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2.006; 18.075 or 18.085

Topics Covered

  1. Continuum Viewpoint and the Equation of Motion
  2. Static Fluids
  3. Mass Conservation
  4. Inviscid Flow (Differential Approach): Euler's Equation, Bernoulli's Integral, and the Effects of Streamline Curvature
  5. Control Volume Theorems (Integral Approach): Linear Momentum Theorem, Angular Momentum Theorem, First and Second Laws of Thermodynamics
  6. Navier-Stokes Equation and Viscous Flow
  7. Similarity and Dimensional Analysis
  8. Boundary Layers, Separation and the Effect on Drag and Lift
  9. Vorticity and Circulation
  10. Potential Flow, Lift, Drag, and Thrust
  11. Surface Tension and its Effect on Flows
  12. Introduction to Turbulence (if time)


The suggested text is: Amazon logo Kundu, Pijush K., and Ira M. Cohen. Fluid Mechanics. 3rd ed. Burlington, MA: Elsevier, 2004. ISBN: 9780121782535.
This book is strongly recommended and readings from it will be assigned.

Another excellent book is: Amazon logo Fay, James A. Introduction to Fluid Mechanics. Cambridge, MA: MIT Press, 1994. ISBN: 9780262061650.
Fay's book is at the advanced undergraduate level, but covers most of the topics dealt with in the lectures. The lectures will cover some material with greater rigor or different emphasis; special notes are provided for selected topics, as indicated in the outlines. Students are responsible for material covered in class or indicated in the course outlines.

The following book is required for all students, as the source of most assigned homework problems: Shapiro, Ascher H., and Ain A. Sonin. Advanced Fluid Mechanics Problems. (Self-published manuscript.)

For Section 5 (Control Volume Theorems), a revised set of problems is posted in assignments, with hints and answers as well as some full solutions and examples. This is part of an on-going updating of the problems and the way they are presented.

Knowledgeable students will be able to read equally profitably from alternative texts and readings, provided they are in the habit of reading broadly and searching out references that satisfy them on the fundamentals. For instance:

Amazon logo Tritton, D. Physical Fluid Dynamics. 2nd ed. New York, NY: Oxford University Press, 1988. ISBN: 9780198544937.

Amazon logo Schlichting, H. Boundary Layer Theory. 7th ed. New York, NY: McGraw Hill, 1979. ISBN: 9780070553347.

For excellent reviews of the state of the art in all areas of fluid mechanics, see Annual Review of Fluid Mechanics, Vol. 1 (1969) to Vol. 37 (2005).

Finally, there is an excellent CD-ROM available with English, French and German language content: Amazon logo Homsey, G. M., et al. Multimedia Fluid Mechanics. New York, NY: Cambridge University Press, 2004. ISBN: 9780521604765.

Homework Problems and Tutorial Sessions

Homework problems from Shapiro and 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.

New for 2005; detailed solutions for some of the problems will be prepared by the Teaching Assistant and will be posted online weekly.

The main purpose of this course is not so much to feed the students with "advanced" material (the topics covered do not in fact appear terribly advanced) as 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 a 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, except perhaps to help the instructors remember the students' names. 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.


There will be two one-hour quizzes during the term, announced well in advance. In order to minimize time pressures, we prefer to give the (nominally) one-hour 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.

Quizzes and the exam will permit a limited number of pages of open notes (and 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.


Quiz 1 25%
Quiz 2 25%
Final Exam 50%

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 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.