MA 797-002: Special Topics: Fluid Mechanics

Tu Th 4:30 - 5:45 p.m. Room: SAS 1220

Office: SAS 3228

**Office Hours:**: Wednesdays, 2:00-3:00pm,
and
by appointment.

undergraduate level linear partial differential equations. Other mathematics and physics will be reviewed as needed.

**Grading**:

1. Weekly
Homework
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
final
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.)

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,

physics and engineering. Topics will include discussion of physical concepts

such as viscosity and surface tension, and mathematical formulations of

Stokes flow, lubrication theory, boundary layers, potential flow, as well as

presentations on stability and waves.

Tentative schedule (with 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, 4.2-8

2 weeks: water waves. 3.1-3.5

5 weeks: Stokes flow, thin films. 7.4-10.

shock waves, KdV equation. 3.9-11.

Notes: homework solutions; additional materials. Watch this space!

Jacobian notes.

Homework 1 solutions

Homework 2 solutions

Homework 3 solutions

Homework 4 solutions

Homework 5 solutions

Homework 6 solutions

Homework 9 solutions

**Objectives:**** **

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,

will enable you to comprehend research presentations, read advanced materials in fluids, and discuss

fluid mechanics concepts with some confidence.

Homework 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.

Additional Policies:

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 questions.

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 at

http://www.ncsu.edu/policies/academic_affairs/courses_undergrad/REG02.20.3.php

Academic Integrity Statement: Students are expected to follow university policies on academic integrity

and the Honor Pledge, which may be viewed by following the links at:

http://www.ncsu.edu/policies/academic_affairs/courses_undergrad/REG02.20.7.php

Further Statements: Reasonable accommodations will be made for students with verifiable disabilities.

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 costs.

Statement on laboratory safety or risk assumption in courses requiring physical activity or field trips: None