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## UNIT SYSTEMS## Fundamental Dimensions
Physics is a science based upon exact measurement of physical quantities that are dependent upon three fundamental dimensions. The three fundamental or primary dimensions are Menu
## Mass
## Length
## Time
## UnitsA number alone is not sufficient to describe a physical quantity. For example, to say that "a pipe must be 4 long to fit" has no meaning unless a unit of measurement for length is also specified. By adding units to the number, it becomes clear, "a pipe must be 4 feet long to fit." The unit defines the magnitude of a measurement. If we have a measurement of length, the unit used to describe the length could be a foot or yard, each of which describes a different magnitude of length. The importance of specifying the units of a measurement for a number used to describe a physical quantity is doubly emphasized when it is noted that the same physical quantity may be measured using a variety of different units. For example, length may be measured in meters, inches, miles, furlongs, fathoms, kilometers, or a variety of other units. Units of measurement have been established for use with each of the fundamental dimensions mentioned previously. The following section describes the unit systems in use today and provides examples of units that are used in each system. ## Unit SystemsThere are two unit systems in use at the present time, English units and International System of Units (SI). In the United States, the English system is currently used. This system consists of various units for each of the fundamental dimensions or measurements. These units are shown in Table 1. Table 1The English system is presently used in the field of engineering and throughout the United States. The foot-pound-second (FPS) system is the usual unit system used in the U.S. when dealing with physics. Over the years there have been movements to standardize units so that all countries, including the United States, will adopt the SI system. The SI system is made up of two related systems, the meter-kilogram-second (MKS) system and the centimeter-gram-second (CGS) system. The MKS and CGS systems are much simpler to use than the English system because they use a decimal-based system in which prefixes are used to denote powers of ten. For example, one kilometer is 1000 meters, and one centimeter is one one-hundredth of a meter. The English system has odd units of conversion. For example, a mile is 5280 feet, and an inch is one twelfth of a foot. The MKS system is used primarily for calculations in the field of physics while both the MKS and CGS systems are used in the field of chemistry. The units for each of these systems are shown in Tables 2 and 3 below. Table 2Table 3The following tables show approximate lengths, masses, and times for some familiar objects or events. Table 4Table 5Table 6## Derived MeasurementsMost physical quantities have units that are combinations of the three ## AreaArea is the product of two lengths (e.g., width x length for a rectangle); thus, it has the units of length squared, such as square inches (in.2) or square meters (m2). - 1 m x 1 m= 1 m2
- 4 in. x 2 in. = 8 in.2
## VolumeVolume is the product of three lengths (e.g., length x width x depth for a rectangular solid); thus, it has the units of length cubed, such as cubic inches (in.3) or cubic meters (m3). The MKS and CGS unit systems have a specific unit for volume called the liter (l). One liter is equal to 1000 cubic centimeters (1 l = 1000 cm3). - 2 in. x 3 in. x 5 in. = 30 in.3
## DensityDensity is a measure of the mass of an object per unit volume; thus, it has units of mass divided by length cubed such as kilograms per cubic meter (kg/m3) or pounds per cubic foot (lbs/ft3). - 15 lbs/5 ft3 = 3 lbs/ft3
## VelocityVelocity is the change in length per unit time; thus, it has units such as kilometers per hour (km/h) or feet per second (ft/s). ## AccelerationAcceleration is a measure of the change in velocity or velocity per unit time; thus, it has units such as centimeters per second per second (cm/s2) or feet per second per second (ft/s2). ## Unit Conversions
People working in industrial facilities are often exposed to both the English and SI systems of units in their work. In some cases, the measurements that are taken or read from an instrument will be different from those required by a procedure. This situation will require the conversion of measurements to those required by the procedure. ## Conversion FactorsConversion factors are based on relationships of equivalents from different measurement systems. These conversion factors are then applied to the given measurement in order to convert it to the units that are required. The equivalent relationships between different units of measurement are defined in conversion tables. Some examples from conversion tables are given below. A typical conversion table is shown in Table 7. Table 7## Unit ConversionTo convert from one measurement unit to another measurement unit (for example, to convert 5 feet to inches), first select the appropriate equivalent relationship from the conversion table (for this example, 1 foot = 12 inches). Conversion is basically a multiplication by 1. We can divide both sides of the equation 1 ft = 12 inches by 1 foot to obtain the following. ## Steps for Unit ConversionUsing the following example, we will step through the process for converting from a given set of units to a desired set of units. Convert 795 m to ft. If an equivalent relationship between the given units and the desired units cannot be found in the conversion tables, multiple conversion factors must be used. The conversion is performed in several steps until the measurement is in the desired units. The given measurement must be multiplied by each conversion factor (ratio). After the common units have been canceled out, the answer will be in the desired units. It is possible to perform all of the conversions in a single equation as long as all of the appropriate conversion factors are included. Example: A Swedish firm is producing a valve that is to be used by an American supplier. The Swedish firm uses the MKS system for all machining. To conform with the MKS system, how will the following measurements be listed? - Valve stem
- 57.20 in.
- Valve inlet and outlet
- I.D. 22.00 in.
- O.D. 27.50 in.
Examples of common conversion factors are shown in Table 8. Table 8 |