APP MTH 7075 - Fluid Mechanics

North Terrace Campus - Semester 1 - 2014

Fluid flows are important in many scientific and technological problems including atmospheric and oceanic circulation, energy production by chemical or nuclear combustion in engines and stars, energy utilisation in vehicles, buildings and industrial processes, and biological processes such as the flow of blood. Considerable progress has been made in the mathematical modelling of fluid flows and this has greatly improved our understanding of these problems, but there is still much to discover. This course introduces students to the mathematical description of fluid flows and the solution of some important flow problems. Topics covered are: the mathematical description of fluid flow in terms of Lagrangian and Eulerian coordinates; the derivation of the Navier-Stokes equations from the fundamental physical principles of mass and momentum conservation; use of the stream function, velocity potential and complex potential are introduced to find solutions of the governing equations for inviscid, irrotational flow past bodies and the forces acting on those bodies; analytic and numerical solutions of the Navier-Stokes equation.

• General Course Information
Course Details
Course Code APP MTH 7075 Fluid Mechanics Applied Mathematics Semester 1 Postgraduate Coursework North Terrace Campus 3 Up to 3 hours per week MATHS 1012 MATHS 2201 or MATHS 2102, MATHS 2202 or MATHS 2101 assignments 30%, final exam 70%
Course Staff

Course Coordinator: Associate Professor Ben Binder

Office: Ingkarni Wardli, Rm 659
Phone: 8313 3244
Administrative Enquiries: School of Mathematical Sciences Office, Level 6, Ingkarni Wardli
Course Timetable

The full timetable of all activities for this course can be accessed from Course Planner.

• Learning Outcomes
Course Learning Outcomes
Students who successfully complete the course should:

1. understand the basic concepts of fluid mechanics.
2. understand the mathematical description of fluid flow.
3. understand the conservation principles governing fluid flows.
4. be able to solve inviscid flow problems using stream functions and velocity potentials.
5. be able to compute forces on bodies in fluid flows.
6. be able to solve (analytical and numerical) viscous flow problems.
7. be able to use mathematical software packages (Maple and Matlab) in solution methods.

This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:

University Graduate Attribute Course Learning Outcome(s)
Knowledge and understanding of the content and techniques of a chosen discipline at advanced levels that are internationally recognised. all
An ability to apply effective, creative and innovative solutions, both independently and cooperatively, to current and future problems. 5,6,7,8
A proficiency in the appropriate use of contemporary technologies. 8
A commitment to continuous learning and the capacity to maintain intellectual curiosity throughout life. all
• Learning Resources
None.
Recommended Resources
1. Elementary fluid dynamics, Acheson, Oxford University Press
2. An introduction to fluid mechanics, Batchelor, Cambridge University Press
Online Learning
This course uses MyUni exclusively for providing electronic resources, such as lecture notes, assignment papers, sample solutions, discussion boards, etc. It is recommended that students make appropriate use of these resources.
• Learning & Teaching Activities
Learning & Teaching Modes
This course relies on lectures as the primary delivery mechanism for the material. Tutorials supplement the lectures by providing exercises and example problems to enhance the understanding obtained through lectures. A sequence of written assignments provides assessment opportunities for students to gauge their progress and understanding.

The information below is provided as a guide to assist students in engaging appropriately with the course requirements.

 Activity Quantity Workload hours Lectures 30 90 Tutorials 6 18 Assignments 5 48 TOTALS 156
Learning Activities Summary
Lecture Outline

1. Course outline and overview
2. Lagrangian and Eulerian desription of fluid flow
3. Pathlines, streamlines and streaklines
4. Pathlines, streamlines and streaklines
5. Suffix notation
6. Tensor notation
7. Material derivative
8. Velocity gradient tensor; fluid decomposition; rate-of-strain tensor
9. Rate-of-rotation tensor; vorticity and irrotational flow
10. Mass conservation; incompressible flow
11. Streamfunction
12. Equations of motion; external and internal forces
13. Stress tensor and Cauchy’s equation of motion
14. Navier-Stokes equations
15. Exact solutions of the Navier-Stokes equations
16. Exact solutions of the Navier-Stokes equations
17. Fourier spectral methods
18. Fourier spectral methods
19. Applications of spectral methods
20. Chebyshev spectral methods
21. Chebyshev spectral methods
22. Applications of spectral methods
23. Eulers equations, conservative forces, hydrostatics
24. Bernoulli's equation
25. Velocity potential; Laplace equation
26. Flow past closed bodies
27. Force on a body
28. Circulation and Kelvin’s circulation theorem
29. Complex potential flow and the Cauchy-Riemann equations
30. Course summary and  possible non-examinable topics: conformal transformation, Joukowski transformation and flow past an aerofoil, Stokes flow, boundary layer flows, Dynamic similarity

Tutorial Outline

1. Lagrangian and Eulerian flow visualisation
2. Decomposition of local fluid motion and conservation of mass
3. Conservation of momentum and analytic solutions to the Navier Stokes equations
4. Numerical solutions using spectral methods
5. Eulers equations and complex potential
6. Revison tutorial
Specific Course Requirements
None.
• Assessment

The University's policy on Assessment for Coursework Programs is based on the following four principles:

1. Assessment must encourage and reinforce learning.
2. Assessment must enable robust and fair judgements about student performance.
3. Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
4. Assessment must maintain academic standards.

Assessment Summary
 Component Weighting Objective Assessed Assignments 30% All Exam 70% All
Assessment Related Requirements
An aggregate score of at least 50% is required to pass the course.
Assessment Detail
 Assessment Item Distributed Due Date Weighting Assignment 1 Week 1 Week 3 6% Assignment 2 Week 3 Week 5 6% Assignment 3 Week 7 Week 9 6% Assignment 4 Week 9 Week 11 6% Assignment 5 Week 11 Week 12 6%
Submission
All written assignments are to be submitted to the designated hand-in boxes within the School of Mathematical Sciences with a signed cover sheet attached. Late assignments will not be accepted. Assignments will have a two week turn-around time for feedback to students.

Grades for your performance in this course will be awarded in accordance with the following scheme:

M10 (Coursework Mark Scheme)
FNS   Fail No Submission
F 1-49 Fail
P 50-64 Pass
C 65-74 Credit
D 75-84 Distinction
HD 85-100 High Distinction
CN   Continuing
NFE   No Formal Examination
RP   Result Pending

Further details of the grades/results can be obtained from Examinations.

Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.

Final results for this course will be made available through Access Adelaide.

• Student Feedback

The University places a high priority on approaches to learning and teaching that enhance the student experience. Feedback is sought from students in a variety of ways including on-going engagement with staff, the use of online discussion boards and the use of Student Experience of Learning and Teaching (SELT) surveys as well as GOS surveys and Program reviews.

SELTs are an important source of information to inform individual teaching practice, decisions about teaching duties, and course and program curriculum design. They enable the University to assess how effectively its learning environments and teaching practices facilitate student engagement and learning outcomes. Under the current SELT Policy (http://www.adelaide.edu.au/policies/101/) course SELTs are mandated and must be conducted at the conclusion of each term/semester/trimester for every course offering. Feedback on issues raised through course SELT surveys is made available to enrolled students through various resources (e.g. MyUni). In addition aggregated course SELT data is available.

• Student Support
• Policies & Guidelines
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