Theoretical fluid mechanics /

• Κύριος συγγραφέας: Fitzpatrick, Richard 1963- (συγγραφέας.)
• Μορφή: Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Bristol : IOP Publishing, c2017.
• Σειρά: IOP expanding physics.
• Θέματα: Ρευστομηχανική

Theoretical Fluid Mechanics' has been written to aid physics students who wish to pursue a course of self-study in fluid mechanics. It is a comprehensive, completely self-contained text with equations of fluid mechanics derived from first principles, and any required advanced mathematics is eit...

Πίνακας περιεχομένων:

• 1. Mathematical models of fluid motion
• 1.1. Introduction
• 1.2. What is a fluid?
• 1.3. Volume and surface forces
• 1.4. General properties of the stress tensor
• 1.5. Stress tensor in a static fluid
• 1.6. Stress tensor in a moving fluid
• 1.7. Viscosity
• 1.8. Conservation laws
• 1.9. Mass conservation
• 1.10. Convective time derivative
• 1.11. Momentum conservation
• 1.12. Navier-Stokes equation
• 1.13. Energy conservation
• 1.14. Equations of incompressible fluidflow
• 1.15. Equations of compressible fluid flow
• 1.16. Dimensionless numbers in incompressible flow
• 1.17. Dimensionless numbers in compressible flow
• 1.18. Fluid equations in Cartesian coordinates
• 1.19. Fluid equations in cylindrical coorinates
• 1.20. Fluid equations in spherical coordinates
• 1.21. Exercises
• 2. Hydrostatics
• 2.1. Introduction
• 2.2. Hydrostatic pressure
• 2.3. Buoyancy
• 2.4. Equilibria of floating bodies
• 2.5. Vertical stability of floating bodies
• 2.6. Angular stability of floating bodies
• 2.7. Determination of metacentric height
• 2.8. Energy of a floating body
• 2.9. Curve of buoyancy
• 2.10. Rotational hydrostatics
• 2.11. Equilibrium of a rotating liquid body
• 2.12. Maclaurin spheroids
• 2.13. Jacobi ellipsoids
• 2.14. Roche ellipsoids
• 2.15. Exercises
• 3. Surface tension
• 3.1. Introduction
• 3.2. Young-Laplace equation
• 3.3. Spherical interfaces
• 3.4. Capillary length
• 3.5. Angle of contact
• 3.6. Jurin's law
• 3.7. Capillary curves
• 3.8. Axisymmetric soap-bubbles
• 3.9. Exercises
• 4. Incompressible inviscid flow
• 4.1. Introduction
• 4.2. Streamlines, stream tubes, and stream filaments
• 4.3. Bernoulli's theorem
• 4.4. Euler's momentum theorem
• 4.5. d'Alembert's paradox
• 4.6. Flow through an orifice
• 4.7. Sub-critical and super-critical flow
• 4.8. Flow over a shallow bump
• 4.9. Stationary hydraulic jumps
• 4.10. Tidal bores
• 4.11. Flow over a broad-crested weir
• 4.12. Vortex lines, vortex tubes, and vortex filaments
• 4.13. Circulation and vorticity
• 4.14. Kelvin's circulation theorem
• 4.15. Irrotational flow
• 4.16. Exercises
• 5. Two-dimensional incompressible inviscid flow
• 5.1. Introduction
• 5.2. Two-dimensional flow
• 5.3. Velocity potentials and stream functions
• 5.4. Two-dimensional uniform flow
• 5.5. Two-dimensional sources and sinks
• 5.6. Two-dimensional vortex filaments
• 5.7. Two-dimensional irrotational flow in cylindrical coordinates
• 5.8. Flow past a cylindrical obstacle
• 5.9. Motion of a submerged cylinder
• 5.10. Inviscid flow past a semi-infinite wedge
• 5.11. Inviscid flow over a semi-infinite wedge
• 5.12. Two-dimensional jets
• 5.13. Exercises
• 6. Two-dimensional potential flow
• 6.1. Introduction
