In this chapter, we explore the basics of fluid mechanics. We will think about how to describe fluids and look at the kinds of things they can do.

Unusually, and a little defensively, the title of this chapter highlights what we won’t talk about, rather than what we will. Fluids have a property known as viscosity. This is an internal friction force acting within the fluid as diferent layers rub together. It is crucially important in many applications. In spite of its importance, we will start our journey into the world of fluids by ignoring viscosity altogether. Such flows are called inviscid. This will allow us to build intuition for the equations of fluid mechanics without the complications that viscosity brings. Moreover, the flows that we find in this section will not be wasted work. As we will see later, they give a good approximation to viscous flows in certain regimes where the more general equations reduce to those studied here.

The motion of fluids is a complex area of physics because of the non-linearity of their equations of motion. As an introduction to the field, a selection of important results in the motions of fluids and gases, illustrating the richness and complexity of the subject as well as the often non-intuitive features of fluid flow, are presented.The topics include Bernoulli’s equations, gravity waves in shallow and deep water, viscous flow, Stokes’ formula for viscous flow past a spherical body, vorticity and Kelvin’s circulation theorem. The emphasis is upon the physics of the problems, rather than the mathematical complexities involved.