Outline

Overview

Fluid Dynamics is the study of systems which allow for a macroscopic description in some continuum limit. It is not limited to the study of liquids such as water but includes our atmosphere and even car traffic. Whether a system can be treated as a fluid, depends on the spatial scales involved. Fluid dynamics presents a cornerstone of applied mathematics and comprises a whole gamut of different mathematical techniques, depending on the question we ask of the system under consideration. The course will discuss applications from engineering, physics and mathematics: How and in what situations a system which is not necessarily liquid can be described as a fluid? The link between an Eulerian description of a fluid and a Lagrangian description of a fluid, the basic variables used to describe flows, the need for continuity, momentum and energy equations, simple forms of these equations, geometric and physical simplifying assumptions, streamlines and stream functions, incompressibility and irrotationality and simple examples of irrotational flows. By the end of this unit, students will have received a basic understanding into fluid mechanics and have acquired general methodology which they can apply in their further studies in mathematics and/or in their chosen discipline.

Unit details and rules

Unit code	MATH4074
Academic unit	Mathematics and Statistics Academic Operations
Credit points	6
Prohibitions ?	MATH3974
Prerequisites ?	(A mark of 65 or above in 12cp of MATH2XXX) or (12cp of MATH3XXX)
Corequisites ?	None
Assumed knowledge ?	(MATH2961 and MATH2965) or (MATH2921 and MATH2922)
Available to study abroad and exchange students	No

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:
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:
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:
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:

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 sydney.edu.au/students/guide-to-grades.

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.

You may only use artificial intelligence and writing assistance tools in assessment tasks if you are permitted to by your unit coordinator, and if you do use them, you must also acknowledge this in your work, either in a footnote or an acknowledgement section.

Studiosity is permitted for postgraduate units unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission.

Learning support

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.

Weekly schedule

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

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

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.

Outcomes
Graduate qualities

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

LO1. Explain and apply the fundamentals of fluid mechanics
LO2. Explain 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 an Eulerian description of a fluid and a Lagrangian description of a fluid.
LO4. Explain the general framework of asymptotics - simplifying equations by exploiting small parameters and scaling regimes and geometric as well as physical assumptions
LO5. Describe kinematic and dynamic flows using complex analysis, PDE theory and perturbation theory.
LO6. Recall and explain the basic definitions of stream function, velocity potential, incompressibility, irrotationality and other fundamental quantities to describe fluids
LO7. Synthesis ideas about with added circulation; and apply to Laplace's equation and the use of complex variable methods for its solution in two dimensions; airfoil theory and the derivation of the formula for life; basic understanding of how aircraft fly.
LO8. Explain the distinction of high and low Reynolds number flows
LO9. Explain ideas of hydrodynamic stability and give examples of calculations; and transitions to turbulence via a sequence of bifurcations; the turbulent closure problem and other difficulties; Kolmogorov's theory for the spectrum of turbulent eddies.
LO10. Explain 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
Learning outcomes

Responding to student feedback

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

No changes have been made since this unit was last offered.

Additional information

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 MATH4074 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

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.

Current students

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Assessment summary

Assessment criteria

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Weekly schedule

Weekly schedule

Attendance and class requirements

Study commitment

Learning outcomes

Learning outcomes

Graduate qualities

Outcome map

Responding to student feedback

Responding to student feedback

Additional information

Additional information

Disclaimer

On this page

Useful links

Media

Student links

About us

Connect

Current students

MATH4074: Fluid Dynamics

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

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Assessment summary

Assessment criteria

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Weekly schedule

Weekly schedule

Attendance and class requirements

Study commitment

Learning outcomes

Learning outcomes

Graduate qualities

Outcome map

Responding to student feedback

Responding to student feedback

Additional information

Additional information

Disclaimer

On this page

Useful links

Media

Student links

About us

Connect