Density

Density

Air is thus not a continuum. If it were, the density at a point would be defined as follows : considering the mass M of a small volume V of air surrounding the point, the density would be
the limiting ratio of M/V as V vanishes. But we must suppose that the volume V enclosing the point is contracted only until it is small compared with the scale of variation of density, while it still remains large compared with the mean distance separating the molecules. Clearly,however, V can become very small before the continuous passage of molecules in all directions across its bounding surface can make indefinite the number of molecules enclosed and M or M/V uncertain. Density is thus defined as the ratio of the mass of this very small, though finite, volume of air i.e. of the aggregate mass of the molecules enclosed to the volume itself. Density is denoted by p, and has the dimensions M/Z.

In Aerodynamics it is convenient to use the slug-ft.-sec. system of units.* At 15 C. and standard pressure 1 cu. ft. of dry air weighs 0-0765 Ib. This gives p = 0-0765/g = 0-00238 slug per cu. ft.
It will be necessary to consider in many connections lengths, areas, and volumes that ultimately become very small. We shall tacitly assume a restriction to be imposed on such contraction as discussed above. To take a further example, when physical properties are attached to a '
point' we shall have in mind a sphere of very small but sufficient radius centred at the geometrical point.