Special Topics: Fluid Mechanics
Tu Th 4:30 - 5:45 p.m. Room: SAS 1220
Instructor: Michael Shearer http://www4.ncsu.edu/~shearer/home0.html
Office: SAS 3228 Phone:
Office Hours:: Wednesdays, 2:00-3:00pm,
Fluid Dynamics, by D.J. Acheson, Oxford University Press,
Undergraduate mechanics (Physics course), vector calculus, matrices,
undergraduate level linear partial differential
equations. Other mathematics and
physics will be reviewed as needed.
Assignments (70% of final
grade) due Thursdays (but not always).
2. Quizzes (10% of final
grade): definitions and equations.
3. Final project in pairs (20% of
grade): presentations in last two weeks of class; reports in exam week.
Basic Grading Scale:
90%-100%: A, 80%-89%:
B, etc. (+ and - will also be used.)
course, fluid mechanics
will be presented from a mathematics perspective.
The equations of fluid
mechanics will be introduced, and areas of active research
will be discussed.
The course is suitable for graduate students in mathematics,
engineering. Topics will include discussion of physical concepts
viscosity and surface tension, and mathematical formulations of
lubrication theory, boundary layers, potential flow, as well as
on stability and waves.
sections from Acheson):
4 weeks: Derivation of equations of fluid flow: Navier-Stokes and
Euler. 1.2-5, 2.2, 3.2, 5.1, 6.2-4.
3 weeks: exact solutions and potential flow - complex variables. 2.3-4,
2 weeks: water waves. 3.1-3.5
5 weeks: Stokes flow, thin films. 7.4-10.
shock waves, KdV equation. 3.9-11.
additional materials. Watch this space!
Homework 1 solutions
Homework 3 solutions
Homework 4 solutions
Homework 5 solutions
Homework 6 solutions
Homework 9 solutions
This is an
introductory course to familiarize you with basic ideas of fluid
Concepts, terminology and calculations will
be presented in class, through references to the
textbook and through movies archived at MIT: http://web.mit.edu/fluids/www/Shapiro/ncfmf.html
At the end of the semester,
should have a good working knowledge of fluid mechanics, which
enable you to comprehend research presentations, read advanced
materials in fluids, and discuss
fluid mechanics concepts with some confidence.
assignments will be roughly weekly. They will be extensive exercises to
practice concepts and
calculations in fluid mechanics, and to extend the material presented
in class. Short in-class quizzes will be
used to keep concepts and definitions of terms sharp. In the last few
weeks of class, we will organize the
class into pairs. Each pair will choose a topic to explore, will give a
presentation in the last two weeks of
class, and will submit a written report during the final exam period.
1. I encourage you to discuss homework with other students, or with me
during office hours.
2. I expect you to read sections of the book around the time of
lectures and homework from those sections.
3. You are expected to attend all classes on time. Classroom discussion
and questions in class help clarify
issues in this course, so please feel free to participate by asking
4. Arriving late for a class or leaving early is very disruptive of
class. If you need to leave early, please
let me know at the beginning of class, and sit near the door so you can
slip out quietly.
5. Assignments handed in late will not be accepted.
Attendance regulations can be found
Academic Integrity Statement:
Students are expected to follow university policies on academic
and the Honor Pledge, which may be viewed by following the links at:
Reasonable accommodations will be made for students with verifiable
In order to take advantage of available accommodations, students must
register with Disability Services for
Students at 1900 Student Health Center, Campus Box 7509, 515-7653. For
more information on NC State's
policy on working with students with disabilities, please see the
Academic Accommodations for Students
with Disabilities Regulation (REG02.20.1)
There are no pass through charges for this course, such as field trip
Statement on laboratory safety or risk assumption in courses requiring
physical activity or field trips: None