This preview shows pages 1–3. Sign up to view the full content.
1
CBE 2124 Levicky
Units
Base
(or
fundamental
) units: units of mass, length, time, temperature, current, light
intensity. All other units can be expressed as combinations of these fundamental units.
For example, force (e.g. Newtons) is equal to mass length/time
2
(e.g. kg m/s
2
).
Derived or compound units
: Units such as Newtons (N) that are combinations of
fundamental units. Sometimes, these combinations are given their own names (example
N, erg, watt).
Systems of units:
Main systems of units in use are the International System of Units (
SI)
,
the centimetergramsecond system of units (
cgs)
, and the
American
engineering
system
of units (AES). The fundamental units in these systems are as follows:
S
I
c
g
s
A
E
S
Mass
k
g
g
l
b
m
Length
m
c
m
f
t
Time
s
s
s
Often, prefixes are attached to a unit to indicate scale or magnitude.
peta
10
15
tera
10
12
giga
10
9
mega
10
6
kilo
10
3
deka 10
1
deci
10
1
centi
10
2
milli 10
3
micro 10
6
nano 10
9
pico
10
12
femto 10
15
atto
10
18
For example: 1 kilometer = 1000 meters, 1 microliter = 10
6
liters.
Mathematical manipulation of dimensioned quantities
1). Two quantities can only be added or subtracted if they have the same units. This also
means that equations must be dimensionally homogeneous – that is, all additive terms in
an equation must have the same units.
(see Example 2.61)
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document2
2). If multiplying or dividing two quantities, the units do not have to be the same. The
units from the quantities being multiplied or divided likewise multiply or divide. Thus
1 m divided by 2 s yields 0.5 m/s.
1 kg multiplied by 9.8 m/s
2
yields 9.8 kg m/s
2
.
If two quantities being divided have the same units, or two quantities being multiplied
have reciprocal (e.g. m and m
1
) units, the units cancel and the result will be
dimensionless
. As you’ll see later on, dimensionless quantities play an important role in
chemical engineering as they simplify calculations and even help minimize the number of
measurements that need to be taken to characterize the behavior of a chemical or
biological system. They are used extensively in the
scaleup
of processes and in
similitude analysis
.
3). Exponents, transcendental functions (i.e. trigonometric, logarithmic, and exponential
functions), and arguments of transcendental functions are dimensionless (recall: what is
an argument to a function?).
4). The conversion of units from one to another (e.g. meters to inches, pounds mass (lb
This is the end of the preview. Sign up
to
access the rest of the document.
 Fall '11
 Levicky

Click to edit the document details