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Unit outline_

MATH3974: Fluid Dynamics (Advanced)

Semester 1, 2023 [Normal day] - Camperdown/Darlington, Sydney

This unit of study provides an introduction to fluid dynamics, starting with a description of the governing equations and the simplifications gained by using stream functions or potentials. It develops elementary theorems and tools, including Bernoulli's equation, the role of vorticity, the vorticity equation, Kelvin's circulation theorem, Helmholtz's theorem, and an introduction to the use of tensors. Topics covered include viscous flows, lubrication theory, boundary layers, potential theory, and complex variable methods for 2-D airfoils. The unit concludes with an introduction to hydrodynamic stability theory and the transition to turbulent flow.

Unit details and rules

Academic unit Mathematics and Statistics Academic Operations
Credit points 6
Prerequisites
? 
An average mark of 65 or more in (12 credit points of MATH2XXX)
Corequisites
? 
None
Prohibitions
? 
MATH4074
Assumed knowledge
? 

[MATH2961 and MATH2965] or [MATH2921 and MATH2922]

Available to study abroad and exchange students

Yes

Teaching staff

Coordinator Sharon Stephen, sharon.stephen@sydney.edu.au
Type Description Weight Due Length
Supervised exam
? 
Final exam
Long answer questions only.
60% Formal exam period 2 hours
Outcomes assessed: LO1 LO2 LO3 LO4 LO5 LO6 LO7 LO8 LO9 LO10
Assignment Assignment 1
Solve the given problems and write down the solutions.
10% Week 04
Due date: 19 Mar 2023 at 23:59

Closing date: 29 Mar 2023
8-10 pages (as a guide)
Outcomes assessed: LO1 LO2 LO3
Assignment Assignment 2
Solve the given problems and write down the solutions.
15% Week 08
Due date: 23 Apr 2023 at 23:59

Closing date: 04 May 2023
10-14 pages (as a guide)
Outcomes assessed: LO1 LO2 LO3 LO4 LO5 LO6
Assignment Assignment 3
Solve the given problems and write down the solutions.
15% Week 12
Due date: 19 May 2023 at 23:59

Closing date: 29 May 2023
10-14 pages (as a guide)
Outcomes assessed: LO1 LO2 LO3 LO4 LO5 LO6 LO7 LO8

Assessment summary

Detailed information for each assessment can be found on Canvas.

  • Assignments: There are three assignments, which must be submitted electronically, as PDF files only, in Canvas by the deadline. It is your responsibility to check that your assignment has been submitted correctly. Penalties apply for late submission. A mark of zero will be awarded for all submissions more than 10 days past the original due date. Further extensions past this time will not be permitted.
  • Examination: The final exam for this unit is compulsory and must be attempted. Failure to attempt the final exam will result in an AF grade for the course. Further information about the exam will be made available at a later date on Canvas. If a second replacement exam is required, this exam may be delivered via an alternative assessment method, such as a viva voce (oral exam). The alternative assessment will meet the same learning outcomes as the original exam. The format of the alternative assessment will be determined by the unit coordinator.

 

 

 

Assessment criteria

The University awards common result grades, set out in the Coursework Policy 2014 (Schedule 1).

As a general guide, a high distinction indicates work of an exceptional standard, a distinction a very high standard, a credit a good standard, and a pass an acceptable standard.

Result name

Mark range

Description

High distinction

85 - 100

Representing complete or close to complete mastery of the material.

Distinction

75 - 84

Representing excellence, but substantially less than complete mastery.

Credit

65 - 74

Representing a creditable performance that goes beyond routine knowledge and understanding, but less than excellence.

Pass

50 - 64

Representing at least routine knowledge and understanding over a spectrum of topics and important ideas and concepts in the course.

Fail

0 - 49

When you don’t meet the learning outcomes of the unit to a satisfactory standard.

For more information see guide to grades.

Late submission

In accordance with University policy, these penalties apply when written work is submitted after 11:59pm on the due date:

  • Deduction of 5% of the maximum mark for each calendar day after the due date.
  • After ten calendar days late, a mark of zero will be awarded.

Academic integrity

The Current Student website provides information on academic integrity and the resources available to all students. The University expects students and staff to act ethically and honestly and will treat all allegations of academic integrity breaches seriously.

We use similarity detection software to detect potential instances of plagiarism or other forms of academic integrity breach. If such matches indicate evidence of plagiarism or other forms of academic integrity breaches, your teacher is required to report your work for further investigation.

