MA0332: Fluid Dynamics

School Cardiff School of Mathematics
Department Code MATHS
Module Code MA0332
External Subject Code G100
Number of Credits 10
Level L6
Language of Delivery English
Module Leader Dr David Binding
Semester Spring Semester
Academic Year 2014/5

Outline Description of Module

A lecture based module which develops classical applied mathematical material introduced in Level Two modules and in Autumn Semester Level Three modules.

Prerequisite Modules: MA0235 Elementary Fluid Dynamics, MA2301 Vector Calculus

On completion of the module a student should be able to

  • understand the theory behind the Navier-Stokes equations and apply it to simple flow situations.;
  • apply appropriate approximations in order to simplify the governing equations and  gain insight to complex flows such as those encountered in lubrication and boundary layers;
  • appreciate the role of hydrodynamics within the area of continuum mechanics and thus understand dispersive waves

How the module will be delivered

27 - 50 minute lectures

Students are also expected to undertake at least 50 hours private study including preparation of solutions to given exercises.

Skills that will be practised and developed

Students will gain insight into the mathematical modelling of physical and industrial processes. In particular they will see how to link specific elements of a mathematical development with a corresponding physical process and thereby justify appropriate approximations. Likewise, they will gain experience at analysing mathematical solutions in terms of the physical responses that are predicted. 
 
The need to describe processes and procedures and interpret results will enhance communication skills.

How the module will be assessed

Formative assessment is carried out by means of regular tutorial exercises.  Feedback to students on their solutions and their progress towards learning outcomes is provided during lectures.  

The summative assessment is the written examination at the end of the module.  This gives students the opportunity to demonstrate their overall achievement of learning outcomes.  It also allows them to give evidence of the higher levels of knowledge and understanding required for above average marks.

The examination paper has a choice of three from four equally weighted questions.

Assessment Breakdown

Type % Title Duration(hrs)
Exam - Spring Semester 100 Fluid Dynamics 2

Syllabus content

  • Resumé of vector calculus and curvilinear coordinates
  • Tensor analysis
  • Fundamentals of Continuum Mechanics
    • Kinematics
    • Conservation of mass.
    • Forces acting on a body.
    • Definition of the stress tensor.
    • Symmetry of the stress tensor.
    • Equations of motion.
    • Motion of a material element.
  • Viscous Flow
    • Newtonian fluids.
    • Derivation of the Navier-Stokes equations.
    • Conservation of energy
    • Boundary conditions.
    • Some exact solutions: Flows in infinite channels, Rectilinear flow in pipes
    • Approximate solutions: Non-dimensionalisation, Reynold’s number, Dynamic similarity, Boundary layer theory, Lubrication theory
  • An introduction to Wave theory

Essential Reading and Resource List

Theoretical Hydrodynamics, Milne-Thomson, L. M., Macmillan

Background Reading and Resource List

Not applicable.

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