Undergraduate Programme and Module Handbook 2010-2011 (archived)

# Module MATH4081: CONTINUUM MECHANICS IV

## Department: Mathematical Sciences

### MATH4081: CONTINUUM MECHANICS IV

Type | Open | Level | 4 | 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) OR Fundamental Physics A (PHYS1111) OR Foundations of Physics I (PHYS1122)) AND mathematics modules to the value of 100 credits in Years 2 and 3, with at least 40 credits at Level 3, and including Analysis in Many Variables II (MATH2031).

#### Corequisites

- None.

#### Excluded Combination of Modules

- Continuum Mechanics III (MATH3101).

#### 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.
- Reading material on a topic related to: hydrodynamic stability, turbulence.

#### Learning Outcomes

Subject-specific Knowledge:

- By the end of the module students will: be able to solve complex, unpredictable and specialised problems in Continuum Mechanics.
- have an understanding of specialised and complex theoretical mathematics in the field of Continuum Mechanics.
- have mastered a 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.
- have an advanced understanding in one of the following areas: hydrodynamic stability, turbulence.

Subject-specific Skills:

- In addition students will have highly specialised and advanced mathematical skills in the following areas: Modelling.
- They will be able to formulate and use mathematical models in various situations.

Key Skills:

- Students will be able to study independently to further their knowledge of an advanced topic.

#### 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 complex and specialised problems.

#### Teaching Methods and Learning Hours

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

Lectures | 40 | 2 per week | 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 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