Units and dimensions

A study in any science must include measurement and calculation, which presupposes an agreed system of units in terms of which quantities can be measured and expressed. There is one system that has come to be accepted for most branches of science and engineering, and for aerodynamics in particular, in most parts of the world. That system is the Systeme International d’Unites, commonly abbreviated to SI units, and it is used throughout this book, except in a very few places as specially noted.

It is essential to distinguish between the terms ‘dimension’ and ‘unit’. For example, the dimension ‘length’ expresses the qualitative concept of linear displacement, or distance between two points, as an abstract idea, without reference to actual quantitative measurement. The term ‘unit’ indicates a specified amount of the quantity. Thus a metre is a unit of length, being an actual ‘amount’ of linear displacement, and

so also is a mile. The metre and mile are different units, since each contains a different amount of length, but both describe length and therefore are identical dimensions[1] Expressing this in symbolic form:

x metres = [L] (a quantity of x metres has the dimension of length) x miles = [L] (a quantity of x miles has the dimension of length) x metres Ф x miles (x miles and x metres are unequal quantities of length)

[х metres] = [x miles] (the dimension of x metres is the same as the dimension of x miles).