Study information

# Fluid Dynamics - 2023 entry

MODULE TITLE CREDIT VALUE Fluid Dynamics 15 MTH3007 Dr Joanne Mason (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11 weeks 0 0
 Number of Students Taking Module (anticipated) 152
DESCRIPTION - summary of the module content

The aim of this module is to provide you with a further understanding of the basic concepts of fluid dynamics associated with flow of incompressible (constant density) fluids with both viscosity and inertia. You will learn to translate a physical problem into an appropriate mathematical system. Furthermore, you will learn about the many important applications of fluid dynamics in different branches of science and why solutions of fluid dynamics for many real physical problems cannot be obtained.

This module deals with the flow of incompressible fluids with both viscosity and inertia. The governing equations - the Navier-Stokes equations - admit an incredible variety of solutions, some of which will be presented. Topics covered will include some exact solutions of the NS equation in a variety of coordinate systems, together with similarity solutions and an introduction to boundary layer theory. This module leads on to a number of other modules in stages 3 and 4, for example MTHM019 Fluid Dynamics of Atmospheres and Oceans.

Prerequisite module: MTH2003 Differential Equations & MTH2004 Vector Calculus & Applications, or equivalent

AIMS - intentions of the module

This module is mainly concerned with the flow of viscous fluids, and it aims to provide you with a further understanding of the basic concepts of fluid dynamics associated with real fluids; to show you that there are many important applications of fluid dynamics in different branches of science and, at the same time, to show why solutions of fluid dynamics for many real physical problems cannot be obtained.

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

On successful completion of this module, you should be able to:

Module Specific Skills and Knowledge:

1 explain the basic concepts and equations of viscous fluid flow;

2 prove some key theorems and appreciate solutions of the Navier-Stokes equations in simple geometries.

Discipline Specific Skills and Knowledge:

3 translate a physical problem into an appropriate mathematical system;

4 interpret solutions of these equations in physical terms.

Personal and Key Transferable/ Employment Skills and  Knowledge:

5 demonstrate enhanced ability to formulate and analyse real physical problems using a variety of tools of applied mathematics.

SYLLABUS PLAN - summary of the structure and academic content of the module

1. Fundamentals and basic examples: introduction to module:

- introduction to Navier-Stokes equation, continuity equation, density, mass flux;

- plane Poiseuille and plane Couette flow;

- cylindrical polars, Poiseuille and Couette flow;

- derivation I: Navier-Stokes equation, acceleration, continuity equation;

- derivation II: pressure, strain, viscous stress.

2.  Similarity solutions:

- dimensional analysis;

- Rayleigh problem.

3.  Boundary layers:

- examples;

- boundary layer equation;

- Blasius boundary layer.

4. Sokes flow:

- Stokes equation;

- flow round cylinder and sphere;

- corner eddies;

- uniqueness of Stokes flow.

5. Vorticity and vortex dynamics:

- vorticity equation in 3-D and in 2-D;

- Helmholtz laws, Kelvin circulation theorem;

- vortex stretching;

- Burgers vortex;

6.  Introduction to waves in fluids:

- wave equation and wave parameters (wave number, wave length, wave vector, frequency);

- surface gravity waves;

- phase velocity and group velocity.

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
 Scheduled Learning & Teaching Activities Guided Independent Study Placement / Study Abroad 33 117 0
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
 Category Hours of study time Description Scheduled learning and teaching activities 33 Lectures Guided independent study 20 Coursework Guided independent study 97 Reading, revision, preparation

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Coursework - examples and exercises 10 hours/ 3 to 5 questions per problem sheet (5 sheets) 1-5 Comments on each script, general comments uploaded to ELE, solutions uploaded to ELE, individual feedback on request.

SUMMATIVE ASSESSMENT (% of credit)
 Coursework Written Exams Practical Exams 20 80 0
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Coursework 1 – based on questions submitted for assessment 10 15 hours  All Annotated script and written/verbal feedback
Coursework 2 - based on questions submitted for assessment 10 15 hours All Annotated script and written/verbal feedback
Written Exam – closed book 80 2 hours (Summer) All Written/verbal on request, SRS

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment Form of Re-assessment ILOs Re-assessed Time Scale for Re-reassessment
Written Exam* Written Exam (2 hours) (80%) All August Ref/Def Period
Coursework 1* Coursework 1 (10%) All August Ref/Def Period
Coursework 2* Coursework 2 (10%) All August Ref/Def Period

*Please refer to reassessment notes for details on deferral vs. Referral reassessment

RE-ASSESSMENT NOTES
Deferrals: Reassessment will be by coursework and/or written exam in the deferred element only. For deferred candidates, the module mark will be uncapped.

Referrals: Reassessment will be by a single written exam worth 100% of the module only. As it is a referral, the mark will be capped at 40%.
RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener

Type Author Title Edition Publisher Year ISBN
Set Acheson, D.J. Elementary Fluid Dynamics Clarendon Press 1990 978-0-198-59679-0
Set Batchelor G.K. An Introduction to Fluid Dynamics Cambridge University Press 1999 000-0-521-04118-X
Set Berkshire, Frank H., Malham, Simon J.A. and Stuart, J. Trevor Introductory incompressible fluid mechanics Cambridge University Press 2022 9781009084185
Set Childress, S An Introduction to Theoretical Fluid Mechanics American Mathematical Society 2009 978-0821848883
Set Tritton D.J. Physical Fluid Dynamics 2nd Clarendon Press, Oxford 1988 000-0-198-54493-6
Set Worster, M G Understanding Fluid Flow Cambridge University Press 2009 978-0521132893
CREDIT VALUE ECTS VALUE 15 7.5
PRE-REQUISITE MODULES MTH2004, MTH2003
NQF LEVEL (FHEQ) AVAILABLE AS DISTANCE LEARNING 6 No Tuesday 10th July 2018 Wednesday 22nd February 2023
KEY WORDS SEARCH Fluid flow; pressure; viscosity; vorticity; boundary layer theory; applications of vector calculus.