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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: 2019-20

• None

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## Module will run

Occurrence Teaching cycle
A Autumn Term 2019-20

## 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
Online Exam
Fundamentals of Fluid Dynamics
2 hours 100

None

### Reassessment

Task Length % of module mark
Online Exam
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.