2005/06 Undergraduate Module Catalogue

MATH3512 Viscous Flow

15 creditsClass Size: 100

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2005/06

Pre-requisites

MATH2620 and (MATH3501 or MATH3502) or equivalent.

This module is approved as an Elective

Objectives

The aim of the module is to consider two-dimensional viscous flow in order to provide an understanding of the way viscous fluids behave and insight into how problems of fluid mechanics should be tackled. Both steady and unsteady flows will be considered in pipes, channels and past bodies of various shape. Topics will be illustrated with a range of interesting applications. On completion of this module, students should be able to: a) use control volumes to set up and solve the governing equations for Poiseuille flow, Couette flow and gravity flow down an incline; b) solve steady and unsteady problems for unidirectional viscous flows in channels; c) understand the significance of the Reynolds number in viscous flow; d) solve simple lubrication problems; derive some exact solutions of the Navier-Stokes equations; e) derive the steady boundary layer equations; f) solve for the steady flow of a uniform stream with a pressure gradient over a surface.

Syllabus

The aim of the module is to consider two-dimensional viscous flows in order to provide an understanding of the way fluids behave and gain insight into how problems of fluid dynamics should be tackled. Both steady and unsteady flows will be considered in channels and past bodies of various shape. Small Reynolds Number flows and boundary layer theory (high Reynolds Number flows) will be presented along with their applications. The topics covered are: Introduction to Fluid Mechanics and its applications. Stress; Newton?s law of viscosity. Poiseuille, Couette and gravity flow down an incline via control volumes. Navier-Stokes equations for a viscous incompressible Newtonian fluid. Continuity equation and boundary conditions. Applications to steady and unsteady unidirectional flows in channels. Other exact solutions of the Navier-Stokes equations. Dynamical similarity and the Reynolds number. Low Reynolds flow. Steady flow past bodies at all values at high Reynolds number, flow separation (descriptive). High Reynolds number steady flow. Boundary layer theory.

Teaching methods

Lectures: 25 hours. 5 example classes.

Methods of assessment

One 3 hour examination at end of semester (100%).

Reading list

The reading list is available from the Library website

Last updated: 13/05/2005

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