Paper B3: Physics of Fluid Flows

Synopsis and Reading List, Hilary Term 2010

Professor Peter Read

Fluid dynamics underlies a wide range of physical phenomena in the "real world" on macroscopic scales, with applications for example in engineering, biology, the environmental sciences, geophysics and astrophysics. This course will introduce the study of the macroscopic physics of fluid flows. The topics covered will illustrate a variety of aspects of modern fluid dynamics.

Lecture Synopsis

The course will cover the following topics (The breakdown, lecture by lecture, is approximate. There will be 10 lectures in all, and these will include demonstrations of fluid phenomena, recapitulation of material, and some worked examples.)

Lectures 1, 2. Introduction: Examples of fluid flows in physics, geophysics, aerodynamics, engineering and biology. Fluids as continua. Newton's Second Law for a small element of fluid, leading to the Navier-Stokes equation. Lagrangian and Eulerian viewpoints. Equation for mass conservation.

Lectures 3, 4. Some simple models of fluid flows: Exact solutions of the equations of motion: Poiseuille flow in a pipe, Reynolds's experiment, the Reynolds number; Couette flow between rotating cylinders. Vorticity and its physical interpretation.

Lectures 5, 6. Inviscid flows without vorticity: Electrostatics analogy, applications to aircraft flight. Surface water waves; phase and group velocity; nonlinear waves: the Korteweg-de Vries equation, solitons.

Lecture 7. Very viscous flows: Stokes's Law for the drag on a sphere.

Lectures 8, 9. Rotating flows: rotating reference frames; Taylor-Proudman Theorem; Ekman boundary layers.

Reading list

D J Tritton, Physical Fluid Dynamics, 2nd edition (C.U.P.)

T E Faber, Fluid Dynamics for Physicists (C.U.P.)

D J Acheson, Elementary Fluid Dynamics (O.U.P.)

B Massey and J Ward-Smith, Mechanics of Fluids (Stanley Thornes)

J Lighthill, Waves in Fluids (C.U.P.)

M Van Dyke, An Album of Fluid Motion (Parabolic Press)

For introductory reading: The Feynman Lectures, Vol. II, Sections 40, 41 (Addison Wesley)

.................

For more advanced background: E Guyon, J-P Hulin, L Petit, C D Mitescu, Physical Hydrodynamics (O.U.P.)

Some more nice pictures: M Samimy, K S Breuer, L G Leal and P H Steen, A Gallery of Fluid Motion (C.U.P.)

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Problem set

Download from here (pdf format) - NB UPDATED AND CORRECTED 10 FEB 2009.

Lecture handouts

Set 1 (pdf format).

Set 2 (pdf format).

Set 3 (pdf format).

Set 4 (pdf format).

Set 5 (pdf format).

Set 6 (pdf format).

Set 7 (pdf format).

Additional notes on vortex lines and vortex tubes (pdf format).

Three old exam questions that were given as worked examples (pdf format).

More sample exam questions

There are now several years (2004-08) of Finals questions on this course. For students wanting additional practice, the following exam questions from the former 'Physics of Fluid Flows' Minor Option are fairly close to the topics covered by this course, and may be useful. (However, they are slightly longer - worth 25 marks rather than 20 - than those that are likely to appear in the B3 paper.)

1996: E1,E2, E3; 1997: E1, E2, E3; 1998: E1, E2, E3; 1999: E1, E2, E3; 2000: E1, E2, E3, E4; 2001: E1, E2, E3, E4; 2002: E1, E3; 2003: E1, E3.

To download these papers, go to this link, and click the relevant year under `Final Honour School part B (Old Course)'.

Some links on Fluid Flows

Gallery of Fluid Motion (American Institute of Physics)

Gallery of Fluid Mechanics (Mark Cramer)

Tsunami website, University of Washington

Volcano Video Movie Clips

The Dynamics of Rotating Fluids, AOPP, Oxford University

Atmosphere and Ocean in a Laboratory, Kyoto University

Geophysical Fluid Dynamics Laboratory, School of Oceanography, University of Washington

Geophysical Fluid Dynamics Laboratory, University of Colorado

The Severn Bore

Tornado movies from Stormchase.us

G. I. Taylor

More on G. I. Taylor

The swing of a cricket ball

The physics of football

Aerodynamics in Sports Equipment

Irrotational Flow of an Inviscid Fluid: a nice treatment, with excellent visualisations, leading up to a discussion of flow round aerofoils.

Applications of the Magnus effect: Introduction by a Japanese company to possible applications of rotating devices, based on the Magnus effect, to various engineering problems.

Wind turbine using the Magnus effect (1): Movie of a prototype device for wind power generation.

Wind turbine using the Magnus effect (2): Another movie of a prototype device for wind power generation.

A kite using the Magnus effect

Model of Anton Flettner's rotor ship: A model demonstration of the ship designed by Anton Flettner in the 1920s that used rotating cylinders as sails!

Jacques Cousteau's catamaran, based on Flettner's design of a rotor ship

Simulation of motion of point vortices: a Java applet by Brian Tvedt.

Another simulation of motion of (editable) sets of point vortices: a Java applet courtesy of James Montaldi (Manchester University).

"How do Wings Work?", by Holger Babinsky: uses careful physical arguments and points out common misconceptions!

--> Solitons Home Page (Heriot-Watt University)


Link to Undergraduate Studies in AOPP


Last update: 16 March 2010