Survey of principal concepts and methods of fluid dynamics. Mass conservation, momentum, and energy equations for continua. Navier-Stokes equation for viscous flows. Similarity and dimensional analysis. Lubrication theory. Boundary layers and separation. Circulation and vorticity theorems. Potential flow. Introduction to turbulence. Lift and drag. Surface tension and surface tension-driven flows.

Survey of principal concepts and methods of fluid dynamics. Mass conservation, momentum, and energy equations for continua. Navier-Stokes equation for viscous flows. Similarity and dimensional analysis. Lubrication theory. Boundary layers and separation. Circulation and vorticity theorems. Potential flow. Introduction to turbulence. Lift and drag. Surface tension and surface tension-driven flows.

" The focus of the course is the concepts and techniques for solving the partial differential equations (PDE) that permeate various scientific disciplines. The emphasis is on nonlinear PDE. Applications include problems from fluid dynamics, electrical and mechanical engineering, materials science, quantum mechanics, etc."

A comprehensive treatment of the theory of partial differential equations (pde) from an applied mathematics perspective. Equilibrium, propagation, diffusion, and other phenomena. Initial and boundary value problems. Transform methods, eigenvalue and eigenfunction expansions, Green's functions. Theory of characteristics and shocks. Boundary layers and other singular perturbation phenomena. Elementary concepts for the numerical solution of pde's. Illustrative examples from fluid dynamics, nonlinear waves, geometrical optics, and other applications.

Boundary layers as rational approximations to the solutions of exact equations of fluid motion. Physical parameters influencing laminar and turbulent aerodynamic flows and transition. Effects of compressibility, heat conduction, and frame rotation. Influence of boundary layers on outer potential flow and associated stall and drag mechanisms. Numerical solution techniques and exercises. The major focus of 16.13 is on boundary layers, and boundary layer theory subject to various flow assumptions, such as compressibility, turbulence, dimensionality, and heat transfer. Parameters influencing aerodynamic flows and transition and influence of boundary layers on outer potential flow are presented, along with associated stall and drag mechanisms. Numerical solution techniques and exercises are included.

This course teaches simple reasoning techniques for complex phenomena: divide and conquer, dimensional analysis, extreme cases, continuity, scaling, successive approximation, balancing, cheap calculus, and symmetry. Applications are drawn from the physical and biological sciences, mathematics, and engineering. Examples include bird and machine flight, neuron biophysics, weather, prime numbers, and animal locomotion. Emphasis is on low-cost experiments to test ideas and on fostering curiosity about phenomena in the world.

Dimensional analysis allows us to change the units used to express a value. For instance, it allows us to convert between volume expressed in liters and volume expressed in gallons. The following video gives a brief overview of dimensional analysis, including conversion between the amount of a substance expressed in "number of molecules" and the amount of a substance expressed in "moles of molecules."

Seven basic quantities are the seven dimensions of physical quantities.

This subject provides an introduction to the mechanics of materials and structures. You will be introduced to and become familiar with all relevant physical properties and fundamental laws governing the behavior of materials and structures and you will learn how to solve a variety of problems of interest to civil and environmental engineers. While there will be a chance for you to put your mathematical skills obtained in 18.01, 18.02, and eventually 18.03 to use in this subject, the emphasis is on the physical understanding of why a material or structure behaves the way it does in the engineering design of materials and structures.

This course introduces fluid mechanics, the study of how and why fluids (both gaseous and liquid) behave the way they do. Upon successful completion of this course, the student will be able to: Formulate basic equation for fluid engineering problems; Use the Poiseuille equation, Reynolds number correlations, and Moody chart for description of laminar and turbulent pipe flow; Use tables, figures, and energy equations to predict pressure drop in pipes, across fittings and through pumps and turbines; Use tables and figures to determine the friction energy loss; Perform dimensional analysis and identify important parameters; Calculate pressure distributions, forces on surfaces, and buoyancy; Analyze flow situations and use appropriate methods to obtain quantitative information for engineering applications. (Mechanical Engineering 201)

In this course the fundamentals of fluid mechanics are developed in the context of naval architecture and ocean science and engineering. The various topics covered are: Transport theorem and conservation principles, Navier-Stokes' equation, dimensional analysis, ideal and potential flows, vorticity and Kelvin's theorem, hydrodynamic forces in potential flow, D'Alembert's paradox, added-mass, slender-body theory, viscous-fluid flow, laminar and turbulent boundary layers, model testing, scaling laws, application of potential theory to surface waves, energy transport, wave/body forces, linearized theory of lifting surfaces, and experimental project in the towing tank or propeller tunnel.

Introduction to fundamental concepts in "continuous" applied mathematics. Extensive use of demonstrational software. Discussion of computational and modeling issues. Nonlinear dynamical systems; nonlinear waves; diffusion; stability; characteristics; nonlinear steepening, breaking and shock formation; conservation laws; first-order partial differential equations; finite differences; numerical stability; etc. Applications to traffic problems, flows in rivers, internal waves, mechanical vibrations and other problems in the physical world.

" This course is about mathematical analysis of continuum models of various natural phenomena. Such models are generally described by partial differential equations (PDE) and for this reason much of the course is devoted to the analysis of PDE. Examples of applications come from physics, chemistry, biology, complex systems: traffic flows, shock waves, hydraulic jumps, bio-fluid flows, chemical reactions, diffusion, heat transfer, population dynamics, and pattern formation."