Unit name | Fluid Dynamics 3 |
---|---|

Unit code | MATH33200 |

Credit points | 20 |

Level of study | H/6 |

Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |

Unit director | Dr. Porter |

Open unit status | Not open |

Pre-requisites |
Year 2 Theoretical Physics. OR MATH11009 Mechanics 1 (or MATH10012 ODEs, Curves and Dynamics), MATH20901 Multivariable Calculus, MATH20001 Methods of Complex Functions, and MATH20402 Applied Partial Differential Equations 2 |

Co-requisites |
None |

School/department | School of Mathematics |

Faculty | Faculty of Science |

**Unit Aims**

The course aims to provides the student with the basic mathematical background and tools to model fluid motion and calculate the flow of an ideal fluid in a variety of situations. The course will develop a physical understanding of the important aspects that govern fluid flows that can be observed in a variety of situations in everyday life.

**Unit Description**

This unit introduces many of the fundamental aspects of fluid dynamics, developing the mathematical theory behind ideal (inviscid) fluid flows. The theory is applied to a variety of situations that allow the calculation of the fluid flow and its properties.

The unit demonstrates how mathematics can be used to model complex physical phenomena and illustrates how an applied mathematician uses and develops approximations which capture the essential features of realistic phenomena that are observable in the world around us. Examples include: the lift on an aircraft wing, motion of vortices in the atmosphere, bubbles rising in a liquid, liquid jets, and waves in a tank. Some demonstrations of various flows may be included if there is interest.

**Relation to Other Units**

The ideas of this unit are developed further in Advanced Fluid Dynamics.

After taking this unit, students should:

- be familiar with and able to manipulate the mathematics of a continuum model of fluid flow. This includes how to describe the kinematics of the motion, the notion of fluid pressure and the equations expressing the conservation of mass and momentum within the flow.
- be able to solve a variety of fundamental fluid flow problems using a variety of techniques introduced during the course. These include the theory of flow hydraulics and surface water waves as well as applications of potential theory and some complex-variable techniques.
- be aware of the wide range of applications of fluid mechanics to many practical situations in industry and the environment.
- appreciate how a specific flow fits into the wider context of a physical problem.

Transferable Skills

The student will learn some of the skills involved in mathematical modelling: namely, transforming a real physical problem into a mathematically tractable form and then being able to interpret and communicate the results of the calculation. The unit will also develop and give practice of various analytical and problem-solving techniques.

The unit will be taught through a combination of

- synchronous online and, if subsequently possible, face-to-face lectures
- asynchronous online materials, including narrated presentations and worked examples
- guided asynchronous independent activities such as problem sheets and/or other exercises
- synchronous weekly group problem/example classes, workshops and/or tutorials
- synchronous weekly group tutorials
- synchronous weekly office hours

90% Examination 10% Coursework

Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.

If you fail this unit and are required to resit, reassessment is by a written examination in the August/September Resit and Supplementary exam period.

**Recommended**

- D.J. Acheson,
*Elementary Fluid Dynamics*, Oxford University Press, 1990 - G.K. Batchelor,
*An Introduction to Fluid Dynamics*, Cambridge University Press, 1967 - A.R. Paterson,
*A First Course in Fluid Dynamics*, Cambridge University Press, 1983