Page 20 - Aerodynamics for Engineering Students

Basic concepts and definitions 3

M (mega) - denoting one million
k (kilo) - denoting one thousand
m (milli) - denoting one one-thousandth part
p (micro) - denoting one-millionth part

Thus
1 MW = 1 OOOOOOW
1 mm = 0.001m
1 pm = 0.001 mm
A prefix attached to a unit makes a new unit. For example,

1 mm2 = 1 (nun>' = m2, not 10-~ m2
For some purposes, the hour or the minute can be used as the unit of time.

1.1.3 Units of other physical quantities

Having defined the four fundamental dimensions and their units, it is possible to
establish units of all other physical quantities (see Table 1.1). Speed, for example,
is defined as the distance travelled in unit time. It therefore has the dimension
LT-' and is measured in metres per second (ms-'). It is sometimes desirable and
permissible to use kilometres per hour or knots (nautical miles per hour, see
Appendix 4) as units of speed, and care must then be exercised to avoid errors
of inconsistency.
To find the dimensions and units of more complex quantities, appeal is made to
the principle of dimensional homogeneity. This means simply that, in any valid
physical equation, the dimensions of both sides must be the same. Thus if, for
example, (mass)" appears on the left-hand side of the equation, (massy must also
appear on the right-hand side, and similarly this applies to length, time and
temperature.
Thus, to find the dimensions of force, use is made of Newton's second law of motion
Force = mass x acceleration

while acceleration is speed + time.
Expressed dimensionally, this is
]
Force = [MI x - - T = [MLT-']
[ ; I
Writing in the appropriate units, it is seen that a force is measured in units of
kg m s-~. Since, however, the unit of force is given the name Newton (abbreviated
usually to N), it follows that

1 N = 1 kgmsP2
It should be noted that there could be confusion between the use of m for milli and
its use for metre. This is avoided by use of spacing. Thus ms denotes millisecond
while m s denotes the product of metre and second.
The concept of the dimension forms the basis of dimensional analysis. This is used
to develop important and fundamental physical laws. Its treatment is postponed to
Section 1.4 later in the current chapter.