Handout1 - CBE 2124 Levicky Units Base (or fundamental)...

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1 CBE 2124 Levicky Units Base (or fundamental ) units: units of mass, length, time, temperature, current, light intensity. All other units can be expressed as combinations of these fundamental units. For example, force (e.g. Newtons) is equal to mass length/time 2 (e.g. kg m/s 2 ). Derived or compound units : Units such as Newtons (N) that are combinations of fundamental units. Sometimes, these combinations are given their own names (example N, erg, watt). Systems of units: Main systems of units in use are the International System of Units ( SI) , the centimeter-gram-second system of units ( cgs) , and the American engineering system of units (AES). The fundamental units in these systems are as follows: S I c g s A E S Mass k g g l b m Length m c m f t Time s s s Often, prefixes are attached to a unit to indicate scale or magnitude. peta 10 15 tera 10 12 giga 10 9 mega 10 6 kilo 10 3 deka 10 1 deci 10 -1 centi 10 -2 milli 10 -3 micro 10 -6 nano 10 -9 pico 10 -12 femto 10 -15 atto 10 -18 For example: 1 kilometer = 1000 meters, 1 microliter = 10 -6 liters. Mathematical manipulation of dimensioned quantities 1). Two quantities can only be added or subtracted if they have the same units. This also means that equations must be dimensionally homogeneous – that is, all additive terms in an equation must have the same units. (see Example 2.6-1)
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2 2). If multiplying or dividing two quantities, the units do not have to be the same. The units from the quantities being multiplied or divided likewise multiply or divide. Thus 1 m divided by 2 s yields 0.5 m/s. 1 kg multiplied by 9.8 m/s 2 yields 9.8 kg m/s 2 . If two quantities being divided have the same units, or two quantities being multiplied have reciprocal (e.g. m and m -1 ) units, the units cancel and the result will be dimensionless . As you’ll see later on, dimensionless quantities play an important role in chemical engineering as they simplify calculations and even help minimize the number of measurements that need to be taken to characterize the behavior of a chemical or biological system. They are used extensively in the scale-up of processes and in similitude analysis . 3). Exponents, transcendental functions (i.e. trigonometric, logarithmic, and exponential functions), and arguments of transcendental functions are dimensionless (recall: what is an argument to a function?). 4). The conversion of units from one to another (e.g. meters to inches, pounds mass (lb
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Handout1 - CBE 2124 Levicky Units Base (or fundamental)...

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