The refinement of some of the simple mechanics models obtained in Part A is to be undertaken in this chapter and the next. Thus, for example, in Chapter 2 the problem of free fall under gravity was considered. The medium through which the object moves was completely ignored and so was the size and shape of the falling object. In this chapter these features will be included and it will be seen that two new forces become relevant – the drag force and the buoyant force. These forces provide the mechanism for some phenomena not present in the model of Chapter 2: the decrease in acceleration of all free falling objects, and the ability of some objects such as balloons to rise rather than fall.

The differential equations obtained in this chapter are first-order linear with constant coefficients or first-order separable. Knowledge of Section 11.1 of Chapter 11 is therefore required.

Some basic fluid mechanics

As an object moves through a fluid, a force is exerted by the fluid on the object which is in the opposite direction to the motion of the object. This force is called the drag force. To gain an understanding of the quantities influencing the drag force in a fluid, it is necessary first to discuss two fundamental properties of a fluid: the viscosity and Reynolds' number.

Viscosity

Gases and liquids are collectively known as fluids since they can both be made to flow if a force is applied.