• 6.2. Complex functions
• 6.3. Cauchy-Riemann relations
• 6.4. Complex velocity potential
• 6.5. Complex velocity
• 6.6. Method of images
• 6.7. Conformal maps
• 6.8. Schwarz-Christoffel theorem
• 6.9. Free streamline theory
• 6.10. Complex line integrals
• 6.11. Blasius' theorem
• 6.12. Exercises
• 7. Axisymmetric incompressible inviscid flow
• 7.1. Introduction
• 7.2. Axisymmetric flow
• 7.3. Stokes stream function
• 7.4. Axisymmetric velocity fields
• 7.5. Axisymmetric irrotational flow in spherical coordinates
• 7.6. Uniform flow
• 7.7. Point sources
• 7.8. Dipole point sources
• 7.9. Flow past a spherical obstacle
• 7.10. Motion of a submerged sphere
• 7.11. Conformal maps
• 7.12. Flow around a submerged oblate spheroid
• 7.13. Flow around a submerged prolate spheroid
• 7.14. Exercises
• 8. Incompressible boundary layers
• 8.1. Introduction
• 8.2. No-slip condition
• 8.3. Boundary layer equations
• 8.4. Self-similar boundary layers
• 8.5. Boundary layer on a flat plate
• 8.6. Wake downstream of a flat plate
• 8.7. Von K�arm�an momentum integral
• 8.8. Boundary layer separation
• 8.9. Criterion for boundary layer separation
• 8.10. Approximate solutions of boundary layer equations
• 8.11. Exercises
• 9. Incompressible aerodynamics
• 9.1. Introduction
• 9.2. Kutta-Zhukovskii theorem
• 9.3. Cylindrical airfoils
• 9.4. Zhukovskii's hypothesis
• 9.5. Vortex sheets
• 9.6. Induced flow
• 9.7. Three-dimensional airfoils
• 9.8. Aerodynamic forces
• 9.9. Ellipsoidal airfoils
• 9.10. Simple flight problems
• 9.11. Exercises
• 10. Incompressible viscous flow
• 10.1. Introduction
• 10.2. Flow between parallel plates
• 10.3. Flow down an inclined plane
• 10.4. Poiseuille flow
• 10.5. Taylor-Couette flow
• 10.6. Flow in slowly-varying channels
• 10.7. Lubrication theory
• 10.8. Stokes flow
• 10.9. Axisymmetric Stokes flow
• 10.10. Axisymmetric Stokes flow around a solid sphere
• 10.11. Axisymmetric Stokes flow in and around a fluid sphere
• 10.12. Exercises
• 11. Waves in incompressible fluids
• 11.1. Introduction
• 11.2. Gravity waves
• 11.3. Gravity waves in deep water
• 11.4. Gravity waves in shallow water
• 11.5. Energy of gravity waves
• 11.6. Wave drag on ships
• 11.7. Ship wakes
• 11.8. Gravity waves in a flowing fluid
• 11.9. Gravity waves at an interface
• 11.10. Steady flow over a corrugated bottom
• 11.11. Surface tension
• 11.12. Capillary waves
• 11.13. Capillary waves at an interface
• 11.14. Wind-driven waves in deep water
• 11.15. Exercises
• 12. Terrestrial ocean tides
• 12.1. Introduction
• 12.2. Tide-generating potential
• 12.3. Decomposition of tide-generating potential
• 12.4. Expansion of tide-generating potential
• 12.5. Surface harmonics and solid harmonics
• 12.6. Planetary rotation
• 12.7. Total gravitational potential
• 12.8. Planetary response
• 12.9. Laplace tidal equations
• 12.10. Harmonics of the forcing term in the Laplace tidal equations
• 12.11. Response to the equilibrium harmonic
• 12.12. Global ocean tides
• 12.13. Non-global ocean tides
• 12.14. Useful lemma
• 12.15. Transformation of Laplace tidal equations
• 12.16. Another useful lemma
• 12.17. Basis eigenfunctions
• 12.18. Auxiliary eigenfunctions
• 12.19. Gyroscopic coefficients
• 12.20. Proudman equations
• 12.21. Hemispherical ocean tides
