These lecture notes provide a introduction to fluid mechanics, aimed at undergraduates. The full set of lecture notes come in around 240 pages and can be downloaded here. Please do email me if you find any typos or corrections.
2. The Navier-Stokes Equation: PDF
Stress, Strain and viscosity; Newtonian fluids; dissipation. The no-slip boundary condition; Couette flow; Poiseuille flow; Vorticity and the Burgers vortex. Reynolds number. Stokes flow; Stokes' drag law; Moffat eddies; Swimming at low Reynolds number; Hele-Shaw flow. The boundary layer, Prandtl's equation; Blasius' solution; Falkner-Scan boundary layers; separation. 3. Waves: PDF
Surface waves; free boundary conditions; surface tension and capillary waves. Gravity waves. Shallow water waves, geostrophic balance, Poincare waves, Coastal Kelvin waves, Equatorial waves including Rossby waves, Yanai waves and Kelvin waves, topologically protected waves. Sound waves; compressible fluids; heat transport and thermodynamics; viscosity and damping. Non-linear sound waves; the method of characteristiscs; wave steepening; Burgers' equation. Shocks; supersonic flows; Rankine-Huginiot jump conditions and relations. 4. Instabilities: PDF
Kevlin-Helmsholtz instability; the vortex sheet; Rayleigh-Taylor instability. Rayleigh-Plateau instability. Rayleigh-Benard convection; the Boussinesq approximation. Instabilities of shear flows; Rayleigh's criterion; Fjortoft's criterion; the semi-circle theorem. 5. Turbulence: PDF
Mean flow; Reynolds averaging and the Reynolds-averaged Navier Stokes equation; Reynolds stress and eddy viscosity. Kolmogorov's dimensional analysis (K41). Velocity correlation functions and structure functions, the von Karman relation and the von Karman-Howarth relation. Kolmogorov's 4/5's law.
Fluids on the Web Michael McIntyre's fluid mechanics roadshow.
Fluid Mechanics II by John Hinch, University of Cambridge.
Fluids by Caroline Terquem, University of Oxford.
Fluid Dynamics by Stephen Childress, NYU
Waves by Stephen Cowley, University of Cambridge.
Advanced Fluid Dynamics by Chiang Mei, MIT.
Advanced Fluid Dynamics by Lennon O'Naraigh, University College Dublin (focussing on hydrodynamic stability).
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Notes on Numerical Fluid Mechanics and Multidisciplinary Design publishesstate-of-art methods (including high-performance methods) for numerical fluidmechanics, numerical simulation and multidisciplinary design optimization. Theseries includes proceedings of specialized conferences and workshops, as wellas relevant project reports and monographs.
An introduction to the quantum Hall effect. The first half uses only quantum mechanicsand is at a levelsuitable for undergraduates. The second half covers more advanced field theoretic techniques of Chern-Simonsand conformal field theories.
An introduction to fluid mechanics, aimed at undergraduates. The course covers the basic flows arising from the Euler and Navier-Stokes equations, including discussions of waves, stability, and turbulence.
An introduction to statistical mechanics and thermodynamics,aimed at final year undergraduates. After developing the fundamentals of the subject, the course covers classical gases, quantum gases and phase transitions.
An elementary course on elementary particles. This is, by some margin, the least mathematically sophisticated of all my lecture notes, requiring little more than high school mathematics. The lectures provide a pop-science, but detailed, account of particle physics and quantum field theory.
Quantum Field Theory An introductory course on quantum field theory, aimed at first year graduate students. It covers the canonical quantization of scalar, Dirac and vector fields. Videos are also included.
These notes provide an introduction to the fun bits of quantum field theory, in particular those topics relatedto topology and strong coupling. They are aimed at beginning graduate students and assumea familiarity with the path integral.
