Calculators using

To use Equation (10b), we require virial coefficients which depend on temperature. As discussed in Appendix A, these coefficients are calculated using the correlation of Hayden and O Connell (1975). The required input parameters are, for each component critical temperature T, critical pressure P, ... 

To illustrate calculations for a binary system containing a supercritical, condensable component. Figure 12 shows isobaric equilibria for ethane-n-heptane. Using the virial equation for vapor-phase fugacity coefficients, and the UNIQUAC equation for liquid-phase activity coefficients, calculated results give an excellent representation of the data of Kay (1938). In this case,the total pressure is not large and therefore, the mixture is at all times remote from critical conditions. For this binary system, the particular method of calculation used here would not be successful at appreciably higher pressures. 

Figure 17 shows results for the acetonitrile-n-heptane-benzene system. Here, however, the two-phase region is somewhat smaller ternary equilibrium calculations using binary data alone considerably overestimate the two-phase region. Upon including a single ternary tie line, satisfactory ternary representation is obtained. Unfortunately, there is some loss of accuracy in the representation of the binary VLB (particularly for the acetonitrile-benzene system where the shift of the aceotrope is evident) but the loss is not severe. 

However, when carboxylic acids are present in a mixture, fugacity coefficients must be calculated using the chemical theory. Chemical theory leads to a fugacity coefficient dependent on true equilibrium concentrations, as shown by Equation (3-13). ... 

Equilibrium constants,, for all possible dimerization reactions are calculated from the metastable, bound, and chemical contributions to the second virial coefficients, B , as given by Equations (6) and (7). The equilibrium constants, K calculated using Equation (3-15). 

Finally, at low pressures, the liquid fugacity can be calculated using Equation (5), i.e. we can assume that <() = 1 and that the Poynting correction = 1. 

CALCULATION USING K-FACTORS CALCULATED IN SUBROUTINE VPLOK... 

Second virial coefficients are calculated using the equations for the Hayden-0 Connell correlation (see Appendix A). 

Bubble-point and dew-point pressures are calculated using a first-order iteration procedure described by the footnote to Equation (7-25). 

Calculate factors for those streams which require a specification different from that of the reference using Eq. (7.23) or Eq. (7.24). If Eq. (7.23) is to be used, then the actual network area Anetwork must first be calculated using either Eq. (7.6) or Eq. (7.19) and (VuNiTs or - SHELLS, whichever is appropriate. 

Lattice energies may be derived from the Born-Haber cycle or calculated using the Kapustinskii equation. ... 

A quantitative theory of rate processes has been developed on the assumption that the activated state has a characteristic enthalpy, entropy and free energy the concentration of activated molecules may thus be calculated using statistical mechanical methods. Whilst the theory gives a very plausible treatment of very many rate processes, it suffers from the difficulty of calculating the thermodynamic properties of the transition state. 

The acentric factor is calculated using Edmister s equation (1948) ... 

Each fluid is described by a BWR equation of state whose coefficients are adjusted to obtain simultaneously the vapor pressure, enthalpies of liquid and gas as well as the compressibilities. The compressibility z of any fluid is calculated using the equation below ... 

The specific heat of gases at constant pressure is calculated using the principle of corresponding states. The for a mixture in the gaseous state is equal to the sum of the C g of the ideal gas and a pressure correction term ... 

The Cpg of real gas is calculated using the equation derived from the Lee and Kesler model ... 

When the critical constants for a pure substance or the pseudocritical constants for a petroleum fraction are known, the vapor pressure for hydrocarbons and petroleum fractions can be calculated using the Lee and Kesler equations ... 

For direct measurement from core samples, the samples are mounted in a holder and gas is flowed through the core. The pressure drop across the core and the flowrate are measured. Providing the gas viscosity (ji) and sample dimensions are known the permeability can be calculated using the Darcy equation shown below. 

