Values clarifying

By objective. The process goal of filtration may be diy solids (the cake is the product or value), clarified liquid (the filtrate is the product of value), or both. Good sohds recovery is best obtained by cake filtration, while clarification of the liquid is accomplished by either depth or cake filtration. 

In order to compare the cost-effectiveness of the two measures, the cost-effectiveness ratio for both measures is calculated. The cost-effectiveness ratio for safety measures 1 and 2 is equal to C /Z and C2/Z2, respectively. Safety measure 1 is more cost-effective than safety measure 2 if Ci/Z < C2IZ2. To see whether safety measure 1 is preferred to status quo or not, the cost-effectiveness ratio has to be compared with a reference value, R. The reference value clarifies how much money the decision-maker is willing to pay to obtain one unit of effectiveness. Implementation of the safety measure is preferred to status quo if the decision-maker is willing to pay more to obtain one unit of effectiveness than the cost-effectiveness index expresses, which means that safety measure 1 is preferred to status quo if / > (C,/Z,). 

The CP table. Identification of the essential matches in the region of the pinch is clarified by use of a CP table. In a CP table, the CP values of the hot and cold streams at the pinch are listed in descending order. 

One of the most sensitive tests of the dependence of chemical reactivity on the size of the reacting molecules is the comparison of the rates of reaction for compounds which are members of a homologous series with different chain lengths. Studies by Flory and others on the rates of esterification and saponification of esters were the first investigations conducted to clarify the dependence of reactivity on molecular size. The rate constants for these reactions are observed to converge quite rapidly to a constant value which is independent of molecular size, after an initial dependence on molecular size for small molecules. The effect is reminiscent of the discussion on the uniqueness of end groups in connection with Example 1.1. In the esterification of carboxylic acids, for example, the rate constants are different for acetic, propionic, and butyric acids, but constant for carboxyUc acids with 4-18 carbon atoms. This observation on nonpolymeric compounds has been generalized to apply to polymerization reactions as well. The latter are subject to several complications which are not involved in the study of simple model compounds, but when these complications are properly considered, the independence of reactivity on molecular size has been repeatedly verified. 

This result is known as the Carothers equation. It is apparent that this expression reduces to Eq. (5.4) for the case of f = 2. Furthermore, when f exceeds 2, as in the AA/BB/Af mixture under consideration, then n is increased over the value obtained at the same p for 7= 2. A numerical example will help clarify these relationships ... 

Progress in modelling and analysis of the crack problem in solids as well as contact problems for elastic and elastoplastic plates and shells gives rise to new attempts in using modern approaches to boundary value problems. The novel viewpoint of traditional treatment to many such problems, like the crack theory, enlarges the range of questions which can be clarified by mathematical tools. 

Sedimentation Equipment. Centrifugal sedimentation equipment is usually characterized by limiting flow rates and theoretical settling capabihties. Feed rates in industrial appHcations may be dictated by Hquid handling capacities, separating capacities, or physical characteristics of the soHds. Sedimentation equipment performance is illustrated in Figure 8 on the basis of nominal clarified effluent flow rates and the appHcable values. The... 

The net percentage of soflds in the clarifier underflows increases in going from the first to the second to the third clarifier. Typical values are 11, 15, and 21% soflds, respectively. Clarifier operations have been investigated by computer simulation studies (17). 

Precipitation. Filtered overflow from the first clarifier, 20% BaS solution, is fed to an agitated tank where, on tight control, carbonate values are added in slight excess of stoichiometric requirements. The excess carbonate suppresses soluble barium which would otherwise later precipitate in equipment. 

Adsorption of bath components is a necessary and possibly the most important and fundamental detergency effect. Adsorption (qv) is the mechanism whereby the interfacial free energy values between the bath and the soHd components (sofld soil and substrate) of the system are lowered, thereby increasing the tendency of the bath to separate the soHd components from one another. Furthermore, the soHd components acquire electrical charges that tend to keep them separated, or acquire a layer of strongly solvated radicals that have the same effect. If it were possible to foUow the adsorption effects in a detersive system, in all their complex ramifications and interactions, the molecular picture of soil removal would be greatly clarified. 

