# Fluid Mechanics: An Introduction To The Theory ...

Relativistic fluid dynamics studies the macroscopic and microscopic fluid motion at large velocities comparable to the velocity of light.[11] This branch of fluid dynamics accounts for the relativistic effects both from the special theory of relativity and the general theory of relativity. The governing equations are derived in Riemannian geometry for Minkowski spacetime.

## Fluid Mechanics: An Introduction to the Theory ...

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.

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.

A A 301 Compressible Aerodynamics (4)Covers aerodynamics as applied to the problems of performance of flight vehicles in the atmosphere; kinematics and dynamics of flow fields; thin airfoil theory; compressible fluids; one-dimensional compressible flow; and two-dimensional supersonic flow. Prerequisite: A A 311. Offered: W.View course details in MyPlan: A A 301

A A 405 Introduction to Aerospace Plasmas (3)Development of introductory electromagnetic theory including Lorentz force and Maxwell's equations. Plasma description. Single particle motions and drifts in magnetic and electric fields. Derivation of plasma fluid model. Introduction to plasma waves. Applications to electric propulsion, magnetic confinement, and plasmas in space and Earth's outer atmosphere. Prerequisite: MATH 224; and either PHYS 123 or PHYS 143. Offered: A.View course details in MyPlan: A A 405

8.04 Quantum Physics I () Prereq: 8.03 and (18.03 or 18.032)Units: 5-0-7Credit cannot also be received for 8.041 Lecture: MW9.30-11 (6-120) Recitation: TR10 (4-257) or TR11 (4-257) or TR1 (26-322) or TR2 (26-322) +finalExperimental basis of quantum physics: photoelectric effect, Compton scattering, photons, Franck-Hertz experiment, the Bohr atom, electron diffraction, deBroglie waves, and wave-particle duality of matter and light. Introduction to wave mechanics: Schroedinger's equation, wave functions, wave packets, probability amplitudes, stationary states, the Heisenberg uncertainty principle, and zero-point energies. Solutions to Schroedinger's equation in one dimension: transmission and reflection at a barrier, barrier penetration, potential wells, the simple harmonic oscillator. Schroedinger's equation in three dimensions: central potentials and introduction to hydrogenic systems.A. HarrowTextbooks (Spring 2023)

8.041 Quantum Physics I () Prereq: 8.03 and (18.03 or 18.032)Units: 2-0-10Credit cannot also be received for 8.04Blended version of 8.04 using a combination of online and in-person instruction. Covers experimental basis of quantum physics: photoelectric effect, Compton scattering, photons, Franck-Hertz experiment, the Bohr atom, electron diffraction, deBroglie waves, and wave-particle duality of matter and light. Introduction to wave mechanics: Schroedinger's equation, wave functions, wave packets, probability amplitudes, stationary states, the Heisenberg uncertainty principle, and zero-point energies. Solutions to Schroedinger's equation in one dimension: transmission and reflection at a barrier, barrier penetration, potential wells, the simple harmonic oscillator. Schroedinger's equation in three dimensions: central potentials and introduction to hydrogenic systems.V.. Vuletic

8.051 Quantum Physics II ()Prereq: 8.04 and permission of instructorUnits: 2-0-10Credit cannot also be received for 8.05Lecture: MW10 (2-105) +finalBlended version of 8.05 using a combination of online and in-person instruction. Together with 8.06 covers quantum physics with applications drawn from modern physics. General formalism of quantum mechanics: states, operators, Dirac notation, representations, measurement theory. Harmonic oscillator: operator algebra, states. Quantum mechanics in three dimensions: central potentials and the radial equation, bound and scattering states, qualitative analysis of wave functions. Angular momentum: operators, commutator algebra, eigenvalues and eigenstates, spherical harmonics. Spin: Stern-Gerlach devices and measurements, nuclear magnetic resonance, spin and statistics. Addition of angular momentum: Clebsch-Gordan series and coefficients, spin systems, and allotropic forms of hydrogen. Limited to 20.B. ZwiebachTextbooks (Spring 2023)

8.286 The Early Universe () Prereq: Physics II (GIR) and 18.03Units: 3-0-9Introduction to modern cosmology. First half deals with the development of the big bang theory from 1915 to 1980, and latter half with recent impact of particle theory. Topics: special relativity and the Doppler effect, Newtonian cosmological models, introduction to non-Euclidean spaces, thermal radiation and early history of the universe, big bang nucleosynthesis, introduction to grand unified theories and other recent developments in particle theory, baryogenesis, the inflationary universe model, and the evolution of galactic structure.A. Guth

