Undergraduate Course: Fluid Dynamics (MATH11248)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 11 (Year 5 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | The course will introduce the mathematical theory of fluid dynamics, including relevant physical quantities (e.g. velocity, vorticity, density, pressure, stress, viscosity), conservation laws (e.g., energy, helicity, circulation), and various mathematical representations (e.g., Eulerian vs Lagrangian). The course will discuss methods for obtaining solutions to the nonlinear fluid equations and apply those solutions to several applied problems (e.g., laminar vs turbulent flow, waves and instabilities). |
| Course description |
Kinematics: continuum model, paths & material surfaces, advective derivatives, kinematic boundary conditions, mass conservation &incompressibility.
Dynamics: momentum (Euler's) equation, hydrostatic balance, Bernoulli's Theorem, Kelvin's Circulation Theorem.
Inviscid-flow applications include (e.g.): irrotational potential flow, conformal maps, point & sheet vortex dynamics.
Viscous-flow applications include (e.g.): laminar stokes flow, boundary layers, turbulence & energy cascades.
Possible additional topics: waves, instabilities and bubbles.
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Information for Visiting Students
| Pre-requisites | This is a Year 4/5 advanced, Honours level course. Visiting students are expected to have an academic profile equivalent to at least the first three years of the BSc (Hons) Mathematics programme (UTMATHB), and should be confident that their background has equipped them to undertake a course at this level. Students should have passed courses equivalent to Honours Differential Equations (MATH10066) or Dynamics and Vector Calculus (PHYS08043); and Computing and Numerics (MATH08065) or Programming and Data Analysis (PHYS08049). |
| High Demand Course? |
Yes |
Course Delivery Information
|
| Academic year 2025/26, Available to all students (SV1)
|
Quota: None |
| Course Start |
Semester 1 |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
100
(
Lecture Hours 22,
Seminar/Tutorial Hours 10,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
64 )
|
| Assessment (Further Info) |
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %
|
| Additional Information (Assessment) |
Coursework : 20%
Examination : 80% |
| Feedback |
Not entered |
| Exam Information |
| Exam Diet |
Paper Name |
Minutes |
|
| Main Exam Diet S1 (December) | MATH11248 Fluid Dynamics | 120 | |
Learning Outcomes
On completion of this course, the student will be able to:
- state and work with the equations governing the motion of an incompressible, inviscid fluid.
- define and work with fluid velocity, vorticity and pressure both mathematically and heuristically.
- present and solve incompressible and non-vortical flow equations using potential theory.
- explain the physical source of viscosity and describe and solve simple viscous flow problems.
|
Reading List
Batchelor, An introduction to fluid dynamics, Cambridge university press, 2000.
Kundu, Cohen & Dowling, Fluid Mechanics, Elsevier 2016.
Landau & Lifshitz, Fluid Mechanics -- Course of Theoretical Physics, Volume 6. Vol. 6. Elsevier, 2013. |
Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | FDy |
Contacts
| Course organiser | Dr Geoff Vasil
Tel: (0131 6)50 4899
Email: gvasil@ed.ac.uk |
Course secretary | Mr Martin Delaney
Tel: (0131 6)50 6427
Email: Martin.Delaney@ed.ac.uk |
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