Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Tutorials: 1 session / week, 1 hour / session (Students attend one of three tutorial sessions per week.)


2.006 Thermal-Fluids Engineering II or 2.06 Fluid Dynamics


18.075 Advanced Calculus for Engineers or 18.085 Computational Science and Engineering I


This course is a survey of principal concepts and methods of fluid dynamics. Topics include 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.


Panton, Ronald L. Incompressible Flow. 4th ed. Wiley, 2013. ISBN: 9781118013434. [Preview with Google Books]

Shapiro, Ascher H., and Ain A. Sonin. Advanced Fluid Mechanics Problems. (Self-published manuscript.)

Other Recommended Textbooks:

Kundu, Pijush K., and Ira M. Cohen. Fluid Mechanics. 6th ed. Academic Press, 2015. ISBN: 9780124059351.

Buy at MIT Press Fay, James A. Introduction to Fluid Mechanics. MIT Press, 1994. ISBN: 9780262061650. [Preview with Google Books]

Tritton, D. J. Physical Fluid Dynamics. Springer, 2013. ISBN: 9780442301323.

Schlichting, H., and K. Gersten. Boundary Layer Theory. Springer, 2000. ISBN: 9783540662709. [Preview with Google Books]

This journal publishes excellent reviews of the state of the art in all areas of fluid mechanics:
Annual Review of Fluid Mechanics

We will occasionally use this DVD in class:

Homsy, G. M., ed. Multimedia Fluid Mechanics. 2nd ed. Cengage Learning, 2011. ISBN: 9780521721691.


Quiz 1 30%
Quiz 2 30%
Final Exam 40%

Extra Credit

You can gain extra credit by turning in, at the conclusion of the final exam, a notebook in which you have reworked and amplified your lecture notes in cohesive, clearly reasoned form. This is not obligatory, and note that your grade will not suffer if you do not do it. Grades will be assigned before the notebooks are examined, and only upward adjustments will be made thereafter. However, thinking through and rewriting the lecture notes, preferably on the same day as the lectures and in consultation with a text, is one of the most effective forms of study, and well worth the effort. Please do not bother to turn in a pretty version of what is on the blackboard: Extra credit will be given only when it is apparent that thought has gone into the rewriting and reconsideration of the material.

Assignments and Tutorial Sessions

Homework problems from Shapiro & Sonin's Advanced Fluid Mechanics Problems are indicated in the course outline for each topic. The homework problems are not to be turned in. Instead, they will be discussed in the tutorial sessions. Three tutorials are scheduled per week, but the idea is that each student should come to one session each week, usually the same one. Three sessions are scheduled, partly to accommodate a variety of student schedules and partly to reduce the class size and allow for a more informal atmosphere for discussion.

Detailed solutions for most of the problems have been prepared and will become available on line each week after the recitation. Additional solutions will be prepared by the Teaching Assistants and will be posted online weekly.

The main purpose of this course is not so much to feed students with "advanced" material (the topics covered do not in fact appear terribly advanced). It is instead designed to help students develop a mastery of the underlying principles and the ability to solve, quickly and efficiently, a variety of real fluid mechanics problems from first principles. The lectures present and illustrate the fundamental laws and the methods and modeling approximations that form the basis of fluid mechanics. The problems and tutorials help the students gain mastery of the material and to develop, by practice and trial and error, the mindset of an effective problem solver in fluid mechanics.

Both the assigned problems and the tutorials are entirely voluntary. No problem sets are collected, nor is roll call taken. However, based on repeated experience over many years, you may take our word that your chances of doing well in this course are minimal if you do not independently do at least the assigned problems before the tutorials, and use the tutorials to repair weaknesses and develop new insights. We are ready to help you in every way to master the course material. There is, however, a profound difference between being taught and learning. To quote Benjamin Franklin: "Tell me and I forget, teach me and I may remember, involve me and I learn."


There will be two 90-minutes quizzes during the term and the dates are announced well in advance. In order to minimize time pressures, we prefer to give the 90 minute quizzes in the evening starting at 7 pm, and give students until 9 pm to complete the problems.

There will be a three hour final exam during the final exam week.

Quizzes and the exam will permit you to use your notes, the course textbook, a calculator, and a book of mathematical formulas and tables. No other books will be allowed. The quizzes and the exam will not present you with routine problems, but will probe for mastery of the underlying material and for skill in modeling problems in the simplest possible realistic terms.