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** Equilibrium calculations simplifying assumptions **

** Simplifying assumptions incompressibility **

** Simplifying assumptions no-slip at the wall **

** Simplifying assumptions steady state approximation **

** Simplifying assumptions used in analysis **

Since we make the simplifying assumption that the partial molar volumes are functions only of temperature, we assume that, for our purposes, pressure has no effect on liquid-liquid equilibria. Therefore, in Equation (23), pressure is not a variable. The activity coefficients depend only on temperature and composition. As for vapor-liquid equilibria, the activity coefficients used here are given by the UNIQUAC equation. Equation (15). [Pg.63]

With these simplifying assumptions equations (12 13) and (12.14) reduce to [Pg.163]

The McCabe-Thiele method employs the simplifying assumption that the molal overflows in the stripping and the rectification sections are constant. This assumption reduces the rectifying and stripping operating line equations to [Pg.162]

In the independent particle approximation, the simplifying assumption is made that V i) is an average potential due to a core that consists of the nuclei and all elections other than elechon i [Pg.175]

If we do not make any simplifying assumptions, we must calculate the matrix [Pg.232]

The microscopic contour of a meniscus or a drop is a matter that presents some mathematical problems even with the simplifying assumption of a uniform, rigid solid. Since bulk liquid is present, the system must be in equilibrium with the local vapor pressure so that an equilibrium adsorbed film must also be present. The likely picture for the case of a nonwetting drop on a flat surface is [Pg.378]

The standard chemical potentials are approximately tire same if tire surfactant in each aggregate sees nearly tire same interaction witli tire solvent. This simplifying assumption tlien gives [Pg.2586]

Witn the advent of electronic computers, it is no longer necessary to make drastic simplifying assumptions to reduce the [Pg.25]

Reaction (5) proceeds mostly heterogeneously, reaction (6) mostly homogeneously. This mechanism can be integrated with simplifying assumptions to demonstrate the main features of gas-phase explosion kinetics [8] [Pg.792]

A number of simulation methods based on Equation (7.115) have been described. Thess differ in the assumptions that are made about the nature of frictional and random forces A common simplifying assumption is that the collision frequency 7 is independent o time and position. The random force R(f) is often assumed to be uncorrelated with th particle velocities, positions and the forces acting on them, and to obey a Gaussiar distribution with zero mean. The force F, is assumed to be constant over the time step o the integration. [Pg.405]

X- ) quantities. In practice, the complexity of the general relationship between and X- means that progress requires the introduction of certain simplifying assumptions. These usually follow from symmetry [Pg.1291]

Now in principle each layer will have its own values of a, q, and v, and consequently the summation of Equation (2.11) cannot be carried out unless simplifying assumptions are made. Brunauer, Emmett and Teller made three such assumptions (a) that in all layers except the first the heat of adsorption is equal to the molar heat of condensation q, (b) that in all layers except the first the evaporation-condensation conditions are identical, i.e. that [Pg.44]

Rate laws have also been observed that correspond to there being two kinds of surface, one adsorbing reactant A and the other reactant B and with the rate proportional to 5a x 5b- For traditional discussions of Langmuir-Hinshelwood rate laws, see Refs. 240-242. Many catalytic systems involve a series of intermediates, and the simplifying assumption of steady-state equilibrium is usually made. See Boudart and co-workers [243-245] for a contemporary discussion of such complexities. [Pg.728]

The maximum temperature cross which can be tolerated is normally set by rules of thumb, e.g., FrSQ,75 °. It is important to ensure that Ft > 0.75, since any violation of the simplifying assumptions used in the approach tends to have a particularly significant effect in areas of the Ft chart where slopes are particularly steep. Any uncertainties or inaccuracies in design data also have a more significant effect when slopes are steep. Consequently, to be confident in a design, those parts of the Ft chart where slopes are steep should be avoided, irrespective of Ft 0.75. [Pg.223]

There are different possibilities to address the above set of equations which can be solved provided 2in > 3i, and provided the measured ToF information varies between measurement points. For the purpose of the present work we have taken two simplifying assumptions (a) one virtual source predominates at each measurement point, m and (b) each virtual source predominates at more than one measurement point. Note that assumption (b) ensures the condition 2m > 3i that is necessary to obtain solutions for Equations (2) and (3). These assumptions are justified by considering the defect surface as an acoustic secondary field source. At each measurement point the transducer predominantly receives signals from an [Pg.165]

This is a third set of equations that essentially allows us to locate a virtual source for every two adjacent measurements. Intuitively this can be simply described as finding the point of intersection of two radii of lengths and Therefore the simplifying assumptions [Pg.165]

The kinetics of the ethylene hydration reaction have been investigated for a tungstic oxide—siHca gel catalyst, and the energy of activation for the reaction deterrnined to be 125 kJ/mol (- 30 kcal/mol) (106,120). The kinetics over a phosphoric acid-siHca gel catalyst have been examined (121). By making some simplifying assumptions to Taft s mechanism, a rate equation was derived [Pg.405]

The physical properties of the liquid, rather than those of the vapor, are used For determining the film coefficient for condensation. Nus-selt [2. Ver. Dt.sch. Ing., 60, 541, 569 (1916)] derived theoretical relationships for predicting the film coefficient of heat transfer for condensation of a pure saturated vapor. A number of simplifying assumptions were used in the derivation. [Pg.566]

Table 3 shows results obtained from a five-component, isothermal flash calculation. In this system there are two condensable components (acetone and benzene) and three noncondensable components (hydrogen, carbon monoxide, and methane). Henry s constants for each of the noncondensables were obtained from Equations (18-22) the simplifying assumption for dilute solutions [Equation (17)] was also used for each of the noncondensables. Activity coefficients for both condensable components were calculated with the UNIQUAC equation. For that calculation, all liquid-phase composition variables are on a solute-free basis the only required binary parameters are those for the acetone-benzene system. While no experimental data are available for comparison, the calculated results are probably reliable because all simplifying assumptions are reasonable the [Pg.61]

See also in sourсe #XX -- [ Pg.121 ]

** Equilibrium calculations simplifying assumptions **

** Simplifying assumptions incompressibility **

** Simplifying assumptions no-slip at the wall **

** Simplifying assumptions steady state approximation **

** Simplifying assumptions used in analysis **

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