Fundamentals of Fluid Dynamics - MAT00012H

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  • Department: Mathematics
  • Credit value: 10 credits
  • Credit level: H
  • Academic year of delivery: 2022-23

Related modules

Pre-requisite modules

Co-requisite modules

  • None

Prohibited combinations


Additional information

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.

Module will run

Occurrence Teaching period
A Autumn Term 2022-23

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

 

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 and graduate skills

  • 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.

Indicative assessment

Task % of module mark
Closed/in-person Exam (Centrally scheduled) 100

Special assessment rules

None

Indicative reassessment

Task % of module mark
Closed/in-person Exam (Centrally scheduled) 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.

Indicative reading

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.