Use of generative artificial intelligence (AI) and automated writing tools

You may only use generative AI and automated writing tools in assessment tasks if you are permitted to by your unit coordinator. If you do use these tools, you must acknowledge this in your work, either in a footnote or an acknowledgement section. The assessment instructions or unit outline will give guidance of the types of tools that are permitted and how the tools should be used.

Your final submitted work must be your own, original work. You must acknowledge any use of generative AI tools that have been used in the assessment, and any material that forms part of your submission must be appropriately referenced. For guidance on how to acknowledge the use of AI, please refer to the AI in Education Canvas site.

The unapproved use of these tools or unacknowledged use will be considered a breach of the Academic Integrity Policy and penalties may apply.

Studiosity is permitted unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission as detailed on the Learning Hub’s Canvas page.

Outside assessment tasks, generative AI tools may be used to support your learning. The AI in Education Canvas site contains a number of productive ways that students are using AI to improve their learning.

Simple extensions

If you encounter a problem submitting your work on time, you may be able to apply for an extension of five calendar days through a simple extension.  The application process will be different depending on the type of assessment and extensions cannot be granted for some assessment types like exams.

Special consideration

If exceptional circumstances mean you can’t complete an assessment, you need consideration for a longer period of time, or if you have essential commitments which impact your performance in an assessment, you may be eligible for special consideration or special arrangements.

Special consideration applications will not be affected by a simple extension application.

Using AI responsibly

Co-created with students, AI in Education includes lots of helpful examples of how students use generative AI tools to support their learning. It explains how generative AI works, the different tools available and how to use them responsibly and productively.

WK Topic Learning activity Learning outcomes
Week 01 Ideal Fluids. Euler's equations, material derivative. Lagrangian and Eulerian view. Lecture (3 hr) LO1 LO2 LO3
Week 02 Vorticity and Bernoulli equation, circulation, Navier-Stokes equation, boundary conditions. Lecture and tutorial (4 hr) LO1 LO2
Week 03 Navier Stokes equations. Reynold numbers, non-dimensionalisation. Simple viscous flows, channel flow, pipe flow. Lecture and tutorial (4 hr) LO1 LO3
Week 04 Viscous flows: Taylor-Couette flow, diffusion of vorticity. Lecture and tutorial (4 hr) LO1 LO3
Week 05 Irrotational and incompressible fluids in two dimensions. Complex potential. Complex analysis methods. Lecture and tutorial (4 hr) LO1 LO4 LO6
Week 06 The method of images. Blasius Theorem. Lift and drag. Conformal transformations. Joukowski transformation. Residue Theorem. Lecture and tutorial (4 hr) LO4 LO6
Week 07 Flow around a circular cylinder. Kelvin's circulation theorem. Helmholtz vortex theorems. The von Karman vortex street. Lecture and tutorial (4 hr) LO4 LO5 LO6
Week 08 Derivation of the Navier-Stokes equation. Tensors. Lecture and tutorial (4 hr) LO1 LO2
Week 09 Dissipation of energy. Low Reynolds number flow. Lecture and tutorial (4 hr) LO1 LO7
Week 10 High Reynolds number flow. Boundary-layer equations. Blasius solution. Singular perturbation problems. Lecture and tutorial (4 hr) LO1 LO4 LO7
Week 11 Hydrodynamic stability. Linear stability analysis. Lecture and tutorial (4 hr) LO4 LO7 LO8 LO9
Week 12 Hydrodynamic stability. Linear stability analysis. Viscous analysis. Squire's theorem. Orr-Sommerfeld equation. Centrifugal instability. Lecture and tutorial (4 hr) LO4 LO7 LO8 LO9
Week 13 Revision Lecture and tutorial (4 hr) LO1 LO2 LO3 LO4 LO5 LO6 LO7 LO8 LO9 LO10

Attendance and class requirements

  • Lecture attendance: You are expected to attend lectures. If you do not attend lectures you should at least follow the lecture recordings available through Canvas in conjunction with the lecture notes.

  • Tutorial attendance: Tutorials start in Week 2. You are expected to attend tutorials where you will work through questions from the tutorial sheet in small groups on the white board. A record of your tutorial attendance is kept. We strongly recommend you attend tutorials regularly to keep up with the material and to engage with the tutorial questions.

Study commitment

Typically, there is a minimum expectation of 1.5-2 hours of student effort per week per credit point for units of study offered over a full semester. For a 6 credit point unit, this equates to roughly 120-150 hours of student effort in total.

