Engineering Rock Mechanics

(Jacob Rumans) #1

xiv Units and symbols


Derived units


From the three base units, all the other mechanical units are derived.
Some of the main derived units are listed below.


Derived Quantity Narneof SIdt Dimensions
quantity symbol SIunit of unit
Area A m2 L
Volume V m3 L
Density P kg m-3 L-3M
Velocity 2, m s-I LT-'
Acceleration a m s-* LT-'
Weight W newton, N m kg s-~ LMT-
Force F newton, N m kg s-' LMT-
Pressure P pascal, Pa N m-2, m-l kg s-' L-'MT-'
Energy E joule, J N m, m2 kg s-' L*MT-*

The name of the SI unit, e.g. newton, is written with an initial lower case
letter, and its abbreviation, e.g. N, is written with an initial upper case
letter.
Note that force is defined through the relation: force = mass x accel-
eration. A newton, N, is the force necessary to accelerate a one kilogram
mass at a rate of one metre per second per second. This is clear for dy-
namic circumstances but the force definition also applies to the concept
and the units used in the static case. When a static force exists, the force
between two stationary objects, the units of force are still m kg s2 with
dimensions Lh4T2 because of the definition of force. Thus, other derived
units, such as Young's modulus, have units of m-l kg s-~ and dimen-
sions L-'MT-2, despite the fact that there may be no time dependency in
their definition.
The most common prefixes used for decimal multiples of units in
engineering rock mechanics are

10-6 10-3 iv 106 109
micro milli kilo mega giga
u mkM G

Symbols used in this book


The main symbols used in this book are listed below, together with
the name of the quantity they represent, the SI unit name (where
appropriate), the SI unit and the dimensions of the unit. Other symbols
and abbreviations introduced for a specific question and answer have
been defined 'locally' in those questions and answers.

'We follow the recommendations in Quantities, Units and Symbols prepared by the
Symbols Committee of the Royal Society, 1975,54pp.
'The term 'dimensions' is used here to mean the complete listing of the dimensions
and exponents, as in L-'MT-', rather than just the Lh4T components, or just their
exponents, -1,l, -2.
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