Skip to main content
Unit outline_

MATH4074: Fluid Dynamics

Semester 1, 2020 [Normal day] - Camperdown/Darlington, Sydney

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

Academic unit Mathematics and Statistics Academic Operations
Credit points 6
Prerequisites
? 
(A mark of 65 or above in 12cp of MATH2XXX ) or (12cp of MATH3XXX )
Corequisites
? 
None
Prohibitions
? 
MATH3974
Assumed knowledge
? 

(MATH2961 and MATH2965) or (MATH2921 and MATH2922)

Available to study abroad and exchange students

No

Teaching staff

Coordinator Holger Dullin, holger.dullin@sydney.edu.au
Type Description Weight Due Length
Final exam Final exam
Long answer questions only. Due Week 16
70% Formal exam period 3 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 05
Due date: 29 Mar 2020 at 23:59
Standard written math assignment
Outcomes assessed: LO1 LO2 LO3
Assignment Assignment 2
Solve the given problems and write down the solutions.
10% Week 09
Due date: 26 Apr 2020 at 23:59
Standard written math assignment
Outcomes assessed: LO1 LO2 LO3 LO4 LO5
Assignment Assignment 3
Solve the given problems and write down the solutions
10% Week 13
Due date: 31 May 2020 at 23:59
Standard written math assignment
Outcomes assessed: LO1 LO2 LO3 LO4 LO5 LO6 LO7

Assessment summary

3 x assignments (30%); final exam (70%). To pass the course at least 50% in the final exam is necessary.

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
Week 02 Vorticity and Bernoulli equation. Lecture (3 hr) LO1 LO2
Week 03 Navier Stokes equations. Reynold numbers, non-dimensionalisation. Pipe-flows. Lecture (3 hr) LO1 LO3
Week 04 Viscous flows: Taylor-Couette flow, diffusion of vorticity. Lecture (3 hr) LO1 LO3
Week 05 Irrotational and incompressible fluids in two dimensions. Complex potential. Complex analysis methods. Lecture (3 hr) LO1 LO4
Week 06 Lift and drag. Blasius Theorem. Residue Theorem. Flow past a cylinder with rotation. Lecture (3 hr) LO4
Week 07 Conformal maps. Aerofoil theory. Kutta-Joukowsky. Lift of a wing with angle of attack. Lecture (3 hr) LO4
Week 08 Vortex motion. Kelvin-Helmholtz. Lecture (3 hr) LO2
Week 09 Derivation of the Navier Stokes equations. Tensors. Lecture (3 hr) LO3
Week 10 Very viscous flow. Stokes flow past a sphere. Stokes equations. Lecture (3 hr) LO3 LO6
Week 11 Boundary Layers. Lecture (3 hr) LO5 LO6
Week 12 Hydrodynamic Instability. Linear stability analysis. Lecture (3 hr) LO9
Week 13 Revision Lecture (3 hr) LO1 LO2 LO3 LO4 LO5 LO6 LO7 LO8 LO9 LO10
Weekly Fluid Dynamics Tutorial (1 hr)  

Attendance and class requirements

Due to the exceptional circumstances caused by the COVID-19 pandemic, attendance requirements for this unit of study have been amended. Where online tutorials/workshops/virtual laboratories have been scheduled, students should make every effort to attend and participate at the scheduled time. However, penalties will not be applied if technical issues etc prevent attendance.

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. 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
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.

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.