Equivalent-Area Concept

Equivalent-Area Concept The preceding equations for batch operations, particularly Eq. 11-35 can be appliedforthe calculation of heat loss from tanks which are allowed to cool over an extended period of time. However, different surfaces of a tank, snch as the top (which would not be in contact with the tank contents) and the bottom, may have coefficients of heat transfer which are different from those of the vertical tank walls. The simplest way to resolve this difficulty is to nse an equivalent area A in the appropriate equations where... 

The second principle relates to the equivalent-thickness concept of pipe insulation. Since the outer insulation surface area is greater than the interior surface area, the heat flux sees a greater insulation thickness than the installed nominal thickness of the material. This equivalent thickness (eq tk) is used as the insulation thickness for the thermal calculation, but the nominal thickness is used for calculating the surface area per Unear foot of insulated pipe.The equation for equivalent thickness is ... 

Per capita flow varies from <378 L/d (2) for a residential community to >1134 L/d for highly industrialized areas. The concept of population equivalent is used for evaluating industrial waste contributions to sewage. It is appHed when planning for hydrauhc and BOD loadings. 

The European philosophy on area classification varies from that of the United. States and Canada. Specifically, in Europe and most other inter national areas, the Zone concept is utilized. An area in which an expio sive gas-air mixture is continuously present, or present for long perioiK of time, is referred to as Zone 0. The vapor space of a closed, but vented, process vessel or storage tank is an example. An area in which an explosive gas-air mixture is likely to occur in normal operations is designated Zone 1. An area in which an explosive gas-air mixture is less likely to occur, and if it does occur will exist only for a short time, is designated Zone 2. Zone 0 and Zone 1 correspond to Division 1 in the U.S. and Canada System. Zone 2 is equivalent to Division 2. 

In the models discussed thus far in this section, emphasis has been placed on electrostatic effects and solvent polarity. An alternative view that to some extent takes other forces into account begins with the idea that, in order to dissolve a solute molecule in a solvent, energy is required to create a cavity in the solvent the solute is then inserted into this cavity. In Section 8.2 we saw that the energy to create a cavity can be expressed as a product of the surface area of the cavity and the surface tension of the solvent. An equivalent expression is obtained as the product of the volume of the cavity and the pressure exerted by the solvent, and we now explore this concept. 

The concept of growth functions is covered in more detail in Sec. 3.6. Liu and Litster (1993a) looked at two cases ofEq. (7). The first assumed that k = 0, which is equivalent to assuming that, on average, each particle spends the same amount of time in the spray over a long period of time. Thus, G should be proportional to the projected surface area of the particle (assumed spherical) or... 

This conception of an 8, 2 reaction as an electron-shift process is obviously equivalent to its conception as an inner sphere electron transfer, i.e. a single electron transfer concerted with the breaking of the R—X bond and the formation of the R—Nu bond. Faced with an experimental system, however, the first question—ET or 8 2 —still remains, whatever intimate description of the 8, 2 reaction one may consider most appropriate. If this is thought of in terms of inner sphere electron transfer, the question thus raised is part of the more general problem of distinguishing outer sphere from inner sphere electron-transfer processes (Lexa et ai, 1981), an actively investigated question in other areas of chemistry, particularly that of coordination complex chemistry (Taube, 1970 Espenson, 1986). 

The concept of specific area defined by Equation (1) is important because this is a quantity that can be measured experimentally for finely divided solids without any assumptions as to the shape or uniformity of the particles. We discuss the use of gas adsorption to measure Asp in Chapter 9. If the particles are known to be uniform spheres, this measured quantity may be interpreted in terms of Equation (2) to yield a value of Rs. If the actual system consists of nonuniform spheres, an average value of the radius may be evaluated by Equation (2). Finally, even if the particles are nonspherical, a quantity known as the radius of an equivalent sphere may be extracted from experimental values. This often proves to be a valuable way of characterizing an array of irregularly shaped particles. We have a good deal more to say about average dimensions in this chapter and about equivalent spheres in Chapter 2. 

Identification of area as the two-dimensional equivalent of volume is a straightforward geometrical concept. That tt should be interpreted as the two-dimensional equivalent of pressure is not so evident, however, even though the notion was introduced without discussion in Chapter 6, Section 6.6. Figure 7.3 helps to clarify this equivalency as well as suggest how to compare quantitatively two- and three-dimensional pressures. The figure sketches a possible profile of the air-water surface with an adsorbed layer of amphipathic molecules present. In... 

Another useftil concept is flux. Flux is defined as the number of molecules penetrating a unit area of an imaginary plane in a unit of time. The usual units are mol/(cm2 s), and the sign identifies the direction of motion, positive toward and negative away from the plane. The prior assertion that equilibrium demands no net mass transport is equivalent to a requirement that the sum of the fluxes of all components is exactly zero at any test plane within the system. Flux is a measure of the rate of mass transport at a fixed point. Its electrochemical relevance stems from the direct relationship it holds to electrode current. 

The concept of the surface diameter may be mostly used in the field of adsorption and reaction engineering, where the equivalent surface exposure area is important. The determination of the surface area depends on the method of measurements for example, permeametry can give a much lower area than does gas adsorption. The latter often includes the contribution of pore surface area, which is accessible to the gas molecules. The determination of particle surface area by gas adsorption is given in 1.2.2.4. The fundamentals of gas adsorption are further covered in 1.4.1. 

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