Geology Reference
In-Depth Information
40
I. Introduction to Geology
engineers have devised a simple way to keep these
numbers and their units straight. It sometimes is
described as dimensional analysis because we are
measuring or calculating the dimensions of a feature,
although that term has other meanings and it is based
on the need to arrive at the answer in specific units. To
make unit conversions, which are sometimes lengthy
and complicated, we set up a dimensional equation,
with the given quantity and units on the left and the
desired units (the ones we wish to have after the con-
version) on the right.
A familiar example of this conversion technique
is given by the following problem. If we wish to con-
vert 1 hour into seconds and we know the number of
minutes in an hour and the number of seconds in a
minute we can set up a relationship to do the conver-
sion. This relationship covers the numbers and the
units portions of our data. All except the unit you want
(what you will have after the conversion) cancel each
other. Here we use seconds, minutes, hours as the
units of the quantity we are working with. We use the
rule (as in algebra) that zeros and the same units on the
top and bottom of the same side of an equation can be
cancelled or simplified. Although the answer to this
problem can be done in your head, let us see what the
relationship would look like for the conversion of
hours to seconds.
FIGURE 3.2
Tangent (opposite side/adjacent side) of angle y
is a/b.
150ft/3 miles = 50 feet/mile or 50 feet per mile.
For those who recall geometry and trigonometry, this
relationship of rise over the run is the tangent of the
slope angle. In the example in Figure 3.2, it is the angle y.
rise = a; run = b
a/b = tan y
We can convert this fraction for slope between A and B
in Figure 3.1 to a slope angle by using the inverse tan
function on a calculator, which may be labeled tan
-1
.
Slope = 400/2000 = 0.2 (0.2 is the tangent of the slope
angle).
The angle that has a tangent of 0.2 is about 11.3 degrees
or 11 degrees 19 minutes.
Rates
1.
List the unit you are seeking as part of a proportion-
ality on the right side of the page (below it is seconds,
given in italics).
Although the determination of slope (above) is really a
rate calculation (how does the elevation change with
distance), we often think of rates as change over time.
The rate of movement of your car is given in miles per
hour (mph or miles/hour) or in km/hr. The general
relationship is velocity = distance/time. The slash or
the "per" indicates one quantity over the other, in this
case rate. The velocity of water in a stream or the
movement of debris in a landslide is usually described
in feet per second, meters per second, or miles per
hour. In Figure 1.4, the ranges in rates for many geo-
logic processes are given in m/s, mm/s, km/y, m/y,
and mm/y. These could be written as mm/yr or even
mm yr
-1
, where the -1 superscript for the yr indicates
1/yr and means per year.
In addition, the rate of use of a quantity such as
miles per gallon or liters per kilometer in transporta-
tion is familiar to most of us. In the geosciences we also
speak of the volume of material per time in the dis-
charge of river. For example, river flow in English units
is measured using cubic feet per second, or cfs, units.
2.
Set up the relation to convert to this unit by elimina-
tion of the other units by cancellation.
3.
Carry over and reduce the numerical parts of the
relationship where possible.
Note: Although we can only add and subtract
like values, we can combine and convert units by mul-
tiplying and dividing as in the case below.
1 hour = 1 hr
X
(60 min/1 hr)
X
(60 sec/1 min)
= 60
X
60 sec = 3,600 seconds
Note that hours and minutes both cancel out as units
during this conversion; the answer is in seconds.
We could mix dimensions such as distance and
time (miles and hours) as we change miles per hour to
meters per second:
60 miles/hour = (60 miles/hr)
X
(1 hr/3600 sec)
X
(1km/0.6214 miles)
X
lOOOm/lkm = 26.8
m/sec
Conversions
When working practical problems, measurements in
many different units may need to be combined to arrive
at an answer. In so doing we need to be able to convert
the units and the amounts of the quantities readily,
without becoming confused. Fortunately, scientists and
We could change mass and volume dimensions as we
seek to determine the weight of a cubic foot of gold,
as described below. The density of gold is 19.3
