From drinking fountains at playgrounds, water systems in homes, and working bathrooms at schools to hydraulic bridges and levee systems, fluid mechanics are an essential part of daily life. Fluid mechanics, the study of how forces are applied to fluids, is outlined in this unit as a sequence of two lessons and three corresponding activities. The first lesson provides a basic introduction to Pascal's law, Archimedes' principle and Bernoulli's principle and presents fundamental definitions, equations and problems to solve with students, as well as engineering applications. The second lesson provides a basic introduction to above-ground storage tanks, their pervasive use in the Houston Ship Channel, and different types of storage tank failure in major storms and hurricanes. The unit concludes with students applying what they have learned to determine the stability of individual above-ground storage tanks given specific storm conditions so they can analyze their stability in changing storm conditions, followed by a project to design their own storage tanks to address the issues of uplift, displacement and buckling in storm conditions.

Students are presented with a challenge question that they must answer with scientific and mathematical reasoning. The challenge question is: "You have a large rock on a boat that is floating in a pond. You throw the rock overboard and it sinks to the bottom of the pond. Does the water level in the pond rise, drop or remain the same?" Students observe Archimedes' principle in action in this model recreation of the challenge question when a toy boat is placed in a container of water and a rock is placed on the floating boat. Students use terminology learned in the classroom as well as critical thinking skills to derive equations needed to answer this question.

Students use their understanding of projectile physics and fluid dynamics to find the water pressure in water guns. By measuring the range of the water jets, they are able to calculate the theoretical pressure. Students create graphs to analyze how the predicted pressure relates to the number of times they pump the water gun before shooting.

This is in class lab activity where students will explore the buoyant force.

This course forms an introduction to a selection of mathematical topics that are not covered in traditional mechanical engineering curricula, such as differential geometry, integral geometry, discrete computational geometry, graph theory, optimization techniques, calculus of variations and linear algebra. The topics covered in any particular year depend on the interest of the students and instructor. Emphasis is on basic ideas and on applications in mechanical engineering. This year, the subject focuses on selected topics from linear algebra and the calculus of variations. It is aimed mainly (but not exclusively) at students aiming to study mechanics (solid mechanics, fluid mechanics, energy methods etc.), and the course introduces some of the mathematical tools used in these subjects. Applications are related primarily (but not exclusively) to the microstructures of crystalline solids.

This course teaches the art of guessing results and solving problems without doing a proof or an exact calculation. Techniques include extreme-cases reasoning, dimensional analysis, successive approximation, discretization, generalization, and pictorial analysis. Applications include mental calculation, solid geometry, musical intervals, logarithms, integration, infinite series, solitaire, and differential equations. (No epsilons or deltas are harmed by taking this course.) This course is offered during the Independent Activities Period (IAP), which is a special 4-week term at MIT that runs from the first week of January until the end of the month.

This resource presents a collection of essays developed from the author's experience teaching the course Fluid Dynamics of the Atmosphere and Ocean, offered to graduate students entering the MIT/WHOI Joint Program in Oceanography. The collection includes the following three essays:
Essay 1: Lagrangian and Eulerian Representations of Fluid Flow (revised and expanded in 2024)

Part 1: Kinematics and the Equations of Motion
Part 2: Advection of Parcels and Fields

Essay 2: Dimensional Analysis of Models and Data Sets: Similarity Solutions and Scaling Analysis
Essay 3: A Coriolis Tutorial (revised and expanded in 2023)

Part 1: The Coriolis Force, Inertial and Geostrophic Motion
Part 2: A Rotating Shallow Water Model and Geostrophic Adjustment
Part 3: Beta Effects and Western Propagation
Part 4: Wind-Driven Ocean Circulation and the Sverdrup Relation
Part 5: On the Seasonally-Varying Circulation of the Arabian Sea

The goal of this resource is to help each student master the concepts and mathematical tools that make up the foundation of classical and geophysical fluid dynamics. These essays treat these topics in considerably greater depth than a comprehensive fluids textbook can afford, and they are accompanied by data files (MATLAB® and Fortran) to allow some application and experimentation. They should be suitable for self-study.

This project is a classroom investigation where students design a chemical torpedo out of pipettes, baking soda and vinegar to travel down a rain gutter. While working on the project the students will have to analyze their design, interpret their success and failures, adapt their creation and compete against other students in distance and velocities of their launched torpedo.

Turbulent flows, with emphasis on engineering methods. Governing equations for momentum, energy, and species transfer.
Turbulence: its production, dissipation, and scaling laws. Reynolds averaged equations for momentum, energy, and species transfer. Simple closure approaches for free and bounded turbulent shear flows. Applications to jets, pipe and channel flows, boundary layers, buoyant plumes and thermals, and Taylor dispersion, etc., including heat and species transport as well as flow fields. Introduction to more complex closure schemes, including the k-epsilon, and statistical methods in turbulence.

The basic objective of Unified Engineering is to give a solid understanding of the fundamental disciplines of aerospace engineering, as well as their interrelationships and applications. These disciplines are Materials and Structures (M); Computers and Programming (C); Fluid Mechanics (F); Thermodynamics (T); Propulsion (P); and Signals and Systems (S). In choosing to teach these subjects in a unified manner, the instructors seek to explain the common intellectual threads in these disciplines, as well as their combined application to solve engineering Systems Problems (SP). Throughout the year, the instructors emphasize the connections among the disciplines.

Students are introduced to the similarities and differences in the behaviors of elastic solids and viscous fluids. Several types of fluid behaviors are described Bingham plastic, Newtonian, shear thinning and shear thickening along with their respective shear stress vs. rate of shearing strain diagrams. In addition, fluid material properties such as viscosity are introduced, along with the methods that engineers use to determine those physical properties.

This course discusses theoretical concepts and analysis of wave problems in science and engineering. Examples are chosen from elasticity, acoustics, geophysics, hydrodynamics, blood flow, nondestructive evaluation, and other applications.