Conversion factor defined

Since three unit systems are in common use, it is often necessary to convert the magnitudes of quantities from one system to another. This is accomplished by using conversion factors. Only the defined conversion factors for the base units are required since conversion factors for all other units can be calculated from them. Interconversions between the SI and cgs systems are simple. Both use the same standards for time, temperature, and the mole, and only the decimal conversions defined by Eqs. (1.16) and (1.17) are needed. The SI and fps systems also use the second as the standard for time the three conversion factors defined for mass, length, and temperature by Eqs. (1.26), (1.27), and (1.28), respectively, are sufficient for all conversions of units between these two systems. 

The principal unit system of this book is the SI sieme International d Unites) but to accommodate other systems, practically all (992 of a total of 1017) numbered equations are written so that they can be used with any consistent set of units. In order to permit this, it is necessary to include in all expressions involving dimensions of both force and mass the conversion factor defined through Newton s second law of motion,... 

Pressure is defined as force per unit of area. The International System of Units (SI) pressure unit is the pascal (Pa), defined as 1.0 N /m. Conversion factors from non-SI units to pascal are given in Table 1 (see also Units and conversion factors front matter). An asterisk after the sixth decimal place indicates that the conversion factor is exact and all subsequent digits are 2ero. Relationships that are not followed by an asterisk are either the results of physical measurements or are only approximate. The factors are written as numbers greater than 1 and less than 10, with 6 or fewer decimal places (1). 

U.S. regulations define this standard as foUows proof spirit shaU be held to be that alcohoHc Hquor which contains one-half its volume of alcohol of a specific gravity of 0.7939 at 15.6°C ie, the figure for proof is always twice the percent alcohol content by volume. For example, 100° proof means 50% alcohol by volume. In the United Kingdom as weU as Canada, proof spirit is such that at 10.6°C alcohol weighs exactiy twelve-thirteenths of the weight of an equal bulk of distiUed water. A proof of 87.7° indicates an alcohol concentration of 50%. A conversion factor of 1.142 can be used to change British proof to U.S. proof. 

This conversion factor is exact the inch is defined to be exactly 2.54 cm. The other factors listed in this column are approximate, quoted to four significant figures. Additional digits are available if needed for vary accurate calculations. For example, the pound is defined to be 453.59237 g. 

Table 18.3 I Electrical Units Unit Defining Relation Conversion Factors... 

Designers, manufacturers, and operators of boilers continue to use many of these terms, without undue deference to unit standardization, to define, measure, and report on plant steam-raising capacities power output) and operating parameters. (In continuance of this common practice therefore, many of these various terms are freely used in discussions throughout this book.) However, to familiarize the reader and minimize confusion, some energy terms and notes are provided here. A more complete list of units and conversion factors is provided in the appendix. 

Integers and exact numbers In multiplication or division by an integer or an exact number, the uncertainty of the result is determined by the measured value. Some unit conversion factors are defined exactly, even though they are not whole numbers. For example, 1 in. is defined as exactly 2.54 cm and the 273.15 in the conversion between Celsius and Kelvin temperatures is exact so 100.000°C converts into 373.150 K. 

It should be noted that a dimensional analysis of this problem results in one more dimensionless group than for the Newtonian fluid, because there is one more fluid rheological property (e.g., m and n for the power law fluid, versus fi for the Newtonian fluid). However, the parameter n is itself dimensionless and thus constitutes the additional dimensionless group, even though it is integrated into the Reynolds number as it has been defined. Note also that because n is an empirical parameter and can take on any value, the units in expressions for power law fluids can be complex. Thus, the calculations are simplified if a scientific system of dimensional units is used (e.g., SI or cgs), which avoids the necessity of introducing the conversion factor gc. In fact, the evaluation of most dimensionless groups is usually simplified by the use of such units. 

This equation defines the permeability (K) and is known as Darcy s law. The most common unit for the permeability is the darcy, which is defined as the flow rate in cm3/s that results when a pressure drop of 1 atm is applied to a porous medium that is 1 cm2 in cross-sectional area and 1 cm long, for a fluid with viscosity of 1 cP. It should be evident that the dimensions of the darcy are L2, and the conversion factors are (approximately) 10 x cm2/darcy C5 10-11 ft2/darcy. The flow properties of tight, crude oil bearing, rock formations are often described in permeability units of millidarcies. 