8.292[J] Fluid Physics ()(Same subject as 1.066[J], 12.330[J])Prereq: 5.60, 8.044, or permission of instructorUnits: 3-0-9Lecture: TR2.30-4 (4-145)A physics-based introduction to the properties of fluids and fluid systems, with examples drawn from a broad range of sciences, including atmospheric physics and astrophysics. Definitions of fluids and the notion of continuum. Equations of state and continuity, hydrostatics and conservation of momentum; ideal fluids and Euler's equation; viscosity and the Navier-Stokes equation. Energy considerations, fluid thermodynamics, and isentropic flow. Compressible versus incompressible and rotational versus irrotational flow; Bernoulli's theorem; steady flow, streamlines and potential flow. Circulation and vorticity. Kelvin's theorem. Boundary layers. Fluid waves and instabilities. Quantum fluids.L. BourouibaTextbooks (Spring 2023)

These lecture notes provide a detailed introduction to the bosonic string and conformal field theory, aimed at "Part III" (i.e. masters level) students. The full set of lectures notes can be downloaded here and weigh in at around 210 pages. Individual sections can be downloaded below.

Using readily available experimental thermophoretic particle-velocity data it is shown, contrary to current teachings, that for the case of compressible flows independent dye- and particle-tracer velocity measurements of the local fluid velocity at a point in a flowing fluid do not generally result in the same fluid velocity measure. Rather, tracer-velocity equality holds only for incompressible flows. For compressible fluids, each type of tracer is shown to monitor a fundamentally different fluid velocity, with (i) a dye (or any other such molecular-tagging scheme) measuring the fluid's mass velocity v appearing in the continuity equation and (ii) a small, physicochemically and thermally inert, macroscopic (i.e., non-Brownian), solid particle measuring the fluid's volume velocity v(v). The term "compressibility" as used here includes not only pressure effects on density, but also temperature effects thereon. (For example, owing to a liquid's generally nonzero isobaric coefficient of thermal expansion, nonisothermal liquid flows are to be regarded as compressible despite the general perception of liquids as being incompressible.) Recognition of the fact that two independent fluid velocities, mass- and volume-based, are formally required to model continuum fluid behavior impacts on the foundations of contemporary (monovelocity) fluid mechanics. Included therein are the Navier-Stokes-Fourier equations, which are now seen to apply only to incompressible fluids (a fact well-known, empirically, to experimental gas kineticists). The findings of a difference in tracer velocities heralds the introduction into fluid mechanics of a general bipartite theory of fluid mechanics, bivelocity hydrodynamics [Brenner, Int. J. Eng. Sci. 54, 67 (2012)], differing from conventional hydrodynamics in situations entailing compressible flows and reducing to conventional hydrodynamics when the flow is incompressible, while being applicable to both liquids and gases.

This course is an introduction to fluid mechanics, and emphasizes fundamental concepts and problem-solving techniques. Topics to be covered include fluid properties (density, viscosity, vapor pressure, surface tension); fluid statics (hydrostatic pressure, pressure forces on planar and curved surfaces); fluid kinematics (flow visualization, vorticity, Reynolds transport theorem); control volume analysis (conservation laws of mass, momentum, and energy, Bernoulli equation); dimensional analysis (dimensional homogeneity, method of repeating variables, experimental testing, similarity); internal flows (pipe flows, major and minor losses, piping networks, matching pumps to systems); differential analysis (Navier-Stokes equation, creeping flow, potential flow, boundary layers); external flows (lift and drag, pressure vs. friction drag); and compressible flow (isentropic flow through nozzles, shock waves). Brief introductions to computational fluid dynamics (CFD), and turbomachinery (pumps and turbines) will also be provided.

Specification of components such as shafts, bearings, and power transformers; optimal designs for operational, environmental, and manufacturing requirements. ME 360 Mechanical Design (3) This course is required for all mechanical engineering students. It is an introduction to analysis and design of mechanical components. It helps provide practical insight into theory provided by prerequisites in engineering mechanics and materials science. Students initially perform yielding and fatigue failure predictions for general structural elements and then focus on specific mechanical components such as gears, fluid film bearing, rolling element bearings, screws, shafts, and springs. Use and interpretation of finite element analyses (FEA) are also introduced. The overall goals are for students to learn to make basic design decisions regarding the suitability of different materials in mechanical components (e.g. steel versus aluminum), and to make basic design decisions regarding the suitability of different components in a mechanical system (e.g. ball bearings versus fluid film bearings). 041b061a72