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## MTH3007 - Fluid Dynamics (2019)

MODULE TITLE | Fluid Dynamics | CREDIT VALUE | 15 |
---|---|---|---|

MODULE CODE | MTH3007 | MODULE CONVENER | Dr Joanne Mason (Coordinator) |

DURATION: TERM | 1 | 2 | 3 |
---|---|---|---|

DURATION: WEEKS | 11 weeks | 0 | 0 |

Number of Students Taking Module (anticipated) | 152 |
---|

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.

Prerequisite module: MTH2004 Vector Calculus & Applications, or equivalent

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.

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

**M****odule 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.

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 un fluids:

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

- surface gravity waves;

- phase velocity and group velocity.

Scheduled Learning & Teaching Activities | 33.00 | Guided Independent Study | 117.00 | Placement / Study Abroad | 0.00 |
---|

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 |

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. |

Coursework | 20 | Written Exams | 80 | Practical Exams | 0 |
---|

Form of Assessment | % of Credit | Size of Assessment (e.g. duration/length) | ILOs Assessed | Feedback Method |
---|---|---|---|---|

Coursework – based on questions submitted for assessment | 20 | 2 assignments, 30 hours total | All | Annotated script and written/verbal feedback |

Written Exam – closed book | 80 | 2 hours | All | Written/verbal on request, SRS |

Original Form of Assessment | Form of Re-assessment | ILOs Re-assessed | Time Scale for Re-reassessment |
---|---|---|---|

All above | Written Exam (100%) | All | August Ref/Def Period |

Referred and deferred assessment will be by examination. For referrals, only the examination will count, a mark of 40% being awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original coursework mark.

information that you are expected to consult. Further guidance will be provided by the Module Convener

Reading list for this module:

Type | Author | Title | Edition | Publisher | Year | ISBN | Search |
---|---|---|---|---|---|---|---|

Set | Acheson, D.J. | Elementary Fluid Dynamics | Clarendon Press | 1990 | 978-0-198-59679-0 | [Library] | |

Set | Tritton D.J. | Physical Fluid Dynamics | 2nd | Clarendon Press, Oxford | 1988 | 000-0-198-54493-6 | [Library] |

Set | Batchelor G.K. | An Introduction to Fluid Dynamics | Cambridge University Press | 1999 | 000-0-521-04118-X | [Library] | |

Set | Worster, M G | Understanding Fluid Flow | Cambridge University Press | 2009 | 978-0521132893 | [Library] | |

Set | Childress, S | An Introduction to Theoretical Fluid Mechanics | American Mathematical Society | 2009 | 978-0821848883 | [Library] |

CREDIT VALUE | 15 | ECTS VALUE | 7.5 |
---|---|---|---|

PRE-REQUISITE MODULES | MTH2004 |
---|---|

CO-REQUISITE MODULES |

NQF LEVEL (FHEQ) | 6 | AVAILABLE AS DISTANCE LEARNING | No |
---|---|---|---|

ORIGIN DATE | Tuesday 10 July 2018 | LAST REVISION DATE | Friday 30 August 2019 |

KEY WORDS SEARCH | Fluid flow; pressure; viscosity; vorticity; boundary layer theory; applications of vector calculus. |
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