Once y/" has been determined, the impedance change in an eddy-current coil due to the crack can be calculated using the following integral over the crack mouth [3] ... 

The 3D positions of internal defects are calculated with a stereoscopic approach supporting arbitrary sample manipulations using an arbitrary number of views. The volumes of the defects are calculated using intensity evaluation. 

The epipolar constrains calculated using the estimated camera parameters restrict the search for corresponding image features in different images to a ID search. Taking the uncertainty of the epipolar constrains into account, in our approach, the search is restricted to a small area around the epipolar lines in the images. 

The volume of defects is calculated using intensity evaluation. Considering the polychromatic radiation of microfocus X-ray tubes the X-ray beam is represented by an energy dependent intensity distribution Io(E). The intensity Ip behind a sample of thickness s is given by integrating the absorption law over all energies ... 

The case considered above corresponds to R < H. The calculation using formula (1) gives the next results. For example, consider the thickness of dry developer layer h = 20 pm. In the absence of sedimentation process our product family (penetrant and developer indicated above) could not detect the cracks with the depth lo < 1,33 mm of any widths. Nevertheless due to the sedimentation one can get the decrease of developer s thickness from h = 20 pm till h s 5 pm. As a result, our product family can ensure the detection of the cracks with H > 2,3 pm even with very small length lo = 0,4 mm. At the same time if lo = 1 mm, then the cracks with extremely small width H > 0,25 will be revealed. 

One more obvious example illustrates strong influence of particle s sedimentation upon the sensitivity threshold. Assume that we have to ensure the detection of the cracks with the depth 10 > 2 mm in the case when the same product family indicated above is applied and h = 20 pm. The calculation using formula (1) shows that in the absence of sedimentation only the cracks with the width H > 2 pm could be detected. But when the effect of sedimentation results in the reduction of the value of developer layer thickness from h = 20 pm to h = 8 pm, then the cracks of substantially smaller width H > 0,17 pm can be revealed at the same length lo = 2 mm. Therefore we can state that due to the sedimentation of developer s particles the sensitivity threshold has changed being 12 times smaller. Similar results were obtained using formula (2) for larger particles of the developers such as kaolin powder. 

Each experimential values and the calculative values in Fig.7 and Fig.9 are almost corresponding except for the region of the echo height F/B rapidly decreases. This reason is thought that the experiment using a pulse wave but the calculative using a continuous wave. 

The ultrasound wave with the amplitude po enters the contrast agent at the point xq. cu can be calculated using... 

With four transducers the coordinates for the eccentricity can be calculated using X=Vi X- minus X+) and Y=>/2 (Y- minus Y+)... 

Calculate, using the data of Fig. III-9a and Eq. III-53, the surface tension versus mole fraction plot for mixtures of cyclohexane and benzene. 

Calculate 7wh for the cyclohexane-water interface using the Good-Fowkes approach. Repeat the calculation using Eq. IV-13. Compare both results with the experimental value and comment. 

The are essentially adjustable parameters and, clearly, unless some of the parameters in A2.4.70 are fixed by physical argument, then calculations using this model will show an improved fit for purely algebraic reasons. In principle, the radii can be fixed by using tables of ionic radii calculations of this type, in which just the A are adjustable, have been carried out by Friedman and co-workers using the HNC approach [12]. Further rermements were also discussed by Friedman [F3], who pointed out that an additional temi is required to account for the fact that each ion is actually m a cavity of low dielectric constant, e, compared to that of the bulk solvent, e. A real difficulty discussed by Friedman is that of making the potential continuous, since the discontinuous potentials above may lead to artefacts. Friedman [F3] addressed this issue and derived... 

Figure A2.5.6 shows a series of typical p, Fisothemis calculated using equation (A2.5.1). (The temperature, pressure and volume are in reduced units to be explained below.) At sufficiently high temperatures the pressure decreases monotonically with increasing volume, but below a critical temperature the isothemi shows a maximum and a minimum.

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