APP MTH 7075 - Fluid Mechanics
North Terrace Campus - Semester 1 - 2018
General Course Information
Course Code APP MTH 7075 Course Fluid Mechanics Coordinating Unit School of Mathematical Sciences Term Semester 1 Level Postgraduate Coursework Location/s North Terrace Campus Units 3 Contact Up to 3 hours per week Available for Study Abroad and Exchange Y Prerequisites (MATHS 2101 and MATHS 2102) or (MATHS 2201 and MATHS 2202) Assumed Knowledge MATHS 2104 Course Description 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.
Course Coordinator: Dr Trent MattnerEmail: firstname.lastname@example.org
Office: Ingkarni Wardli, Rm 637
Phone: 8313 5079
Administrative Enquiries: School of Mathematical Sciences Office, Level 6, Ingkarni Wardli
The full timetable of all activities for this course can be accessed from Course Planner.
Course Learning OutcomesStudents 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.
University Graduate Attributes
This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:
University Graduate Attribute Course Learning Outcome(s) Deep discipline knowledge
- informed and infused by cutting edge research, scaffolded throughout their program of studies
- acquired from personal interaction with research active educators, from year 1
- accredited or validated against national or international standards (for relevant programs)
all Critical thinking and problem solving
- steeped in research methods and rigor
- based on empirical evidence and the scientific approach to knowledge development
- demonstrated through appropriate and relevant assessment
Recommended Resources1. Elementary fluid dynamics, Acheson, Oxford University Press
2. An introduction to fluid mechanics, Batchelor, Cambridge University Press
Online LearningThis 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 ModesThis 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 TOTAL 156
Learning Activities SummaryLecture 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
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
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 RequirementsNone.
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- Assessment must encourage and reinforce learning.
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Component Weighting Objective Assessed Assignments 30% All Exam 70% All
Assessment Related RequirementsAn aggregate score of at least 50% is required to pass the course.
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%
SubmissionAll 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) Grade Mark Description 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.
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