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# Fundamentals of Fluid Dynamics - MAT00012H

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• Department: Mathematics
• Module co-ordinator: Dr. Mitya Pushkin
• Credit value: 10 credits
• Credit level: H
• Academic year of delivery: 2018-19

• None

• None

## Module will run

Occurrence Teaching cycle
A Autumn Term 2018-19

## Module aims

To introduce students to fundamental notions of continuous mechanics and fluid dynamics

## Module learning outcomes

• Analyse characteristics of a particular flow

• Formulate the governing equations and boundary conditions

• Solve these equations analytically in simple cases

## Module content

[Pre-requisite modules: students must have taken Vector Calculus and one of Applied Mathematics MAT00034I, Applied Mathematics Option 2 MAT00037I or Applied Mathematics for Mathematics and Physics MAT00039I.]

Syllabus

• Brief review of elementary concepts of fluid mechanics: Continuous medium approximation and its applicability; the Lagrangian and Eulerian frameworks for a continuous medium. Inviscid flows. Pressure. The Euler equations.

• The transport theorems. Conservation of mass and momentum.

• Viscous flows and Newtonian fluids. The Navier-Stokes equations (statement).

• Boundary conditions.

• The Reynolds number (basic concept). Low and high Reynolds number flows. (Basic) notion of the boundary layer.

• Hydrostatics

• Elementary flows: uniform and shear flows, spherically symmetric and circular flows, point vortices, sources and sinks.

• Motion of a body in an inviscid fluid. Flow past a sphere moving in an infinite fluid. Cavitation. The drag force and the d’Alembert’s paradox.

• Kinetic energy of a potential inviscid flow of incompressible fluid. Forces on an accelerating body. The added mass.

• Elementary viscous flows. Plane parallel shear flow. Poiseuille flow. The flow due to an impulsively moved plane boundary. Diffusion of vorticity. Circular viscous flows.

• Drag force on a body in a fluid. The drag coefficient.

• Academic skills: The skills taught are used in many areas of applied mathematics and mathematical physics and are essential for modern applications of fluid dynamics.

• Graduate skills: students will develop their ability to assimilate, process and engage with new material quickly and efficiently. They will develop problem-solving skills and learn to analyse critically different approaches.

## Assessment

Task Length % of module mark
University - closed examination
Fundamentals of Fluid Dynamics
2 hours 100

None

### Reassessment

Task Length % of module mark
University - closed examination
Fundamentals of Fluid Dynamics
2 hours 100

## Module feedback

Current Department policy on feedback is available in the undergraduate student handbook. Coursework and examinations will be marked and returned in accordance with this policy.

D J Acheson, Elementary Fluid Dynamics, Oxford University Press.

L M Milne-Thompson, Theoretical Hydrodynamics, Dover.

L D Landau and E M Lifshitz, Fluid Mechanics, Butterworth-Heinemann.

G K Batchelor, An Introduction to Fluid Dynamics, Cambridge University Press.

The information on this page is indicative of the module that is currently on offer. The University is constantly exploring ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.

## Coronavirus (COVID-19): changes to courses

The 2020/21 academic year will start in September. We aim to deliver as much face-to-face teaching as we can, supported by high quality online alternatives where we must.

Find details of the measures we're planning to protect our community.