Undergraduate Programme and Module Handbook 2026-2027
Module MATH3101: Fluid Mechanics III
Department: Mathematical Sciences
MATH3101: Fluid Mechanics III
| Type | Open | Level | 3 | Credits | 20 | Availability | Available in 2026/2027 | Module Cap | Location | Durham |
|---|
Prerequisites
- Mathematical Methods II (MATH2811) OR Mathematical Methods in Physics (PHYS2611) OR Analysis in Many Variables II (MATH2031).
Corequisites
- None.
Excluded Combination of Modules
- None.
Aims
- To introduce the 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
- Kinematics: Eulerian and Lagrangian pictures, velocity field, streamlines and stream functions.
- Compressibility, vorticity and circulation, integrals over material domains.
- Dynamics of ideal fluids: derivation of the incompressible Euler equations, energy, vorticity dynamics, circulation and rotating frames.
- Water waves: free-surface boundaries, linearisation, travelling and standing waves.
- Compressible flow: barotropic fluids, sound waves, nonlinearity.
- Hydrodynamic stability: normal mode analysis, Rayleigh-Taylor and Kelvin-Helmholtz instabilities.
- Dynamics of viscous fluids: Newtonian fluids, derivation of the Navier-Stokes equations, exact solutions, dynamical similarity, boundary layers.
Learning Outcomes
Subject-specific Knowledge:
- Fundamental concepts in the kinematics of fluids.
- Derivation of equations of motion for both ideal and viscous fluids, including incompressible and compressible flows.
- Behaviour of ideal and viscous fluids, including conservation laws, dynamical similarity and boundary layers.
- Water waves and free surface boundaries, and sound waves.
- Basic concepts in hydrodynamic stability including normal mode analysis and common instabilities.
Subject-specific Skills:
- Be able to solve novel and/or complex problems in Fluid Mechanics.
- Demonstrate an understanding of theoretical mathematics relevant to Fluid Mechanics and the ability to apply it appropriately.
Key Skills:
- Basic mathematical skills in the following areas: problem solving, modelling, computation.
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.
- Problem classes show how to solve example problems in an ideal way, revealing also the thought processes behind such solutions.
- Assignments for self-study develop problem-solving skills and enable students to test and develop their knowledge and understanding.
- Formatively and summatively assessed assignments provide practice in the application of logic and a high level of rigour as well as feedback for the students and the lecturer on the 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 | Attendance Monitored |
|---|---|---|---|---|---|
| Lectures | 40 | 2 per week for 20 weeks | 1 Hour | 40 | |
| Problem Classes | 10 | 4 in Michaelmas; 4 in Epiphany; 2 in Easter | 1 Hour | 10 | Yes ■ |
| Preparation and Reading | 150 | ||||
| Total | 200 |
Summative Assessment
| Component: Examination | Component Weighting: 70% | ||
|---|---|---|---|
| Element | Length / duration | Element Weighting | Resit Opportunity |
| On Campus Written Examination | 2 hours | 100% | |
| Component: Summative Assignments | Component Weighting: 30% | ||
| Element | Length / duration | Element Weighting | Resit Opportunity |
| Assignment | 100% | ||
Formative Assessment:
Four assignments to be submitted.
■ Students who do not attend monitored activities shown under Teaching Methods and Learning Hours, or who fail to complete the summative or formative assessment(s) specified above, may be subject to the Academic Progress procedures defined in the University's General Regulation V, and may be required to leave the University.