## APP MTH 4102 - Fluid Mechanics - Honours

### North Terrace Campus - Semester 1 - 2019

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 4102 Fluid Mechanics - Honours School of Mathematical Sciences Semester 1 Undergraduate North Terrace Campus 3 Up to 3 hours per week (MATHS 2101 or MATHS 2202) and (MATHS 2102 or MATHS 2201) MATHS 2104 Honours students only 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: Dr Trent Mattner

Office: Ingkarni Wardli, Rm 637
Phone: 8313 5079
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.

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
4,5,6,7
• Learning Resources
None.
##### Recommended Resources
1. Elementary fluid dynamics, Acheson, Oxford University Press.
2. An introduction to fluid mechanics, Batchelor, Cambridge University Press.
3. Introduction to Theoretical and Computational Fluid Dynamics, Pozrikidis, Oxford 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.

• 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 tests and written assignments provides the 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 27 81 Tutorials 6 18 Tests 3 33 Assignments 2 24 TOTALS 156
##### Learning Activities Summary
 Week 1 Eulerian and Lagrangian coordinates, pathlines, streaklines, streamlines. Week 2 Suffix notation, material derivative. Week 3 Decomposition of local fluid motion. Week 4 Mass conservation, incompressible flow, stream function. Week 5 Forces, Cauchy equation of motion, Navier-Stokes equations. Week 6 Solutions of the Navier-Stokes equations Week 7 Fourier pseudospectral methods Week 8 Fourier pseudospectral methods Week 9 Euler equations, Bernoulli equation, velocity potential, Laplace equation Week 10 Souces, sinks, dipoles, superposition, forces on bodies, circulation. Week 11 Complex potential Week 12 Dynamic similarity

• 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 Tests 18% All Assignments 12% 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 Test 1 Week 4 6% Assignment 1 Week 5 Week 7 6% Test 2 Week 8 6% Assignment 2 Week 9 Week 12 6% Test 3 Week 12 6%
##### Submission
Assignments must be submitted according to the policies and procedures published on the Fluid Mechanics - Honours MyUni site.

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

M11 (Honours Mark Scheme)
Fail A mark between 1-49 F
Third Class A mark between 50-59 3
Second Class Div B A mark between 60-69 2B
Second Class Div A A mark between 70-79 2A
First Class A mark between 80-100 1
Result Pending An interim result RP
Continuing Continuing CN

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
• Fraud Awareness

Students are reminded that in order to maintain the academic integrity of all programs and courses, the university has a zero-tolerance approach to students offering money or significant value goods or services to any staff member who is involved in their teaching or assessment. Students offering lecturers or tutors or professional staff anything more than a small token of appreciation is totally unacceptable, in any circumstances. Staff members are obliged to report all such incidents to their supervisor/manager, who will refer them for action under the university's studentâ€™s disciplinary procedures.

The University of Adelaide is committed to regular reviews of the courses and programs it offers to students. The University of Adelaide therefore reserves the right to discontinue or vary programs and courses without notice. Please read the important information contained in the disclaimer.

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