## MA3FM-Fluid Mechanics

Module Provider: Mathematics and Statistics
Number of credits: 10 [5 ECTS credits]
Level:6
Terms in which taught: Autumn term module
Pre-requisites: MA2DE Differential Equations
Non-modular pre-requisites:
Co-requisites:
Modules excluded: MA4FM Fluid Mechanics
Current from: 2020/1

Module Convenor: Dr Alex Lukyanov

Type of module:

Summary module description:
The objective of this course is to provide an elementary, but rigorous mathematical presentation of continuum description, to introduce concepts and basic principles of fluid mechanics.

Aims:
The objective of this course is to provide an elementary, but rigorous mathematical presentation of continuum description, to introduce concepts and basic principles of fluid mechanics. In particular, the aim is to introduce tensors and elements of tensor algebra, governing equations and their application to modelling and solution of representative fluid mechanical problems relevant to industry and environment, to show various mathematical approaches and assumptions commonly used in the analysis of liquid flows. The module has been developed for students who have little or no experience in fluid mechanics.

Assessable learning outcomes:
By the end of the module students are expected to be able to:
- Use tensor notations and basic techniques of tensor algebra
- Formulate fluid mechanical problems with appropriate set of boundary conditions.
- Use different mathematical techniques to analyse representative fluid mechanical problems relevant to applications in industry and environment studies.

Outline content:
The principles of fluid mechanics are at the heart of numerous natural processes and technological applications ranging from new tools used in emerging technologies, such as micro and nano-fluidics, used in pharmacy, to biological and medical applications of fluid dynamics, modelling of aircraft dynamics and climate research.

The behaviour of a fluid mechanical system is governed, in general, by a set of partial differential equations, the Navier-Stokes equations. In practice, thi s set of differential equations has to be augmented with boundary conditions in order to obtain unique solutions to particular fluid mechanical problems. The mathematical theory of fluid motion provides techniques for formulating and analysing such problems. Simple examples of such systems are liquid flows in channels, river flows, and flows past solid bodies, such as aircraft wings, vortex motion in the atmosphere. Other applications arise in a wide range of subjects, including biology, microfl uidics and aerospace engineering. In this course, the emphasis will be on the systems with simplified geometry and/or that can be modelled by a simplified set of differential equations. During the course, we consider rigorous mathematical foundation of fluid mechanics and then turn our attention to some well-known practical problems.

Content:
1. Tensors, tensor calculus and applications
2. The Reynolds Transport Theorem, the Navier-Stokes equations and admissible set o f boundary conditions
3. Static problems, inviscid flows, potential theory, stagnation-point flow, basic two-dimensional potential flows, irrotational flows and origin of lift
4. Scaling analysis, boundary layers, viscous flows
5. Shallow water approximation and water waves

Brief description of teaching and learning methods:
Lectures supported by problem sheets and lecture-based tutorials.

Contact hours:
 Autumn Spring Summer Lectures 20 Tutorials 6 Guided independent study: 74 Total hours by term 0 0 Total hours for module 100

Summative Assessment Methods:
 Method Percentage Written exam 90 Written assignment including essay 10

Summative assessment- Examinations:
Two hours.

Summative assessment- Coursework and in-class tests:
One examination paper and one assignment.

Formative assessment methods:
Problem sheets.

Penalties for late submission:

The Module Convenor will apply the following penalties for work submitted late:

• where the piece of work is submitted after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for that piece of work will be deducted from the mark for each working day[1] (or part thereof) following the deadline up to a total of five working days;
• where the piece of work is submitted more than five working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.
The University policy statement on penalties for late submission can be found at: http://www.reading.ac.uk/web/FILES/qualitysupport/penaltiesforlatesubmission.pdf
You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Assessment requirements for a pass:
A mark of 40% overall.

Reassessment arrangements:
One examination paper of 2 hours duration in August/September - the resit module mark will be the higher of the exam mark (100% exam) and the exam mark plus previous coursework marks (90% exam, 10% coursework).