MAT3106 Vector Calculus and the Mathematical Modelling of Fluid Flows

Contents

• Staffing
• Requisites
• Rationale
• Synopsis
• Objectives
• Topics
• Texts
• Reference materials
• Student workload
• Assessment details
• Important assessment information
• Assessment notes
• Production date
• PDF version

STAFFING

REQUISITES

RATIONALE

Concepts and methods for the modelling and analysis of vector functions in space are required for an understanding of the principles that permeate much of applied mathematics, mathematical physics and engineering science. These principles are developed in the context of their application to the dynamics of fluid flow as it is important in industrial and environmental problems.

SYNOPSIS

First this course unifies vector algebra and differential calculus into the calculus of vector functions. It develops the differential and integral calculus, establishes their properties, and shows how these properties give useful formula in general coordinate systems. The course integrates the application of these mathematical tools to inviscid and incompressible fluid dynamics. It then extends the modelling of dynamics to the flow of a Newtonian viscous fluid such as air and water. Applications to channel flows, boundary layers, wakes, jets and lubrication are developed. This course is offered only in even numbered years.

OBJECTIVES

On completion of this course students will be able to:

1. use conservation principles to mathematically model inviscid fluid mechanics (Assignment 1, Exam);
2. use vector calculus to anlayse the structure of physical fields in Cartesian coordinates (Assignment 1, exam);
3. interpret and evaluate integrals over curves, surfaces and spatial domains (Assignment 1, Exam);
4. appreciate the close connection between advanced mathematical concepts and real physical processes (Assignments 1 and 2, Exam);
5. use and understand the fundamental equations describing viscous fluid flow (Assignment 2, Exam);
6. mathematically analyse and interpret fluid flows involving thin films, viscous flows around bodies, or in boundary layers (Assignment 2, Exam).

TOPICS

TEXT and MATERIALS required to be PURCHASED or accessed

ALL textbooks and materials are available for purchase from USQ BOOKSHOP (unless otherwise stated). Orders may be placed via secure internet, free fax 1800642453, phone 07 46312742 (within Australia), or mail. Overseas students should fax +61 7 46311743, or phone +61 7 46312742. For costs, further details, and internet ordering, use the 'Textbook Search' facility at http://bookshop.usq.edu.au click 'Semester', then enter your 'Course Code' (no spaces).

Introductory Book 2008, Course MAT3106 Vector Calculus and Mathematical Modelling of Fluid Flows, USQ Distance Education Centre, Toowoomba.

Kreyszig, E 2006, Advanced Engineering Mathematics, 9th edn, Wiley, New York.

Ockendon, H & Ockendon, JR 1995, Viscous Flow, Cambridge University Press.

Study Book 2008, Course MAT3106 Vector Calculus and Mathematical Modelling of Fluid Flows, USQ Distance Education Centre, Toowoomba.

REFERENCE MATERIALS

Reference materials are materials that, if accessed by students, may improve their knowledge and understanding of the material in the course and enrich their learning experience.

Some electronic resources for this course may be available via its home page: http://www.sci.usq.edu.au/courses/MAT3106

Hughes, WF & Brighton, JA 1999, Schaum's Outline of Theory and Problems of Fluid Dynamics, 3rd edn, McGraw-Hill, New York.

Schlichting, H 2000, Boundary-layer theory, 8th edn, Springer, Berlin.

Study Book 2007, Course MAT2100 Algebra and Calculus II, USQ Distance and e-Learning Centre, Toowoomba.

Study Book 2008, Course MAT3105 Harmony of Partial Differential Equations, USQ Distance and e-Learning Centre, Toowoomba.

Van Dyke, M 1982, An Album of Fluid Motion, The Parabolic Press, Stanford, California.

Videorecording : Barker, A (Producer), BBC TV Production for the Open University Engineering Mechanics: solids and fluids (Available: ).

Videorecording : Encyclopedia Britannica Educational Corporation, Castle Hill, NSW Flow Visualisation (Available: ).

Videorecording : Encyclopedia Britannica Educational Corporation, Castle Hill, NSW Fluid Dynamics of Drag: Part II (Available: ).

Videorecording : Encyclopedia Britannica Educational Corporation, Castle Hill, NSW Fundamentals of Boundary Layers (Available: ).

Videorecording : Encyclopedia Britannica Educational Corporation, Castle Hill, NSW Low Reynolds Number Flow (Available: ).

Videorecording : National Committee for Fluid Mechanics Films, Encyclopedia Britannica Pressure Fields and Fluid Acceleration (Available: ).

White, FM 2003, Fluid Mechanics, 5th edn, McGraw-Hill, New York.

STUDENT WORKLOAD REQUIREMENTS

ASSESSMENT DETAILS

NOTES

1.

Further details about the due dates are given in the Study Schedule of the Introductory Book.

2.

Examination dates will be available during the semester. Please refer to the examination timetable when published.

IMPORTANT ASSESSMENT INFORMATION

1. Attendance requirements:
   It is the students' responsibility to attend and participate appropriately in all activities (such as lectures, tutorials, laboratories and practical work) scheduled for them, and to study all material provided to them or required to be accessed by them to maximise their chance of meeting the objectives of the course and to be informed of course-related activities and administration.
2. Requirements for students to complete each assessment item satisfactorily:
   To complete each of the assessment items satisfactorily, students must obtain at least 50% of the marks available for each assessment item.
3. Penalties for late submission of required work:
   If students submit assignments after the due date without (prior) approval of the examiner then a penalty of 5% of the total marks gained by the student for the assignment may apply for each working day late up to ten working days at which time a mark of zero may be recorded. No assignments will be accepted after model answers have been posted.
4. Requirements for student to be awarded a passing grade in the course:
   To be assured of receiving a passing grade a student must achieve at least 50% of the total weighted marks available for the course.
5. Method used to combine assessment results to attain final grade:
   The final grades for students will be assigned on the basis of the aggregate of the weighted marks obtained for each of the summative assessment items in the course.
6. Examination information:
   In an Open Examination, candidates may have access to any material during the examination except the following: electronic communication devices, bulky materials, devices requiring mains power and material likely to disturb other students.
7. Examination period when Deferred/Supplementary examinations will be held:
   Students who obtain an overall passing mark, but who do not perform satisfactorily in an examination, may, at the discretion of the Examiner, be granted a Supplementary examination. Students will be granted a Deferred examination only if they perform satisfactorily in all other assessment items. Any Deferred or Supplementary examinations for this course will be held during the examination period at the end of the semester of the next offering of this course.
8. University Regulations:
   Students should read USQ Regulations 5.1 Definitions, 5.6. Assessment, and 5.10 Academic Misconduct for further information and to avoid actions which might contravene University Regulations. These regulations can be found at the URL http://www.usq.edu.au/corporateservices/calendar/part5.htm or in the current USQ Handbook.

ASSESSMENT NOTES

This version produced 24 Nov 2008.