Educ. Reso. for Part. Techn. 024Q-Nelson
<http://www.erpt.org/024Q/Nelsb-00.htm>
Copyright © 2002 Ralph Nelson, Licensed to ERPT
Dispersing Powders in Liquids, Part 2, by Ralph D. Nelson, Jr.
--- 7: Units, Constants, and Symbols ---
Units and Conversion Factors
Systéme Internationale (SI) units have been used throughout this treatise.
Below are tables of conversion factors to aid in comparing equations and converting data
from the cgs (centimeter-gram-second) units that were used
in the older scientific literature and tabulations
and from the foot-pound units that were used
in the older English and American engineering literature and tabulations.
For a more extensive discussion of units and conversions consult
Oldshue, J. Y., Chem. Eng. Prog. 73, 135-138 (August, 1977)
Rehm, T. R., "SI for AIChE", Amer. Inst. of Chem. Eng., New York, 1979.
Here are a few problems and cautions regarding the use of SI units
and of several other conventions:
- U.S. and European conventions for the decimal separator:
I use the U.S. conventions that
-- the decimal point is used to separate digits
representing values greater than unity from those digits
representing values less than unity.
-- the comma may (or may not) be used to set off groups
of three digits before the decimal point for ease in reading.
Thus I write two thousand five hundred grams as 2,500 g and
two and a half kilograms as 2.5 kg
and one-half a kilogram as 0.5 kg.
In the European style these would be 2.500 g, 2,5 kg, and 0,5 kg.
This difference can obviously cause significant errors.
It is a particular problem when you retrieve a few values from literature
and tabulations written in the style that you do not normally use
and forget that a decimal point is "really" a comma and vice versa.
- One base unit uses a prefix: The base unit for mass (the kilogram)
uses a prefix (kilo-) as part of the base unit name, so the prefixes
for multiples of this base unit are based on one-thousandth
of the base unit (the gram). Thus one-millionth of a kilogram is a milligram
and not a micro-kilogram.
- The mole in based on 0.012 kg of carbon: A mole is defined
as the amount of a substance containing the same number of fundamental units
as there are atoms in 0.012 kg of carbon-12, so in SI units molar masses
are not in a convenient range for tabulation. For example, the molar mass
(often called the "molecular weight") for water is 0.01802 kg/mol.
It is easy for people familiar with the common forms of the periodic table
to add up the cgs values and write 79.90 for the molar mass of TiO2,
both neglecting to write the units and thus overlooking the fact
that in the SI system it should be written as 0.07990 kg/mol.
- The pH system must be more explicitly based on the activity ratio
and not on activity: The logarithm function should have as an argument
a dimensionless number. The correct expression for the pH -- a measure of acidity --
for an aqueous system involves the ratio of the activity of the hydrogen ion
(related to its concentration multiplied by an activity coefficient
to correct for non-ideality) to its activity in some standard state.
The standard state activity for pH is set as 1 mol/L -- which in SI units
is 1,000 mol/m3. The general expression is then
[8a] 
In cgs units this becomes
pH = - log10 [
act,C CH+ / (1 mol/L)]
while in SI units it is
pH = - log10 [act,C CH+
/ (1,000 mol/m3)]
Since the activity coefficients for dilute solutions are essentially unity
and the denominator in cgs units in unity, we may think of the pH as being defined
as pH = - log10 C. While this may give good values when C is expressed
in mol/L, the pH will off by 3 if C is expressed in mol/m3 and the
standard concentration is not explicitly included (with proper units).
If you always include units in your calculations you will probably discover
there is a problem and thus start looking for the source of the problem.
- Use an equivalent if it simplifies the units: If a calculation
results in a multiplier with all four units m, kg, s, and A, consider
making a substitution based on the unit equivalence
A2 = kg m3 / s4.
- The factor 4
appears in different places in SI
and cgs systems: The factor of 4 that appears
in equations involving charge or potential and formulated using the
cgs-esu convention has been incorporated into the value of
0 in the SI system, so the equations
in this treatise have a factor 0
where older scientific literature
has /(4).
Use of the cgs-esu form of the equation rather than the SI form will
cause the result to be off by 40
or 1.112 * 10-10.
E.1.1 SI Base Units
---------- ---- ------
Quantity Unit Symbol
---------- ---- ------
length meter m
mass kilogram kg
time second s
electric current ampere A
temperature kelvin K
chemical substance mole mol
luminous intensity candela cd
[next is a mathematical unit rather than a physical unit]
angle of arc radian rad
E.1.2 SI Prefixes
-------- ---------- ------
Prefix Multiplier Symbol
-------- ---------- ------
mega- 106 M
kilo- 103 k
centi- 10-2 c
milli- 10-3 m
micro- 10-6 
namo- 10-9 n
E.1.3 Derived SI Units with Special Names
-------- ---- ------ ---------- ---------------
Quantity Unit Symbol Equivalent Base Equivalent
-------- ---- ------ ---------- ---------------
frequency hertz Hz s-1 same
force newton N kg m s-2 same
energy joule J N m kg m2 s-2
pressure pascal Pa N/m2 kg s-2
power watt W J/s kg m2 s-3
in electrical terms W V A m-1 s A2
potential volt V W/A m-1 s A
resistance ohm 
V/A s2/m
charge coulomb C A s same
capacitance farad F C/s m
flux weber Wb J/A m-1 s2 A
flux density tesla T Wb/m2 m-3 s2 A
inductance henry H Wb/A m-1 s2
E.1.4 Conversions from Non-SI Units
---- ------ -------------
Unit Symbol SI Equivalent
---- ------ -------------
Angstrom A 10-10 m
atmosphere atm 101.325 kPa
Debye = 10-10 esu Angstroms
D 3.336 * 10-30 C m
degree o 0.017453 rad
dyne - 10-5 N
erg - 10-7 J
gram-calorie of energy (thermal)
cal 4.184 J
kilogram-calorie of energy (used with foodstuff)
kcal 4.184 kJ
liter L 0.001 m3
micron m 10-6 m
millimeters of mercury in a barometer (pressure)
mmHg 133.3 Pa
poise p 0.1 Pa s
pounds-force per square inch (pressure)
PSI 6.895 kPa
statcoulomb or electrostatic unit
esu 3.336 * 10-10 C
molecular polarizability [C m2 / V]
coating thickness [m]
viscosity [Pa s]
j stoichiometry coefficient for jth species [--]
volume fraction [--]
density [kg / m3]
charge surface charge density [C / m2]
shear stress [N / m2]
j fraction of surface sites occupied by jth species [--]
angular rotation frequency [rad / s]
zeta potential of a particle [V]
prefix indicating the difference between the value of
the parameter following at two states of the system [--]
surface concentration [mol / m2]
0 electrostatic potential at particle surface [V]
j prefix indicating multiplication of parameters following
for all values of the index j [--]
i prefix indicating summation of parameters following
for all values of the index i [--]