Page 816 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

Appendix A: International System of Units 771

A.10 CONVERSIONS FOR UNCOMMON 3. AWWA (1982) recognizes the units, mm=s as more
convenient and so the conversion gives
DERIVED UNITS
HLR ¼ 1:0 million gal=acre=day
Many of the derived units in the environmental engineering 5
1:1 10 m=s
field are not common to other fields, and so may not be
¼ 0:011 mm=s
listed in many conversion tables. Therefore, the conversions
must be done using the conversion factors available. This can
4. A more convenient unit is m=h:
be done most easily by a process of canceling units that are to
mm 3600 1m
be omitted, leaving only the SI units. Using a systematic HLR ¼ 0:011
s h 1000 mm
format for setting up the conversion will help to minimize
¼ 0:0396 m=h
mistakes. The procedure should be familiar to most persons in
0:04 m=h
engineering or science. Example A.7 illustrates the process.
A.11 DIMENSIONAL HOMOGENEITY
Example A.7 Convert 1.0 million gal=acre=day
A requisite to a correct mathematical expression requires
to SI Units
dimensional homogeneity. In other words, both sides of a
given equation must be dimensionally equivalent (Rouse,
In slow sand filtration, the common units for hydraulic
loading rate have been in million gal=acre=day. The unit 1946). The application of SI units ensures that the homogen-
dates back earlier than 1900. After the advent of rapid eity condition is satisfied.
2
filtration, the U.S. Customary unit has been, gal=min=ft . The problem arises mostly when force appears in one term
The latter units do not, however, fit slow sand well, and SI of an equation and mass appears in another term. To handle
2
3
units are more appropriate, that is m =m =s, which reduce the problem, either the force term must be converted to mass
to m=s (but m=h units are more convenient). or the mass term must be converted to a force. Since SI units
are expressed in terms of kg-m-s, the former is preferred if the
1. Express the 1.0 million gal=acre=day in fraction for- choice is arbitrary.
mat, i.e. As another example, if a pressure term is in terms of kPa, the
2
conversion to N=m will help to ensure dimensional homo-
HLR ¼ 1:0 million gal=acre=day geneity. If a viscosity term is in poises in the same equation,
2
the conversion to N-s=m will be helpful. Should a force term
6
1:0 10 gal 2
remain, its conversion from N to kg=s is appropriate (vis-à-vis
acre day 2
¼
from kg=s . to N). The conversion is not necessary, of course, if
there is a reason for the force unit in the final equation.
2. Convert to SI units using conversions from Table
CDQR:
REFERENCES
HLR ¼ 1:0 million gal=acre=day
ASTM, Standard Practice for Use of the International System of
6
1:0 10 gal Units (SI) (The Modernized Metric System), Designation E380-
acre day
¼ 91a, PCN 03-543191-34, American Society for Testing Mater-
ials, Philadelphia, PA, 1991.
6
1:0 10 gal acre
AWWA, AWWA Metrication Committee, Final report on metric
acre day 4:046 873 10 m units and sizes, Journal of the American Water Works Associ-
¼ 3 2
3:785 412 10 3 m 3 day ation, 74(1):27–33, January 1982.
gal 8:640 000 10 s
4 Cardarelli, F., Scientific Unit Conversion, 2nd edn., Springer, Berlin,
Germany, 1999.
¼ 1:082 629 10 5 m=s Carver, G. P., A metric America: A decision whose time has come—
1:1 10 5 m=s For real, NISTIR 4858, Metric Program Technology Services,
National Institute of Standards and Technology, U.S. Depart-
ment of Commerce, Washington, DC, June, 1992.
Significant digits: Note that based upon the accuracy given Construction Subcommittee, Interagency Council on Metric Policy,
in the starting figure, only about two places are justified in Metric Guide for Federal Construction, 1st edn., National
the final converted result. So that conversion factors can be Institute of Building Sciences, Washington, DC, 1991.
traced to the sources, all of the places are used as illustrated Felder, R. M. and Rousseau, R. W., Elementary Principles of Chem-
in Example A.7. The final answer, however, should be ical Processes, John Wiley & Sons, New York, 1978.
rounded so that the number of significant digits retained Hawkins, G. A., Thermodynamics, 2nd edn., John Wiley & Sons,
should neither sacrifice nor exaggerate accuracy. Any digit New York, 1951.
necessary to define a numerical value is said to be signifi- ICMP, Interagency Council on Metric Policy, Metric Guide for
cant. The rule for multiplication or division is that the prod- Federal Construction, 1st edn., National Institute of Building
uct or quotient should contain no more significant digits Sciences, Washington, DC, 1991.
than are contained in the number with the fewest significant Rouse, H., Elementary Mechanics of Fluids, John Wiley & Sons,
digits (i.e., as used in the multiplication or division). New York, 1946.