Neglect

Equations (7b) and (8) into Equation (6), neglecting all third virial coefficients. We then obtain... 

In Equation (13), z and <(iT refer to the monomer of species i while y is the apparent mole fraction of component i, where apparent means that dimerization has been neglected. 

Since attention is here confined to moderate pressures, the last term in Equation (15) can be neglected. The first term in Equation (15) is given by Equation (5), with x s replacing y s. 

For liquid mixtures containing both condensable and noncondensable components. Equation (15) is applicable. However it is now convenient to rewrite that equation. Neglecting, as before, the last term in Equation (15), we obtain ... 

At low pressures, it is often permissible to neglect nonidealities of the vapor phase. If these nonidealities are not negligible, they can have the effect of introducing a nonrandom trend into the plotted residuals similar to that introduced by systematic error. Experience here has shown that application of vapor-phase corrections for nonidealities gives a better representation of the data by the model, oven when these corrections... 

If the data are correlated assuming an ideal vapor, the reference fugacity is just the vapor pressure, P , the Poynting correction is neglected, and fugacity coefficient is assumed to be unity. Equation (2) then becomes... 

Single reactions. Most reaction systems involve multiple reactions. In practice, the secondary reactions can sometimes be neglected, leaving a single primary reaction to consider. Single reactions are of the type... 

The preceding definitions of economic potential and total annual cost can be simplified if it is accepted that they will be used to compare the relative merits of difierent structural options in the flowsheet and difierent settings of the operating parameters. Thus items which will be common to the options being compared can be neglected. 

Japanese industrial success owes much to Japanese management techniques, which we in the West neglect at our peril. The lessons are set out in this important book. 

This method is reserved for heavy fractions. The distillation takes place at low pressure from 1 to 50 mmHg. The results are most often converted into equivalent atmospheric temperatures by using a standard relation that neglects the chemical nature of the components ... 

The effect of pressure is neglected. The limits of this model are easy to understand each component must exist in the liquid state for the Cp/ to be known equally important is that the effect of pressure must be negligible which is the case for < 0.8 and P < 1. 

The difference between the OWC and the FWL is greater in tight reservoirs, and may be up to 30m difference. A difference between gas-oil contact and free oil level exists for the same reasons, but is much smaller, and is often neglected. 

This short-cut method could be repeated to include another variable, and could therefore be an alternative to the previous two methods introduced. This method can always be used as a last resort, but beware that the range of uncertainty narrows each time the process is repeated because the tails of the Input variables are always neglected. This can lead to a false impression of the range of uncertainty in the final result. 

Wells are worked over to increase production, reduce operating cost or reinstate their technical integrity. In terms of economics alone (neglecting safety aspects) a workover can be justified if the net present value of the workover activity is positive (and assuming no other constraints exist). The appropriate discount rate is the company s cost of capital. 

The resistance R is given by the relation. Here, the second term with the amplitude of very little flux in the tube cannot be neglected because it is multiplied by the pulsation (n=27tf. 

Metal-ceramic technology would be -if price problems were neglected- the better choice for a variety of small-power X-ray applications. The problem is that an universal X-ray tube is not (and probably will never be) available. 

Relation 2 allows also to estimate how much deeper a flaw has to be for perception if the granularity increases about 20% as in a mixed system. Neglecting a decrease of the gradient the limiting depth of a flaw would also increase for about 20%, i. e. an increase of 30 pm to 94 pm in this example. 

There are a number of relatively simple experiments with soap films that illustrate beautifully some of the implications of the Young-Laplace equation. Two of these have already been mentioned. Neglecting gravitational effects, a film stretched across a frame as in Fig. II-1 will be planar because the pressure is the same as both sides of the film. The experiment depicted in Fig. II-2 illustrates the relation between the pressure inside a spherical soap bubble and its radius of curvature by attaching a manometer, AP could be measured directly. 

Derive the equation for the capillary rise between parallel plates, including the correction term for meniscus weight. Assume zero contact angle, a cylindrical meniscus, and neglect end effects. 

One problem with this treatment is that it neglects higher-order terms depending on higher moments of i/au that become undefined for slowly decaying interaction potentials (see Problem III-9). 

For the case where the phase /3 is gaseous, cf may be neglected, and quantities ni-65 and III-66 become... 

The thickness of the equivalent layer of pure water t on the surface of a 3Af sodium chloride solution is about 1 A. Calculate the surface tension of this solution assuming that the surface tension of salt solutions varies linearly with concentration. Neglect activity coefficient effects. 

Here (D is the diffusion coefficient and C is the concentration in the general bulk solution. For initial rates C can be neglected in comparison to C/ so that from Eqs. IV-59 and IV-60 we have... 

Assume that an aqueous solute adsorbs at the mercury-water interface according to the Langmuir equation x/xm = bc/( + be), where Xm is the maximum possible amount and x/x = 0.5 at C = 0.3Af. Neglecting activity coefficient effects, estimate the value of the mercury-solution interfacial tension when C is Q.IM. The limiting molecular area of the solute is 20 A per molecule. The temperature is 25°C. 

The ordinary Debye-Huckel interionic attraction effects have been neglected and are of second-order importance. 

On correcting to unit activity Ag (aq), we can obtain E g/Ag - Electron solvation energy is neglected in this definition. 

If the interaction between atoms that are not nearest neighbors is neglected, then the ratios B/A are each equal to the ratio of the number of nearest neighbors to a surface atom (across the dividing plane) to the number of nearest neighbors for an interior atom. The calculation then reduces to that given by Eq. Ill-15. 

Classic nucleation theory must be modified for nucleation near a critical point. Observed supercooling and superheating far exceeds that predicted by conventional theory and McGraw and Reiss [36] pointed out that if a usually neglected excluded volume term is retained the free energy of the critical nucleus increases considerably. As noted by Derjaguin [37], a similar problem occurs in the theory of cavitation. In binary systems the composition of the nuclei will differ from that of the bulk... 

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