Johnstone equation

Express the individual collection efficiency in terms of dp. Use the Johnstone equation ... 

Three identical venturi scrubbers are connected in series. If each operates at the same efficiency and liquid-to-gas ratio, qilqg, calculate the liquid-to-gas ratio, assuming the Johnstone equation to apply. Data are provided below. 

Using the Johnstone equation, solve for the liquid-to-gas ratio, qi/qa. ln(l... 

Unlike the Johnstone equation approach, this method requires specifying two coefficients. The validity and accuracy of the coefficients available from the literature for the contact power theory equations have been questioned. Some numerical values of a and fi for specific particulates and scrubber devices are provided below. 

The glass transition temperatures of copolymers with high content of NVK deviate from Flory-Fox or Gordon-Tailor equations, but they fit the Johnston equation. 

A reasonable agreement can be achieved between the theoretical and practical values of Tg by using the Fox-Johnston equation. 

The three representations that are referred to in this study are (1) macroscopic representations that describe the bulk observable properties of matter, for example, heat energy, pH and colour changes, and the formation of gases and precipitates, (2) submicroscopic (or molecular) representations that provide explanations at the particulate level in which matter is described as being composed of atoms, molecules and ions, and (3) symbolic (or iconic) representations that involve the use of chemical symbols, formulas and equations, as well as molecular structure drawings, models and computer simulations that symbolise matter (Andersson, 1986 Boo, 1998 Johnstone, 1991, 1993 Nakhleh Krajcik, 1994 Treagust Chittleborough, 2001). 

This method was developed by Johnston et al. in 1991 and well described in Ref. [10], according to which the method is introduced as follows. The principle of optical interference is shown schematically in Fig. 1. A coating of transparent solid, typically silica, of known thickness, is deposited on top of the semi-reflecting layer. This solid thus permanently augments the thickness of any oil film present and is known as a "spacer layer. The destructive interference now obeys the equation ... 

These equations are all that is needed to describe a creep test at constant stress, but to describe tensile (or compression) tests, the machine being used must be taken into account because the elastic stiffness of the machine plays an important role. See Gilman and Johnston (1962). 

Use the critical constants for hydrogen given in Table 5.3 to calculate the parameters a and b for the van der Waals and Redlich-Kwong equations for hydrogen. Use each of these equations to calculate the compressibility factor z for hydrogen as a function of l/Vm at 50 K between 0.1 Mpa and 20 MP, and compare your calculated values with the experimental values of Johnston and White [16]. 

Baron, Manning, and Johnstone (B4) have discussed the experimental aspects of the tubular-reactor problem, and an analysis of the results is made by means of the solution to the differential equations for mass... 

Mathivanan, Johnston and Wayner examined the effect of substituents on the rates of cleavage of a-phenoxyacetophenone radical anions (equation 6)43. In this study, the radical anions were generated by trapping solvated electrons produced by laser-induced photoionization of 4,4 -dimethoxystilbene in CH3CN and DMF. Their results show that the fragmentation rate is enhanced when Y is electron withdrawing, but retarded when X is electron withdrawing. 

Equation (27) is known as Johnston s irreducibility criterion (Johnston (I960)). 

Polar effects in radical reactions seem also not quite well understood. There are some attempts to divide radicals into electrophilic and nucleophilic classes (Pryor, 1966 Pryor et al., 1969 Johnston et al., 1966) resembling the pattern of ionic reactants, generally on the basis of the Hammett equation. This classification, however, seems to be alien to the nature of most carbon radicals. In addition reactions (2) the Hammett />-value is usually positive (radical addition to substituted nitrobenzenes Bartlett and Kwart, 1950, 1952 Sinitsyna and... 

Following Twu et al [6] and Johnston et al [7] and simulation packages such as PRO II, the interaction parameter will be allowed to vary with temperature to account for some of the inaccuracies in the equation of state ... 

