# Unit information: Fluid Dynamics 3 in 2015/16

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Unit name Fluid Dynamics 3 MATH33200 20 H/6 Teaching Block 1 (weeks 1 - 12) Professor. Eggers Not open Knowledge of vector calculus and complex functions covered in the second year unit MATH 20900 Calculus 2; also MATH 20402 Applied Partial Differential Equations 2 and first year MATH 11009 Mechanics 1 . MATH33000 is useful but not essential School of Mathematics Faculty of Science

## Description including Unit Aims

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.

General Description of the Unit

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 a aircraft wing, the flow down a bathtub plughole, bubbles rising in a liquid, hydraulic jumps and bores in a fluid flowing within a channel. Some demonstrations of various flows are included.

Relation to Other Units

The ideas of this unit are developed further in the Level 7 unit Advanced Fluid Dynamics.

Further information is available on the School of Mathematics website: http://www.maths.bris.ac.uk/study/undergrad/

## Intended Learning Outcomes

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.
• be able to appreciate how to model other physical systems.

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.

## Teaching Information

Lectures including illustrations and some demonstrations of fluid flows. Worksheets and examples classes follow up some applications of the material covered in the lectures. Regular homework assignments are set and marked.

## Assessment Information

100% Examination

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.