ME 530 - Theoretical Fluid Mechanics

Course Information and Syllabus Outline

Fundamentals of fluid mechanics: governing equations, ideal fluid flows, incompressible viscous fluid flows, compressible flows.

Course catalog description: Derivation of the Navier-Stokes equations; introduction to two- and three-dimensional potential flow theory; viscous flow theory, including the development of Prandtl boundary-layer equations and the momentum integral approach; compressible flow theory, including thermodynamics of shock waves, friction, and heat addition.

Office hours: walk-in or by appointment.

Prerequisites

No formal prerequisites are listed, however, good knowledge of undergraduate-level basic physics and thermodynamics are required. Necessary mathematical skills include familiarity with ordinary and partial differential equations and complex variables.

Technical requirements

The course uses Canvas learning management system. To access the course material, your computer must meet the following requirements.

• A high speed Internet connection is highly recommended.
• Supported browsers include: Internet Explorer, Firefox, and Safari. For a detailed list of supported browsers and operating systems, click here.
• Any computer capable of running a recently updated web browser should be sufficient to access your online course. However, bear in mind that processor speed, amount of RAM and Internet connection speed can greatly affect performance. Many locations offer free high-speed Internet access including UNM Computer Pods.
• Microsoft Office products are available free for all UNM students (more information on the UNM IT Software Distribution and Downloads page).

For UNM Learn Technical Support, call (505) 277-0857 (24/7) or use the “Create a Support Ticket” link in your course.

Grading and Course Policy

The course will be graded on an absolute scale using percentage scores. A 100% score implies that the student has learned all it was possible to learn in the course. 0% indicates no learning. Scores are converted to grades according to the table below.

The instructor hopes that will be no necessity to quantify scores lower than the ones presented in the table. There will be one final exam in the course, and one literature review project. Plagiarism (including "recycling" other students' work from earlier years) will not be tolerated and will be dealt with in accordance with the UNM policy on academic dishonesty. Students are also expected to comply with the UNM copyright policy.

Participation in online discussion within UNM Learn is strongly encouraged. Students are expected to use the online forums and web conferencing within UNM Learn both for interactions with the instructor and for peer-to-peer participation. Participants should follow the UNM netiquette guidelines. The learning management system in the course also provides an option for querying the instructor directly via a course message. The instructor will provide feedback on emails, UNM Learn messages, and forum questions within 48 hours.

Tracking of student activity (number of times course materials have been accessed, number of attempts on homework, etc.) may be useed for statistical purposes to improve the course. Personal student information will not be retained in any such tracking.

Students requiring special accommodations to access the course material or having specific learning needs must notify the instructor and make appropriate arrangements with the UNM Accessibility Resource Center (ARC) no later than the first week of the semester.

For any activities requiring physical presence of the students, the course adheres to UNM inclement weather policy. If UNM Learn is unexpectedly down on the due date of an assignment, please contact the instructor via e-mail: a reasonable extension of the due date shall be granted in the event of a course interruption. The students should also be aware of UNM Learn daily maintenance intervals (4:30-5:30am), as well as of any announced and scheduled downtime.

Homework will be assigned several times throughout the course. As a part of one or more homeworks, students may be asked to participate in an experiment or a computational exercise. Quizzes may be assigned to test comprehension of lecture material. The respective contributions to the final score are:

No late homework submissions will be accepted without extenuating circumstances. If an illness or other unforeseen event prevents you from submitting your homework on time, please notify the instructor no later than 48 hours after the assignment due time to request a due-time extension.

The review paper must be submitted as a PDF file and presented live (or via telepresence) during the last week of classes. The breakdown of the total score for the review is as follows: format and structure of the paper - 15%, completeness of sources - 20%, viability of conclusions - 15%, style of presentation - 25%, substance of presentation - 25%.

The submissions will be graded within one week from the due date.

The exam is open-note and open-book. Make-up exam - by appointment and only with extenuating circumstances. Students requiring special accommodations should contact the instructor before the exam. Partial credit will be given for incomplete problems showing the right steps toward the solution. The literature review project will be assigned before the seventh week of the semester, with the due date not earlier than one month after the date of the assignment. Attendance will have no influence on the grade.

This class is offered both in an online-only form and in a traditional instruction form, depending on the semester. This semester, it is offered online as a combination of PDF class notes and streaming videos, with a possibility of a weekly or bi-weekly recitation session, if requested by students. One lab may be offered, introducing the students to practical flow measurements and visualization. The final exam will be two hours long.

Approximate course outline

The following are the objectives for the course. Each course module will have specific learning objectives listed on the Overview Page. The activities in that module (discussions, assignments, assessments) are developed so that you can demonstrate you have met the objectives. Note that the week-by-week designation of modules below is based on the 16-week version of the course and is approximate. In the eight-week version of the course, material of weeks 1 and 2 as shown would be compressed into Week 1, and so on.

1. Examine and identify the fundamentals of basic conservation equations, governing equations and vorticity

2. State the assumptions of ideal fluid flow theory, derive ideal solutions for bluff body flows, lifting surface flows, and free-surface flows

3. Identify existing solutions for viscous fluid flows at finite and small Reynolds numbers, investigate the fundamentals of boundary layer theory and approximate methods for viscous flow

4. Examine the foundations of compressible flow theory, identify implications for small (acoustic) pressure perturbations and finite perturbations, including shock waves

Presently, the following outline of modules is expected, with superscript numbers denoting the course objective(s) each outline item supports:

Governing Equations:

1. Basic conservation equations (weeks 1 and 2)¹

2. Governing equations for Newtonian fluids (week 2)^1,2,3,4

3. Vorticity (week 2)^1,2,3,4

4. Special forms of conservation equations (week 2)^1,2,3,4

   Ideal fluid flows (incompressible):

5. Complex variable theory and fluid mechanics (week 3)²

6. Potential flow theory in 2D (week 3, 4, 5)²

7. Potential flows in 3D (week 6)²

8. Idealized treatment of surface-wave problems (week 7, 8)²

   Viscous fluid flows (incompressible):

9. Exact solutions for viscous flows (week 9, 10)³

10. Creeping flow (week 11)³

11. Boundary layers (week 11)³

12. Convective flows (week 12)³

    Compressible fluid flows (mostly inviscid):

13. Shock waves (week 14)⁴

14. One-dimensional compressible flows (week 14)⁴

15. Compressible flow in 3D (week 14)⁴

The instructor will appreciate feedback from students on possible improvements to the course content. If there are subjects and/or problems of specific interest, discussion of these can be included.

Useful links

UNM IT technical support – options for live support, help with laptops, passwords, etc.

UNM computer pods and classrooms – locations and software available.

https://www.unm.edu/libraries/ – main and branch campus locations.

http://caps.unm.edu/writing/growl – for help with structure, style, format, and grammar of your report.

Student Health & Counseling (SHAC) Online Services