Page 19 - Aerodynamics for Engineering Students

2 Aerodynamics for Engineering Students

so also is a mile. The metre and mile are different units, since each contains a different
mount of length, but both describe length and therefore are identical dimensions.*
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 # x miles (x miles and x metres are unequal quantities of length)
[x metres] = [x miles] (the dimension of x metres is the same as the dimension
of x miles).

1 .I .I Fundamental dimensions and units
There are four fundamental dimensions in terms of which the dimensions of all other
physical quantities may be expressed. They are mass [MI, length [L], time and
temperature [e].+ A consistent set of units is formed by specifying a unit of particular
value for each of these dimensions. In aeronautical engineering the accepted units
are respectively the kilogram, the metre, the second and the Kelvin or degree Celsius
(see below). These are identical with the units of the same names in common use, and
are defined by international agreement.
It is convenient and conventional to represent the names of these units by abbreviations:
kg for kilogram
m for metre
s for second
"C for degree Celsius
K for Kelvin
The degree Celsius is one one-hundredth part of the temperature rise involved when pure
water at freezing temperature is heated to boiling temperature at standard pressure. In the
Celsius scale, pure water at standard pressure freezes at 0 "C and boils at 100 "C.
The unit Kelvin (K) is identical in size with the degree Celsius ("C), but the Kelvin
scale of temperature is measured from the absolute zero of temperature, which
is approximately -273 "C. Thus a temperature in K is equal to the temperature in
"C plus 273 (approximately).

1 .I .2 Fractions and multiples
Sometimes, the fundamental units defined above are inconveniently large or incon-
veniently small for a particular case. In such cases, the quantity can be expressed in
terms of some fraction or multiple of the fundamental unit. Such multiples and
fractions are denoted by appending a prefix to the symbol denoting the fundamental
unit. The prefixes most used in aerodynamics are:

* Quite often 'dimension' appears in the form 'a dimension of 8 metres' and thus means a specified length.
This meaning of the word is thus closely related to the engineer's 'unit', and implies linear extension only.
Another common example of its use is in 'three-dimensional geometry', implying three linear extensions in
different directions. References in later chapters to two-dimensional flow, for example, illustrate this. The
meaning above must not be confused with either of these uses.
Some authorities express temperature in terms of length and time. This introduces complications that are
briefly considered in Section 1.2.8.