Tensor
  66. 17.01: F.1 Local Equilibrium
  67. 17.02: F.2 Stress on a tilted plane
  68. 17.03: F.3 Symmetry of the stress tensor
  69. 18: Appendix G- Boussinesq Approximation
  70. 18.01: G.1 The Navier-Stokes equation for nearly-uniform density
  71. 18.02: G.2 Alternative derivation
  72. 19: Appendix H- Bernoulli's Equation
  73. 20: Appendix I- Vector Operations in Curvilinear Coordinates
  74. 20.01: I.1 Cylindrical coordinates
  75. 20.02: I.2 Spherical coordinates
  76. 21: Appendix J- The Stokes Drift