	Department of Mathematics & Computer Science

Next: MA2061 Lagrangian and Hamiltonian Dynamics Up: Level 2 Previous: MA2001 Vector Calculus

MA2051 Fluids and Waves

MA2051(=MC227) Fluids and Waves

Credits: 10

Convenor: Dr. M. D. Dampier

Semester: 2

Prerequisites:	essential: MA1051(=MC123), MA2001(=MC224)
Assessment:	Regular coursework: 20%	One and a half hour exam: 80%

Lectures:	18	Problem Classes:	5
Tutorials:	none	Private Study:	52
Labs:	none	Seminars:	none
Project:	none	Other:	none
Surgeries:	none	Total:	75

Course Description

This course develops the ideas of mechanics to a continuous medium using the mathematical tools learnt in the module Vector Analysis, MA2001.

Aims

The course aims to provide a mathematical introduction to the mechanics of inviscid fluids, and to apply the theory to wave phenomena. Waves in other media may also be considered.

Objectives

To understand how to describe fluid flow. To understand the role of contact forces, and to learn how to use the concept of pressure. To be able to use the basic equations of inviscid fluid dynamics in a variety of simple situations. To understand the basic concepts of wave motion - wave equation, frequency, wavelength.

Syllabus

1. Fluids, density, velocity field, conservation of mass.
2. Pressure, material derivative, Euler's equation.
3. Hydrostatics, liquids and gases, atmospheric equilibrium.
4. Steady flow, streamlines, Bernoulli's equation.
5. Streams of constant breadth.
6.Vorticity, irrotational motion.
7.Compressible flow, sound waves.
8.Other examples of wave motion.

Transferable Skills

Ability to apply the laws of classical dynamics to model a class of physical phenomena. Problem solving skills using mathematical tools.

Reading list

Details of Assessment

The final assessment of this module will consist of 20% coursework and 80% from a one and a half hour examination during the January exam period. The 20% coursework contribution will be determined by students' solutions to coursework problems. The examination paper will contain 4 questions with full marks on the paper obtainable from 3 complete answers.