• 12.22. Exercises
• 13. Equilibria of compressible fluids
• 13.1. Introduction
• 13.2. Isothermal atmosphere
• 13.3. Adiabatic atmosphere
• 13.4. Atmospheric stability
• 13.5. Eddington solar model
• 13.6. Exercises
• 14. One-dimensional compressible inviscid flow
• 14.1. Introduction
• 14.2. Thermodynamic considerations
• 14.3. Isentropic flow
• 14.4. Sound waves
• 14.5. Bernoulli's theorem
• 14.6. Mach number
• 14.7. Sonic flow through a nozzle
• 14.8. Normal shocks
• 14.9. Piston-generated shock wave
• 14.10. Piston-generated expansion wave
• 14.11. Exercises
• 15. Two-dimensional compressible inviscid flow
• 15.1. Introduction
• 15.2. Oblique shocks
• 15.3. Supersonic flow in a corner or over a wedge
• 15.4. Weak oblique shocks
• 15.5. Supersonic compression by turning
• 15.6. Supersonic expansion by turning
• 15.7. Detached shocks
• 15.8. Shock-expansion theory
• 15.9. Thin-airfoil theory
• 15.10. Crocco's theorem
• 15.11. Homenergic homentropic flow
• 15.12. Small-perturbation theory
• 15.13. Subsonic flow past a wave-shaped wall
• 15.14. Supersonic flow past a wave-shaped wall
• 15.15. Linearized subsonic flow
• 15.16. Linearized supersonic flow
• 15.17. Flat lifting wings
• 15.18. Exercises
• Appendices. A Vectors and vector fields
• A.1. Introduction
• A.2. Scalars and vectors
• A.3. Vector algebra
• A.4. Cartesian components of a vector
• A.5. Coordinate transformations
• A.6. Scalar product
• A.7. Vector area
• A.8. Vector product
• A.9. Rotation
• A.10. Scalar triple product
• A.11. Vector triple product
• A.12. Vector calculus
• A.13. Line integrals
• A.14. Vector line integrals
• A.15. Surface integrals
• A.16. Vector surface integrals
• A.17. Volume integrals
• A.18. Gradient
• A.19. Grad operator
• A.20. Divergence
• A.21. Laplacian operator
• A.22. Curl
• A.23. Useful vector identities
• A.24. Exercises
• B. Cartesian tensors
• B.1. Introduction
• B.2. Tensors and tensor notation
• B.3. Tensor transformation
• B.4. Tensor fields
• B.5. Isotropic tensors
• B.6. Exercises
• C. Non-Cartesian coordinates
• C.1. Introduction
• C.2. Orthogonal curvilinear coordinates
• C.3. Cylindrical coordinates
• C.4. Spherical coordinates
• C.5. Exercises
• D. Ellipsoidal potential theory
• D.1. Introduction
• D.2. Analysis
• D.3. Exercises
• E. Calculus of variations
• E.1. Introduction
• E.2. Euler-Lagrange equation
• E.3. Conditional variation
• E.4. Multi-function variation
• E.5. Exercises
• F. Solutions to exercises in chapter 1
• G. Solutions to exercises in chapter 2
• H. Solutions to exercises in chapter 3
• I. Solutions to exercises in chapter 4
• J. Solutions to exercises in chapter 5
• K. Solutions to exercises in chapter 6
• L. Solutions to exercises in chapter 7
• M. Solutions to exercises in chapter 8
• N. Solutions to exercises in chapter 9
• O. Solutions to exercises in chapter 10
• P. Solutions to exercises in chapter 11
• Q. Solutions to exercises in chapter 12
• R. Solutions to exercises in chapter 13
• S. Solutions to exercises in chapter 14
• T. Solutions to exercises in chapter 15
• U. Solutions to exercises in appendix A
• V. Solutions to exercises in appendix B
• W. Solutions to exercises in appendix C
• X. Solutions to exercises in appendix D
• Y. Solutions to exercises in appendix E.