We saw in Chapter 1 how real materials, in particular fluids, can be regarded as continuous if the distances over which their gross properties (like density) change is much larger than the molecular spacing. They can then be split up into small elements, to each of which the laws of particle mechanics can be applied. We have also set down those laws. Before applying them, however, we must know what forces act on such an element. As with the body sliding along the table (Fig. 2.7), the forces experienced by a representative fluid element are of two kinds: long-range and short-range.

The forces which act at long range, the body forces, are experienced by all fluid elements; the two most common examples are gravitational and electromagnetic in origin. The electromagnetic force on an element depends on quantities like its electrical charge, but the gravitational force, i.e. the weight of the element, depends only on its mass; this is the only example of body force to be considered from now on. If a fluid element P which occupies the point x at a certain time t has volume V and if the fluid in the neighbourhood of x at that time has density ρ, then the gravitational force on the element is ρVg.

Stress

Short-range forces are exerted on the element P by those other elements with which it is in contact, and by no other. They consist of all the intermolecular forces exerted by molecules just outside the surface of P on the molecules just inside.