Viscous flow

Web address:

Class times

Monday 4,5, weeks 3-8 (Sam Howison) in DH seminar room.
Tuesday 10, weeks 3-8 (John Coats)


  1. Material derivative, transport theorem, mass conservation, incompressibility.
  2. Vectors, tensors, summation convention. Stress tensor, rate of strain tensor.
  3. The general linear, isotropic viscous fluid. Navier-Stokes equation.
  4. Boundary conditions. Exact solutions: plane Poiseuille, Hagen-Poiseuille, Stokes, Taylor-Couette flows.
  5. Jeffery-Hamel flow.
  6. The energy equation.
  7. Dimensional analysis, Reynolds number.
  8. Stream function, vorticity, high Reynolds number flow. Prandtl-Batchelor theorem.
  9. Thermal and viscous boundary layers. Prandtl's boundary layer equations.
  10. Blasius flow, similarity solutions. Separation.
  11. Wakes, theory of flight.
  12. Instability and turbulence.
  13. Slow flow, Stokes equations.
  14. Oseen approximation.
  15. Lubrication theory, slider bearing and squeeze film.
  16. Glaciers and ice sheets.


Further reading

Course materials

These can be downloaded as postscript or pdf files.