Intraparticle Mass Transfer. One way biofilm growth alters bioreactor performance is by changing the effectiveness factor, defined as the actual substrate conversion divided by the maximum possible conversion in the volume occupied by the particle without mass transfer limitation. An optimal biofilm thickness exists for a given particle, above or below which the particle effectiveness factor and reactor productivity decrease. As the particle size increases, the maximum effectiveness factor possible decreases (Andrews and Przezdziecki, 1986). If sufficient kinetic and physical data are available, the optimal biofilm thickness for optimal effectiveness can be determined through various models for a given particle size (Andrews, 1988 Ruggeri et al., 1994), and biofilm erosion can be controlled to maintain this thickness. The determination of the effectiveness factor for various sized particles with changing biofilm thickness is well-described in the literature (Fan, 1989 Andrews, 1988)... 

The value of the conversion factor s is determined by the required efficiency of the conversion of component A. By substituting equations (5,6) into equation (4) we find for the ratio of the total ozone consumption to the amount of ozone needed for the oxidation of component A, defined as the Ozone consumption Factor (OF) ... 

The System Internationale (SI) unit for radioactivity is becquerel (Bq), which is defined as one disintegration per second. The SI units and the conversion factors between curie and SI units are listed in Table 15.2. 

The system defines seven base units (Table 1.7), which are independent of each other but which can be combined in various ways to provide a range of derived units (Table 1.8), each one capable of describing a physical quantity. Coherence is maintained in these derived units because no conversion factors are involved at this stage but in order to provide units of convenient size for different applications a series of standard prefixes may be used. These are multipliers used with coherent units to obtain units of alternative size but only one prefix should be used at a time (Table 1.9). 

Appendix. Conversion Factors for Commonly Used Units Universal Constants and Defined Values and Properties of... 

It performs unit conversions with definable conversion factors. 

For chemical reactions and phase transformations, the energy absorbed or liberated is measured as heat. The principal unit for reporting heat is the calorie, which is defined as the energy needed to raise the temperature of 1 gram of water at l4.5° C by a single degree. The term kilocalorie refers to 1,000 calories. Another unit of energy is the joule (rhymes with school), which is equal to 0.239 calories. Conversely, a calorie is 4.184 joules. The translation of calories to joules, or kilocalories to kilojoules, is so common in chemical calculations that you should memorize the conversion factors. 

This works out because the ampere (the standard unit of current, abbreviated A) is defined as 1 coulomb per second. Because this equation gives you the amount of charge that has passed through the circuit during its operating time, all that remains is to calculate the number of moles of electrons that make up that amount of charge. For this, you use the conversion factor 1 mol e = 96,500 C. 

The conversion factor for absolute reaction rate, /, given for each reaction rate-time curve below also is defined as ... 

The viscosity of Newtonian fluids was defined as the ratio of shear stress to rate of shear r/du/dr (the conversion factor gc being temporarily... 

The third-order nonlinear properties are specified in different ways by different authors and several systems of units are used. The conversions between different systems are not always obvious, as the numerical values of the conversion factors may depend on the definitions of particular properties. Table I lists some of the more important conversion factors and units. It should be noted that conversion of n2 values to /3) values can be performed using Eq. (4) in SI units. A frequently utilized conversion is that between n2 values in SI units (cm2 W1) and in cgs units (esu), namely n2 = (C]y3))/n2, where Q is approximately 0.039.7 Calculation of y values can be performed using Eq. (3). Reference 7 provides a discussion of the pitfalls that arise when applying conversion procedures between nonlinear properties defined in different ways. 

The concentration of a substance in solution is usually expressed as molarity (M), defined as the number of moles of a substance (the solute) dissolved per liter of solution. A solution s molarity acts as a conversion factor between solution volume and number of moles of solute, making it possible to carry out stoichiometry calculations on solutions. Often, chemicals are stored as concentrated aqueous solutions that are diluted before use. When carrying out a dilution, only the volume is changed by adding solvent the amount of solute is unchanged. A solution s exact concentration can often be determined by titration. 

The ratio of the nonlinearity to the various absorption coefficients have been calculated using the conversion factor in equation 6 above. W is the figure of merit defined in reference 3, and given by -... 

The strength of the bioassay approach is that it directly estimates the fraction of natural DOC that can be used by a natural microbial assemblage under defined conditions. However, there are numerous manipulations of water samples during bioassay incubations, and the effects of these manipulations on the measured parameters are not well known. For example, containment of water samples can rapidly alter microbial population structure. Nutrients, rather than carbon, can be limiting for microbial utilization of DOM. Moreover, there are no standard protocols for bioassay experiments. Different indicators of DOM utilization are measured by different investigators, and many of the measured parameters rely on conversion factors that are also quite variable. The extent of DOM utilization also depends upon the duration and temperature of the bioassay experiment. Despite these shortcomings, the bioassay experiment remains the best approach for estimating the bioavailability of DOM. 

Defined values for example, unit conversion factors, mathematical constants, or the values of constants used to relate some SI units to fundamental constants. 

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