Course Catalogue

View Specification Document | Reading List

This course introduces students to the mathematical theory of fluids. In particular, the course develops theory and explores several important applications, such as classical aerofoil theory, water waves
and viscous boundary layers, employing methods from complex analysis, differential equations and asymptotic analysis.

17 x 1 hr lectures and 6 x 1 hr tutorials in a semester

Mandatory Entry Requirements

Mechanics of Rigid and Deformable Bodies (MATHS 4078)

Mathematical Methods (MATHS 4075)

Methods in Complex Analysis (MATHS 4076)

Recommended Entry Requirements

Assessment

90% Examination, 10% Coursework.

Reassessment

In accordance with the University's Code of Assessment reassessments are normally set for all courses which do not contribute to the honours classifications. For non honours courses, students are offered reassessment in all or any of the components of assessment if the satisfactory (threshold) grade for the overall course is not achieved at the first attempt. This is normally grade D3 for undergraduate students, and grade C3 for postgraduate students. Exceptionally it may not be possible to offer reassessment of some coursework items, in which case the mark achieved at the first attempt will be counted towards the final course grade. Any such exceptions are listed below in this box.

Reassessments are normally available for all courses, except those which contribute to the Honours classification. For non Honours courses, students are offered reassessment in all or any of the components of assessment if the satisfactory (threshold) grade for the overall course is not achieved at the first attempt. This is normally grade D3 for undergraduate students and grade C3 for postgraduate students. Exceptionally it may not be possible to offer reassessment of some coursework items, in which case the mark achieved at the first attempt will be counted towards the final course grade. Any such exceptions for this course are described below. 

The main aim of this course is to introduce students to the many important concepts in the mathematical study of fluids and to arm them with a range of techniques to study the wealth of interesting problems that
arise. Fluid dynamics has application in a huge range of disciplines, including the study of stars and aircraft to blood flow and swimming micro-organisms, and has led to the development of a large part of
applied mathematics. This course will present some preliminary ideas of fluid flow and go on to explore aspects of classical aerofoil theory, viscous fluid flow, including the analysis of boundary layers,
and water waves. Additionally, the course will aim to apply and develop the students' knowledge of complex analysis, differential equations and asymptotic methods to facilitate investigation of solution
behaviour.

By the end of this course students will be able to:

a) Define and calculate streamlines, particle paths and streaklines;
b) Define ideal fluids, vorticity, irrotational flows, and circulation, and use these concepts appropriately;
c) Derive Euler's equations, Bernoulii's streamline theorem and the vorticity equation and apply them to given problems;
d) Define the Reynolds number and employ the Navier-Stokes equations with appropriate boundary conditions to find solutions for simple problems, such as for an impulsively moved plane boundary, flow down an inclined plane, flow between two boundaries;
e) Apply complex potential methods to study problems in classical aerofoil theory;
f) Employ the method of images, conformal mapping, the Milne-Thompson circle theorem, Blasius's theorem, and the Kutta-Joukowski lift theorem to find solutions to the problems in e);
g) Establish governing equations for surface waves in a fluid of finite depth, define wave and group velocity,and determine the dispersion relation and particle paths;
h) Derive equations for high Reynolds number flow and the boundary layer approximation, and find appropriate similarity solutions.

Students must submit at least 75% by weight of the components (including examinations) of the course's summative assessment.