Learning outcomes are what students know, understand and are able to do on completion of a unit of study. They are aligned with the University's graduate qualities and are assessed as part of the curriculum.

At the completion of this unit, you should be able to:

  • LO1. explain and apply the fundamentals of fluid mechanics
  • LO2. determine how and in what situations a system which is not necessarily liquid can be described as a fluid.
  • LO3. explain and apply the link between Eulerian and Lagrangian descriptions of a fluid.
  • LO4. apply the general theory of asymptotics to simplify equations by exploiting small parameters, scaling regimes and geometric and physical assumptions.
  • LO5. use complex analysis, PDE theory and perturbation theory to describe kinematic and dynamic flows in structured contexts/examples
  • LO6. apply Laplace’s equation to irrotational flow with added circulation and use complex variable methods to solve for two dimensional flow. Explain aerofoil theory and the derivation of the formula for lift.
  • LO7. explain the distinction between and the features of high and low Reynolds number flows.
  • LO8. explain and apply the concepts of hydrodynamic stability
  • LO9. explain the transition to turbulence, the turbulence closure problem and Kolmogorov’s theorem.
  • LO10. explain and apply the fundamental theory of water waves

Graduate qualities

The graduate qualities are the qualities and skills that all University of Sydney graduates must demonstrate on successful completion of an award course. As a future Sydney graduate, the set of qualities have been designed to equip you for the contemporary world.

GQ1 Depth of disciplinary expertise

Deep disciplinary expertise is the ability to integrate and rigorously apply knowledge, understanding and skills of a recognised discipline defined by scholarly activity, as well as familiarity with evolving practice of the discipline.

GQ2 Critical thinking and problem solving

Critical thinking and problem solving are the questioning of ideas, evidence and assumptions in order to propose and evaluate hypotheses or alternative arguments before formulating a conclusion or a solution to an identified problem.

GQ3 Oral and written communication

Effective communication, in both oral and written form, is the clear exchange of meaning in a manner that is appropriate to audience and context.

GQ4 Information and digital literacy

Information and digital literacy is the ability to locate, interpret, evaluate, manage, adapt, integrate, create and convey information using appropriate resources, tools and strategies.

GQ5 Inventiveness

Generating novel ideas and solutions.

GQ6 Cultural competence

Cultural Competence is the ability to actively, ethically, respectfully, and successfully engage across and between cultures. In the Australian context, this includes and celebrates Aboriginal and Torres Strait Islander cultures, knowledge systems, and a mature understanding of contemporary issues.

GQ7 Interdisciplinary effectiveness

Interdisciplinary effectiveness is the integration and synthesis of multiple viewpoints and practices, working effectively across disciplinary boundaries.

GQ8 Integrated professional, ethical, and personal identity

An integrated professional, ethical and personal identity is understanding the interaction between one’s personal and professional selves in an ethical context.

GQ9 Influence

Engaging others in a process, idea or vision.

Outcome map

Learning outcomes Graduate qualities
GQ1 GQ2 GQ3 GQ4 GQ5 GQ6 GQ7 GQ8 GQ9

This section outlines changes made to this unit following staff and student reviews.

No changes have been made since this unit was last offered.
  • Lectures: Lectures are face-to-face and streamed live with online access from Canvas.
  • Tutorial sheets: The tutorial sheets for a given week will be available on the MATH3974 Canvas page on Tuesday. Solutions to tutorial exercises for week n will usually be posted on Canvas by the afternoon of the Tuesday of week n+1.
  • Ed Discussion forum: https://edstem.org

Work, health and safety

We are governed by the Work Health and Safety Act 2011, Work Health and Safety Regulation 2011 and Codes of Practice. Penalties for non-compliance have increased. Everyone has a responsibility for health and safety at work. The University’s Work Health and Safety policy explains the responsibilities and expectations of workers and others, and the procedures for managing WHS risks associated with University activities.

General Laboratory Safety Rules

  • No eating or drinking is allowed in any laboratory under any circumstances
  • A laboratory coat and closed-toe shoes are mandatory
  • Follow safety instructions in your manual and posted in laboratories
  • In case of fire, follow instructions posted outside the laboratory door
  • First aid kits, eye wash and fire extinguishers are located in or immediately outside each laboratory
  • As a precautionary measure, it is recommended that you have a current tetanus immunisation. This can be obtained from University Health Service: unihealth.usyd.edu.au/

Disclaimer

The University reserves the right to amend units of study or no longer offer certain units, including where there are low enrolment numbers.

To help you understand common terms that we use at the University, we offer an online glossary.