Department of Applied Mathematics and Theoretical Physics
Fluid Dynamics 1B

Lecturer: Prof Natalia Berloff
Office: CMS G1.02
Lecture: Mill Lane Lecture Room 3, Tue., Thu 11
Class web page:

Fluid dynamics investigates the flow of liquids and gases. Non-sticky fluids are the subject of this course, for which the basic equation is the Euler equation, which repesents the law expressing `force equals rate of change of momentum'. A subtlety arises because the rate of change here applies to that following fluid particles, not at a fixed point in space. It is necessary to use the convective derivative: a time derivative following the fluid. The forces driving the motion can be external, such as gravity, or internal, arising from pressure. The fluid motion is often incompressible and irrotational, in which case the flow can be expressed in terms of potentials and the motion is governed by Laplace's equation. The suitations investigated in this course include simple flows in channels, jets, sources and sinks, bubbles, waves and aircraft wings. Suitable introductory reading material can be found in Lighthill's "An Informal Introduction to Theoretical Fluid Mechanics" (Oxford) or Acheson's "Elementary Fluid Dynamics" (Oxford).

Learning outcomes

By the end of this course, you should:

  • understand the basic principles governing the dynamics of parallel viscous flows and flows in which viscosity in negligible;
  • be able to derive and deduce the consequences of the equation of conservation of mass;
  • be able solve kinematics problems such as finding particle paths and streamlines;
  • be able to apply Bernoulli's theorem and the momentum integral to simple problems including river flows;
  • understand the concept of vorticity and the conditions in which it may be assumed to be zero;
  • calculate velocity fields and forces on bodies for simple steady and unsteady flows derived from potentials;
  • understand the theory of surface and interfacial waves and be able to use it to investigate, for example, standing waves in a container;
  • understand fundamental ideas relating to flows in rotating frames of reference, particularly geostrophy.

Professor McIntyre's Lecture Notes

Excellent set of notes from Professor McIntyre. Does not contain parallel viscous flow and geostrophycal flows.

Class Handouts

Example Sheets

Some interesting (and educational) links

History of Fluid Mechanics

Online Journals