In 1961, Ascher Shapiro founded the National Committee for Fluid Mechanics Films (NCFMF) in cooperation with the Education Development Center and released a series of 39 videos and accompanying texts which revolutionized the teaching of fluid mechanics. The films are now hosted by MIT's Office of Digital Learning. The preface to Illustrated Experiments in Fluid Mechanics: The NCFMF Book of Film Notes can be found here. And complete notes for the films can be found here
These notes are intended to provide a description of some aspects of applications of resolvent analysis in fluid mechanics. They are targeted at students beginning research in this or related area, with the goal of providing a bridge between the generic linear algebra of textbooks and the archival journal articles implementing these techniques. With regards to mathematical techniques, a working understanding of fundamental concepts of linear algebra, and in particular the singular value decomposition, as well a familiarity with the goals underlying modal analysis are assumed. Requiring more background in fluid mechanics, the reader will already be familiar with the formulation of resolvent analysis from the Navier-Stokes equations. These notes outline approaches to gaining insight into the characteristics of fluid system by viewing the governing equations in terms of linear dynamics driven by endogenous (nonlinear) or exogenous forcing. Such systems may exhibit laminar or turbulent behavior, may be forced or unforced, and may perhaps be under the influence of control actuation. Physical interpretation of resolvent modes, the importance of mode weights and techniques for data reconstruction, and the incorporation of control into the analysis are covered.
This volume contains 37 invited contributions, collected to celebrate one hundred volumes of the NNFM Series. After a general introduction overviews are given in five parts of the developments in numerical fluid mechanics and related fields. In the first part information about the series is given, its origins are discussed, as well as its environment and the German and European high-performance computer scene. In Part II the co-editors of the series give short surveys over developments in their countries. Current applications, mainly in the aerospace sector, but also in the automotive sector, are discussed in Part III. Applications to flow problems in engineering and physics, ranging from hydraulic machinery to astrophysics, are the topics of Part IV. Algorithms, computer science, commercial CFD, public partnerships in high-performance computing, and hardware development up to petaflops computers are treated in Part V. All volumes, which were published in the series finally are listed in Part VI.
These lecture notes have been prepared as a course in fluid mechanics up to the presentation of the millennium problem listed by the Clay Mathematical Institute. At the end, a very modern aspect of fluid mechanics is covered concerning the subtle issue of its application to high energetic hadronic collisions.
These notes are provided and composed by Mr. Muzammil Tanveer. We are really very thankful to him for providing these notes and appreciates his effort to publish these notes on MathCity.org. These notes are based on lectures delivered by Mr. Muzammil Hussain at GC University Faisalabad.
In this course, students learn how to analyze fluids at rest (fluid statics) and fluids in motion (fluid dynamics). Fluid mechanics topics are distributed between ME 3111 (Fluid Mechanics) and ME 3121 (Intermediate Thermal-Fluids Engineering).
1.1 - Definition of a fluid
1.2 - Pressure
1.3 - Absolute pressure and gage pressure
1.4 - Density
1.5 - Viscosity
1.6 - Continuum approximation
1.7 - Vapor pressure
Concept: Comparing the viscosity of various liquids
Description: Liquids with higher viscosities will flow slower than fluids with lower viscosities, assuming the flow conditions of the liquids are the same. The video also presents a molecular picture of viscosity.
Concept: Dilitant/shear-thickening fluid #1
Description: For some non-Newtonian fluids, the viscosity increases with increasing shear stress. In the video, a small kiddie pool is filled with a shear-thickening fluid and people are able to run on its surface without sinking. Notice that the fluid almost behaves like rubber when strong shear stresses are applied, but flows readily when when weak shear stresses are applied.
Concept: Dilitant/shear-thickening fluid #2
Description: A shear-thickening fluid allows a slow-moving ruler to easily penetrate its surface, but can resist violent blows from a sledgehammer.
Concept: Rigid body rotation
Description: A tank containing water rotates at a certain angular velocity. The water's momentum attempts to carry it away toward the walls, but is kept in check by the pressure of the fluid above it. After the initial sloshing dies down, the water and tank rotate at the same rate and appear as a rigid body, with the free surface forming a paraboloid. The pressure is atmospheric over the entire free surface and the lines of constant pressure (isobars) are parabolic as well.
10.1 - Lagrangian vs. Eulerian descriptions of flow
10.2 - The material derivative
10.3 - Streamlines, streaklines, and pathlines
10.4 - Kinematics of fluid elements (translation and linear deformation)
10.5 - Kinematics of fluid elements (shear strain, rotation, and vorticity
As fluid dynamics is described by non-canonical dynamics, which possess an infinite amount of Casimir invariants, an alternative formulation of Hamiltonian formulation of fluid dynamics can be introduced through the use of Nambu mechanics[1][2] 17dc91bb1f
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