Basic Units of Measurement and Conversions - Basic Mathematics for Water and Wastewater Operators - page 11

To perform this conversion, we need a conversion factor . In this case, we have to
know how many inches make up a foot: 12 inches. Knowing this, we can perform
the calculation in two steps:

1. 60 in. is really 60 ÷ 12 = 5 ft

2. 5 ft + 6 ft = 11 ft

From the example above, it can be seen that a conversion factor changes known quan-
tities in one unit of measure to an equivalent quantity in another unit of measure.
When making the conversion from one unit to another, we must know two things:

1. The exact number that relates the two units

2. Whether to multiply or divide by that number

Confusion over whether to multiply or divide is common; on the other hand, the
number that relates the two units is usually known and thus is not a problem.
Understanding the proper methodology—the “mechanics”—to use for various oper-
ations requires practice and common sense.
Along with using the proper mechanics (and practice and common sense) to make
conversions, probably the easiest and fastest method of converting units is to use a
conversion table. The simplest conversion requires that the measurement be multi-
plied or divided by a constant value. For instance, if the depth of wet cement in a
form is 0.85 foot, multiplying by 12 inches per foot converts the measured depth to
inches (10.2 inches). Likewise, if the depth of the cement in the form is measured
as 16 inches, dividing by 12 inches per foot converts the depth measurement to feet
(1.33 feet).
Table 2.3 lists many of the conversion factors used in water/wastewater treatment.
Note that Table 2.3 is designed with a unit of measure in the left and right columns
and a constant (conversion factor) in the center column.
Note: To convert in the opposite direction (e.g., inches to feet), divide by the factor
rather than multiply.

W eight , C onCentration , and f loW
Using Table 2.3 to convert from one unit expression to another and vice versa is good
practice; however, when making conversions to solve process computations in water
treatment operations, for example, we must be familiar with conversion calculations
based on a relationship between weight, flow or volume, and concentration. The
basic relationship is

Weight = Concentration × (Flow or Volume) × Factor (2.1)

Table 2.4 summarizes weight, volume, and concentration calculations. With prac-
tice, many of these calculations become second nature to users. The calculations are
important relationships and are used often in water/wastewater treatment process
control calculations, so on-the-job practice is possible.