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1.2 SI System of Basic Units Used in This Text and Other Systems

There are three main systems of basic units employed at present in engineering and science. The first and most important of these is the SI (Système International d’Unités) system, which has as its three basic units the meter (m), the kilogram (kg), and the second (s). The other systems are the English foot (ft)–pound (lb)–second (s), or English system, and the centimeter (cm)–gram (g)–second (s), or cgs system.

At present, the SI system has been adopted officially for use exclusively in engineering and science, but the older English and cgs systems are still used. Much of the physical and chemical data, and empirical equations are given in these latter two systems. Hence, engineers should not only be proficient in the SI system, but must also be able to use the other two systems as well.

1.2A SI System of Units

The basic quantities used in the SI system are as follows: the unit of length is the meter (m); the unit of time is the second (s); the unit of mass is the kilogram (kg); the unit of temperature is the kelvin (K); and the unit of an element is the kilogram mole (kg mol). The other standard units are derived from these basic quantities.

The basic unit of force is the newton (N), defined as

  • 1 newton (N) = 1 kg · m/s2

The basic unit of work, energy, or heat is the newton-meter, or joule (J).

  • 1 joule (J) = 1 newton · m (N · m) = 1 kg · m2/s2

Power is measured in joules/s or watts (W).

  • 1 joule/s (J/s) = 1 watt (W)

The unit of pressure is the newton/m2 or pascal (Pa).

  • 1 newton/m2 (N/m2) = 1 pascal (Pa)

The standard acceleration of gravity is defined as

  • 1 g = 9.80665 m/s2

A few of the standard prefixes for multiples of the basic units are as follows: giga (G) = 109, mega (M) = 106, kilo (k) = 103, centi (c) = 10–2, milli (m) = 10–3, micro (μ) = 10–6, and nano (n) = 10–9.

Temperatures are defined in kelvin (K) as the preferred unit in the SI system. However, in practice, wide use is made of the degree Celsius (°C) scale, which is defined by

  • T(°C) = T(K) – 273.15

Note that 1°C = 1 K and that in the case of temperature difference,

  • ΔT(°C) = ΔT(K)

The standard preferred unit of time is the second (s), but time can be in nondecimal units of minutes (min), hours (h), or days (d).

1.2B CGS System of Units

The cgs system is related to the SI system as follows:

  • 1 g mass (g) = 1 × 1023 kg mass (kg)

  • 1 cm = 1 × 1022 m

  • 1 dyne (dyn) = 1 g · cm/s2 = 1 × 1025 newton (N)

  • 1 erg = 1 dyn · cm = 1 × 1027 joule (J)

The standard acceleration of gravity is

  • g = 980.665 cm/s2

1.2C English FPS System of Units

The English system is related to the SI system as follows:

  • 1 lb mass (lbm) = 0.45359 kg

  • 1 ft = 0.30480 m

  • 1 lb force (lbf) = 4.4482 newton (N)

  • 1 ft · lbf = 1.35582 newton · m (N · m) = 1.35582 joules (J)

  • 1 psia = 6.89476 × 103 newton/m2 (N/m2)

  • 1.8°F = 1 K = 1°C (centigrade or Celsius)

  • g = 32.174 ft/s2

The proportionality factor for Newton’s law is

  • gc = 32.174 ft · lbm/lbf · s2

The factor gc in SI units and cgs units is 1.0 and is frequently omitted.

In Appendix A.1, convenient conversion factors for all three systems are tabulated. Further discussions and use of these relationships are given in various sections of the text.

This text uses the SI system as the primary set of units in the equations, example problems, and homework problems. However, the important equations derived in the text are given in a dual set of units, SI and English, when these equations differ. Some example problems and homework problems are also given using English units. In some cases, intermediate steps and/or answers in example problems are also stated in English units.

1.2D Dimensionally Homogeneous Equations and Consistent Units

A dimensionally homogeneous equation is one in which all the terms have the same units. These units can be the base units or derived ones (i.e., kg/s2 · m or Pa). Such an equation can be used with any system of units provided that the same base or derived units are used throughout the equation. No conversion factors are needed when consistent units are used.

The reader should be careful about using any equation and should always check it for dimensional homogeneity. To do this, a system of units (SI, English, etc.) is first selected. Then, units are substituted for each term in the equation and like units in each term canceled out.

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