Undergraduate Programme and Module Handbook 2010-2011 (archived)

# Module MATH3101: CONTINUUM MECHANICS III

## Department: Mathematical Sciences

### MATH3101: CONTINUUM MECHANICS III

Type | Open | Level | 3 | Credits | 20 | Availability | Available in 2011/12 and alternate years thereafter | Module Cap | None. | Location | Durham |
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#### Prerequisites

- (Core Mathematics B2 (MATH1041) AND Analysis in Many Variables II (MATH2031) AND one extra 20 credit Level 2 mathematics module) OR (Analysis in Many Variables II (MATH2031) AND Core Mathematics B1 (if taken in Year 2) AND Core Mathematics B2 (if taken in Year 2)) OR (Fundamental Physics A (PHYS1111) AND Analysis in Many Variables II (MATH2031) AND one extra 20 credit Level 2 mathematics module) OR (Foundations of Physics I (PHYS1122) AND Analysis in Many Variables II (MATH2031) AND one extra 20 credit Level 2 mathematics module.)

#### Corequisites

- One 20 credit Level 3 mathematics module.

#### Excluded Combination of Modules

- Continum Mechanics IV (MATH4081).

#### Aims

- To introduce a mathematical description of fluid flow and other continuous media to familiarise students with the successful applications of mathematics in this area of modelling.
- to prepare students for future study of advanced topics.

#### Content

- Description of fluid flow, stream and streak-lines, vorticity, mass conservation and continuity equation.
- Review of tensors, stress and rate of strain.
- Equation of motion: Navier-Stokes equation.
- Euler equation.
- Equation of equilibrium for a static fluid: Archimedes' principle.
- Energy.
- Bernoulli's equation: irrotational flow.
- Flow of ideal and viscous fluids.
- Waves: linearised waves.
- Elastic media: stress-strain, equation of equilibrium, boundary conditions.
- Sample deformations and associated stresses.
- Waves in elastic media: S and P waves, polarisation, reflection and refraction at boundaries.

#### Learning Outcomes

Subject-specific Knowledge:

- By the end of the module students will: be able to solve novel and/or complex problems in Continuum Mechanics.
- have a systematic and coherent understanding of theoretical mathematics in the fields Continuum Mechanics.
- have acquired coherent body of knowledge of these subjects demonstrated through one or more of the following topic areas: Kinematics of fluid flows.
- Equations of motion and their derivation for fluids.

Subject-specific Skills:

- In addition students will have specialised mathematical skills in the following areas which can be used with minimal guidance: Modelling.
- They will be able to formulate and use mathematical models in various situations.

Key Skills:

#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

- Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
- Assignments for self-study develop problem-solving skills and enable students to test and develop their knowledge and understanding.
- Formatively assessed assignments provide practice in the application of logic and high level of rigour as well as feedback for the students and the lecturer on students' progress.
- The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

#### Teaching Methods and Learning Hours

Activity | Number | Frequency | Duration | Total/Hours | |
---|---|---|---|---|---|

Lectures | 40 | 2 per week for 19 weeks and 2 in term 3 | 1 Hour | 40 | |

Preparation and Reading | 160 | ||||

Total | 200 |

#### Summative Assessment

Component: Examination | Component Weighting: 100% | ||
---|---|---|---|

Element | Length / duration | Element Weighting | Resit Opportunity |

three hour written examination | 100% |

#### Formative Assessment:

Four written assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University