APP MTH 3002 - Fluid Mechanics III

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 3002
    Course Fluid Mechanics III
    Coordinating Unit Applied Mathematics
    Term Semester 1
    Level Undergraduate
    Location/s North Terrace Campus
    Units 3
    Contact Up to 3 hours per week
    Prerequisites MATHS 1012 (Note: from 2015 the prerequisites for this course will be (MATHS 2101 and MATHS 2102) or (MATHS 2201 and MATHS 2202) . Please plan your 2014 enrolment accordingly).
    Assumed Knowledge MATHS 2101 and MATHS 2102 or MATHS 2201 and MATHS 2202, and 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 Staff

    Course Coordinator: Associate Professor Ben Binder

    Email: benjamin.binder@adelaide.edu.au
    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 fluidflows.

    4. be able to solve inviscid flow problems using streamfunctions 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)
    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
    Required 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 the
    students make appropriate use of these resources.

    Link to MyUni login page:
    https://myuni.adelaide.edu.au/webapps/login/ 
  • 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 the assessment opportunities for students to gauge their progress and understanding.
    Workload

    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 

  • 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.

    Course Grading

    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.

  • 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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