Page 815 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

770 Appendix A: International System of Units

While the pound-mass can be understood easily, another Confusion often results in the use of force and mass units in
unit, the poundal has been introduced, which compounds the dealing with density, r, and specific weight, g. Since the numer-
3
issue. The distinctions between these units are delineated by ical value of density when expressed in lb m units, lb m =ft ,is
3
examples. equal to that of the specificweight, lb f =ft , they are often con-
sidered identical. This is not the case, since in the same system of
Example A.5 Illustrate the Distinction between units, they differ by the gravitational acceleration, g,in accord-
Pound-Force and Pound-Mass ance with the relation, g ¼ rg. The unit of density in the
foot-pound-hour system is the slug per cubic foot. According
1. Consider 1.0 slug under the influence of gravita- to the above equation, the specific weight in pounds per cubic
tional acceleration, g, i.e. foot units may be converted to the density unit of slug per cubic
2
foot by dividing by 32.16 ft=s . Hence, the density of water at
F ¼ M g 3 3
688Fis 62.305=32.16 ¼ 1.937 slug=ft or 62.305 lb m =ft .
¼ 1:0 slug 32:2ft=s 2
¼ 32:2 lb force
A.7.2 POUNDAL
By corollary, a force of 1 lb will accelerate a one slug
2
mass at 1 ft=s . As a second corollary, the mass that The combination of units in which one pound-mass is accel-
2
causes 1.0 lb force may be called a pound-mass erated at 1 ft=s , then the result is one poundal, i.e.
(which is 1=32.2 slugs). These are all equivalent
statements. F ¼ M g
2. Now consider 1.0 pound-mass accelerated at gravi- ¼ 1:0 lb-mass 1:0 ft=s 2
tational acceleration, i.e.
¼ 1:0 poundal force
F ¼ M=32:2 g
F ¼ 1:0 slug=32:2 32:2ft=s 2 Stated another way, a force of one poundal will accelerate a
2
¼ 1:0 lb-mass 32:2ft=s 2 mass of 1 lb mass at 1 ft=s .
¼ 1:0 lb force

3. An alternate form of the equation, F ¼ M g,is Example A.6 Convert a Force of 1 lb f to Poundals

F ¼ M (g=g c ) 1. Consider 1.0 slug accelerated at gravitational accel-
32:1740 ft=s 2 eration, g, i.e.
¼ 1lb m 2
32:1740 (lb m ft)=(lb f s )
F ¼ M g
¼ 1b f
Discussion 1:0 poundal force 1:0lb m 1:0ft=s 2
Again, the application of the g c term incorporates
the conversion from lb m to lb f . While the conversion is But 1.0 lbf is attained by 1.0 lb m accelerated at 32.2
2
straightforward using the SI system, and g c is superfluous, ft=s , and therefore, 1.0 lb m ¼ 1.0 lb f =32.2 ft=s 2
the English system requires a great deal of familiarity, and
the use of g c minimizes confusion in the conversion. 1:0 poundal force ¼ 1:0lb f =32:2ft=s 1:0ft=s 2
2
Therefore, 1 lb force is 32.2 poundals of force.
A.7.1.1 Further Notes on the Slug, Pound-Mass,
and Pound-Force
Some further notes on the distinction between the pound- A.8 TEMPERATURE
mass, the slug, and the pound-force are paraphrased from
The SI unit of thermodynamic temperature is the kelvin (K).
Hawkins (1951, p. 76): Consistency of units in engineering
The degree Celsius (8C) is also used. The kelvin temperature,
calculations is important. In many cases, mixed units are
T(K), for the freezing point of water is 273.15 K. The Celsius
employed; this practice leads to serious errors unless careful
temperature, T(8C), is
consideration is given to the conversion of the units.
The main difficulties usually arise in the use of the pound-
force and the corresponding unit of mass, the slug. The slug is T( C) ¼ T(K) 273:15 (A:4)

defined as that mass, which when acted upon by a force of
2
1 lb, will be accelerated at 1 ft=s . A.9 CONVERSION TABLES
There are times, however, when the pound-mass will be
used as a unit of mass. In order to convert from slugs to lb m or The conversions of various common units to SI units are
from lb m to slugs, it is only necessary to remember the relation given in Tables CDQR. More extensive tables are given on
between them, namely, that 32.16 lb m equals 1 slug. Web sites.