An equation relating the viscosity of dispersions to the relation

[Pg.111]

An alternative equation, also derived by Marcus18, is from Johnston s19 BEBO calculation of activation energies. It is specifically useful for these H atom transfer processes. This is Eq. (5), with the terms as above. 

Plasmas typical of C02 laser discharges operate over a pressure range from 1 Torr to several atmospheres with degrees of ionization, that is, nJN (the ratio of electron density to neutral density) in the range from 10-8 to 10-8. Under these conditions the electron energy distribution function is highly non-Maxwellian. As a consequence it is necessary to solve the Boltzmann transport equation based on a detailed knowledge of the electron collisional channels in order to establish the electron distribution function as a function of the ratio of the electric field to the neutral gas density, E/N, and species concentration. Development of the fundamental techniques for solution of the Boltzmann equation are presented in detail by Shkarofsky, Johnston, and Bachynski [44] and Holstein [45]. 

Studies by many authors, e. q. on copolymerizations of styrene with a-methylstyrene (characterized by low Tc, 334 K), appear to agree with the ideas of Lowry. Some author claim, however, that even copolymerization of this pair can be described by the simple copolymerization equation [221], Johnston and Rudin are of the opionion that the depropagation reaction is not as important in this case because only short sequences of a-methylstyrene are produced. The formation of short blocks is accompanied by relatively high polymerization enthalpy. They are thermodynamically more stable than the homopolymer and have a higher Tc. Only at considerably higher copolymerization temperatures (with the pair styrene—a-methylstyrene > 420 K) does the depropagation effect become important. 

H. S. Johnston and D. M. Yost, ibid., 17, 386 (1949). It is of course assumed that this reaction 5 is the slow step in the synthesis of N2O6 and may be equated to the experimental rate constant. However, the data cover a fairly wide range of pressures, and it is difficult to see any other mechanism for this veiy simple reaction. Reaction 2 must of course be fast with respect to reaction 5 for these kinetics to be obeyed, and it appears that reaction 2 must go at about 1 in every 100 collisions betw een NO2 and NO3, which would not be surprising for a recombination reaction of this type. A similar efficiency (1 in 200 collisions) has been found for 2NO2 — N2O4. T. Carrington and... 

A semi-empirical model of the energy barrier to proton transfer is based on a Johnston type equation. According to Johnston [131], the energy barrier in gas phase hydrogen atom abstraction reactions is described by the equation... 

Bradshaw et al. (B3) use Eqs. (40) to derive a differential equation for the turbulent shear stress t. The transport velocity Qa is taken as (Tmei/p), where Tm x is the maximum value of riy) in the boundary layer. G and I are prescribed as functions of the position across the boundary layer, and o is essentially taken as constant. Together with Eqs. (10a,b), Eq. (36) gives a closed set of equations for U, V, and t this system is of hyperbolic type, with three real characteristic lines. Bradshaw et al. construct a numerical solution using the method of characteristics it can also be done using small streamwise steps with an explicit difference scheme (Nl A. J. Wheeler and J. P. Johnston, private communications). There is a great physical appeal to the characteristics, especially since it is found that the solutions along the outward-going characteristic dominates the total solution. This... 

Bradshaw (Bl) extended his MTES method to three-dimensional boundary layers, using the basic ideas to propose model equations for the vector sum and ratios of the two primary stresses, —uv and —wv. Johnston (J1) has compared the result of predictions by this method with his own data for an infinite swept flow. In particular, data show that the stress vector does not align with the strain-rate vector as the Newtonian closures assume. It was hoped Bradshaw s structural model would work better on this flow but Johnston s calculation shows that the angle of the shear stress vector is predicted quite poorly, although the mean velocity is predicted quite well. It is unlikely that MTE methods will ever predict this structural difference well, and one might hope that MRS methods will do considerably better. 

EXAMPLE 7-7 Johnston, Cuta, and Garrett found that the solubility of silver oxide in sodium hydroxide solutions could be expressed by the equation S = 5 x 10 /[OH ] -I- 1.95 X 10 [OH ]. Comparing this equation with (7-36), we find... 

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