The first term on the right side of Eq. (5-179) is so nearly dominant for most furnaces that consideration of the main features of chamber performance is clarified by ignoring the loss terms and Lr or by assuming that they and have a constant mean value. The relation of a modified chamber efficiency T g(1 o) lo modified firing density D/(l — and to the normahzed sink temperature T = T-[/Tp is shown in Fig. 5-23, which is based on Eq. (5-178), with the radiative and convective transfer terms (GSi)/ja(TG — T ) -i- hiAijTc Ti) replaced by a combined radiation/conduction term (GS,) ,a(T - T ). where (GS])/ = (GS])/ + /jiA]/4oTgi Tg is adequately approximated by the arithmetic mean of Tg and T. ... 

Introduction of the local Archimedes criterion helped to clarify nonisothermal jet design procedure. Grimitlyn suggested critical local Archimedes number values, Ar , below which a jet can be considered unaffected by buoyancy forces (moderate nonisothermal jet) Ar, 0.1 for a compact jet, Ar, < 0.15 for a linear jet. 

The ratio to z depends only on (gag-, zjx, = 2/3 tga.g, and the ratio of x, /Xq has a constant value equal to 0.578. To clarify the trajectory equation of inclined jets for the cases of air supply through different types of nozzles and grills, a series of experiments were conducted. The trajectory coordinates were defined as the points where the mean values of the temperatures and velocities reached their maximum in the vertical cross-sections of the jet. It is important to mention that, in such experiments, one meets with a number of problems, such as deformation of temperature and velocity profiles and fluctuation of the air jet trajectory, which reduce the accuracy in the results. The mean value of the coefficient E obtained from experimental data (Fig. 7.25) is 0.47 0.06. Thus the trajectory of the nonisothermal jet supplied through different types of outlets can be calculated from... 

To further clarify the role of magnetic effects on compressibility, a shock compression experiment was performed on an fee 28.5-at. % Ni sample whose initial temperature was raised to 130°C. As is shown in Table 5.1, the compressibility was found to decrease to a value consistent with the nonmagnetic compressibility. Thus, the sharp change in compressibility, the critical values for the transition, and the magnitudes of the compressibility under the various conditions give a clear demonstration that a second-order magnetic transition has been observed, and we will proceed with a quantitative analysis of the transition. 

In many aqueous solutions nickel has the ability to become passive over a wide range of pH values. The mechanism of passivation of nickel and the properties of passive nickel have been studied extensively—perhaps more widely than for any other element, except possibly iron. In recent years the use of optical and surface analytical techniques has done much to clarify the situation . Early studies on the passivation of nickel were stimulated by the use of nickel anodes in alkaline batteries and in consequence were conducted in the main in alkaline media. More recently, however, attention has been directed to the passivation of nickel in acidic and neutral as well as alkaline solutions. 

The situation has now been clarified , and it has been shown that, with a.c., the values obtained are controlled by the capacitance until the frequency has fallen to about 1 Hz. It was shown that under these circumstances, in the absence of corrosion, the resistances of paint films measured by d.c. or a.c. were the same furthermore, no polarisation resistance was detected. 

The vague statement "provided q is not near its extreme values" needs clarifying. Polya (unpublished) proved that (11.2) holds for 2q - 0 p where N p(p-l)/2 Oberschelp [ObeW67] was able... 

Table 5 shows typical values for polyethylene pocket materials of course, for the various producers [60-65] they vary slightly owing to differences in formulation and process. An exact comparison is also difficult, since not all producers state tolerances respectively clarify their statistical base. 

Exercise 1.3. Using the equations introduced in the last problems, generate a potential surface for the H2 molecule assuming that a = —13.6 eV, /3 = —9.5 exp[-/ ] eV (with R in A), D = 0.3 A, and a = 1. Consider only the first iteration with PH = 1 and Z = 1. Adjust the value of /3n to see how it affects the value of the bond energy (the value of E at its minimum). Such a procedure will clarify the point that /3n (as well as the other parameters) are chosen semi-empirically to give the best potential surface for our molecule. 

It must be emphasized that the effective double layer is overall neutral, as the backspillover species (O6, Na6+) are accompanied by their compensating (screening) charge in the metal.32,3,35,36 It must also be clarified that this backspillover formed effective double layer is not in general at its pzc (point of zero charge). This happens only at a specific value of the electrode potential, as in aqueous electrochemistry.37... 

---