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Importance of Units in Technology

In traditional geology the unit of pressure is thebar,
which is about equal to atmospheric pressure. It is
also about equal to the pressure under 10 meters
of water. For pressures deep in the earth we use
thekilobar, equal to 1000 bars. The pressure
beneath 10 km of water, orat the bottom of the
deepest oceanictrenches, is about 1 kilobar.
Beneath the Antarctic ice cap (maximum thickness
about 5 km) the pressure is about half a kilobar at
greatest.In the SI System, the fundamental unit of
length is the meter and mass is the kilogram.
Important units used in geology include:*.Energ
y:Joule: kg-m2/sec2. Five grams moving at 20
meters per second have an energy of one joule.
This is about equal to a sheetof paper wadded up
into a ball andthrown hard.*.Force: Newton: kg-m/
sec2. On the surface of the Earth, with a
gravitational acceleration of 9.8 m/sec2, a newton
is the force exerted by a weight of 102 grams or
3.6 ounces. A Fig Newton weighs about 15 grams;
therefore one SI Newton equals approximately 7 Fig
Newtons.*.Pressure: Pascal = Newton/m2or kg/m-
sec2. A newton spread out over a square meter is
a pretty feeble force. Atmospheric pressureis about
100,000 pascals. A manilafile folder (35 g, 700
cm2area) exerts a pressure of about 5 pascals.By
comparison with traditional pressure units, one bar
= 100,000 pascals. One megapascal (Mpa) equals
10 bars, one Gigapascal (Gpa) equals 10
kilobars.Using Units in CalculationsThe
fundamental rule in using units in calculations is
thatunits obey the same algebraic rules as other
quantitiesExample: Converting Traditional Density
to SI densityDensity is conventionally representedas
grams per cubic centimeter. How do we represent
density in the SI system?1 gram/cm3=(0.001 kg)/
(.01 m)3=10-3kg/10-6m3=1000 kg/m3Thus, to
convert traditional to SI density,multiply by 1000.
Thus, 2.7 gm/cm3= 2700 kg/m3, etc.Example:
Pressure Beneath a Stone BlockWhat's the pressure
beneath a granite block 20 meters long, 15 meters
wide and 10 meters high, with density 2.7 gm/
cm3?First, we find the mass of the block. Mass is
volume times densityor 20 x 15 x 10 m3x 2700
kg/m3=8.1 x 106kg.Note that we have m3times
kg/m3, and the m3terms cancel out to leave the
correct unit, kilograms.Now the force the block
exerts is given by mass times acceleration, in this
case the acceleration of gravity, or 9.8 m/
sec2.Thus the force the block exerts is 8.1x 106kg
x 9.8 m/sec2, or 7.9 x 107kg-m/sec2.Referring to
the SI units listed above, we see that these are
indeed the correct units for force. The block exerts
7.9 x 107newtons of force onthe ground beneath
it.The pressure the block exerts is forcedivided by
area, or 7.9 x 107newtons/(20 m x 15 m) =
265,000 pascals (verify that the units are correct).
This is only 2.65 bars, the pressure beneath 27
meters of water. Scuba divers can stand that
pressure easily, but nobody would want to lie
under a ten-meter thick slab of rock. This should
bother you.It should be intuitively obvious that the
pressure will be the same regardless of the area of
the block. Can you show why this is so?Conversion
FactorsOften students find it hard to decide whether
to multiply or divide by a conversion factor. For
example, one meter = 3.28 feet. To convert 150
feet to meters, do you multiply or divide by 3.28?If
you think of the conversion factor as merely a
number, it can be a puzzle. But consider:1 meter =
3.28 feet. Therefore 1 m/3.28 feet = 1 and 3.28
feet/1 m =1Conversion factors are not just
numbers, but units too.Every conversion factor,
with units included, equals unity. That part about
including units is all-important. So, given a
conversionproblem, use the conversion factor to
eliminate unwanted units, produce desired units, or
both.To convert 150 feet to meters, we want to get
rid of feet and obtain meters. The conversion factor
is 3.28feet/1 m. Multiplying gives us 492 feet2/m2.
It's perfectly correct - it might be a valid part of
some other calculation - but not what we need
here. We need to get rid of feet and obtain meters,
which means we needmeters in the numerator
(upstairs) and feet in the denominator
(downstairs).150 feet x 1m/2.38 feet = 45.7
meters. Feet cancel out, leaving us with only
meters.A more complex example: convert 10 miles
per hour to meters per second. Here,noneof the
units we want in the final answer are present in the
initial quantity. But we know:*.1 mile = 5280 feet*.1
meter = 3.28 feet*.1 hour = 60 minutes*.1 minute =
60 secondsWe want to get rid of miles and hours
and get meters and seconds. So we want our
conversion factors toeliminate miles and hours:10
mi/hr x (5280 feet/1 mi) x (1 hr/60 min)Also, we
want our end result to be inmeters/second so at
some point we will have to haveSomething x
(1m/3.28 feet) x (1 min/60 sec) This is the only
way to get m/sec using the conversion factors
given. We will, of course, have to get rid of the feet
and minutes somehow.Putting it all together we
get10 mi/hr x (5280 feet/1 mi) x (1 hr/60 min) x
(1m/3.28 feet) x (1 min/60 sec) = 4.47 m/secMiles
cancel, hours cancel, feet cancel, minutes cancel,
and we end up with m/sec, just what we
needed.Some people prefer to use a grid
arrangement as shown below:10 miles5280 feet1
m1 hour1 min=4.47 m1 hour1 mile3.28 feet60
min60 sec1 secIn this example we get rid of miles
and feet to get meters first, then we get rid of hours
and minutes to get seconds.Stress TermsStress is
defined as force per unit area. It has the same units
as pressure, and in fact pressure is one special
variety of stress. However, stress is a much more
complex quantity than pressure because it varies
both with direction and with the surface it acts
on.CompressionStress that acts to shorten an
object.TensionStress that acts to lengthen an
object.Normal StressStress that acts perpendicular
to a surface. Can be either compressionalor
tensional.ShearStress that acts parallel to a
surface. It can cause one object to slide over
another. It also tends to deform originally
rectangular objects into parallelograms. The most
general definition is that shear acts to change the
angles in an object.HydrostaticStress (usually
compressional) that isuniform in all directions. A
scuba diver experiences hydrostatic stress. Stress
in the earth is nearly hydrostatic. The term for
uniform stress in the earth islithostatic.Directed
StressStress that varies with direction.

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