Efficiency expression for

It is seen that Eq. (8) is very similar to Eq. (7) except that the velocity used is the outlet velocity, not the average velocity, and that the diffusivity of the solute in the gas phase is taken as that measured at the column outlet pressure (i.e., atmospheric). The shape of the //versus u curve is hyperbolic it has a minimum value of // i at the optimum velocity Uopt (i e., at the optimum velocity, the column will have a maximum efficiency). Expressions for //min and Mopt can be obtained by differentiating Eq. (8) with respect to u and equating to zero, solving for Mop, and substituting Mop, for u in Eq. (8) to obtain // , . 

Frequency-dependent higher-order properties can now be obtained as derivatives of the real part of the time-average of the quasi-energy W j- with respect to the field strengths of the external perturbations. To derive computational efficient expressions for the derivatives of the coupled cluster quasi-energy, which obey the 2n-(-1- and 2n-(-2-rules of variational perturbation theory [44, 45, 93], the (quasi-) energy is combined with the cluster equations to a Lagrangian ... 

This equation gives a compact and efficient expression for the orbital transformation matrix appearing in Eq. (1.52). 

The caustic current efficiency expression for diaphragm cells can be derived from the NaOH material balance in a similar way, employing Eqs. (82) to (86) (see Fig. 4.4.3 for a schematic of the material balance across the ceU, taking into account the BCLs). Thus,... 

Table 1. Values of different efficiency expressions for the cycle in Figure 1. T is in Kelvin scale.

A drawback of the SCRF method is its use of a spherical cavity molecules are rarely exac spherical in shape. However, a spherical representation can be a reasonable first apprc mation to the shape of many molecules. It is also possible to use an ellipsoidal cavity t may be a more appropriate shape for some molecules. For both the spherical and ellipsoi cavities analytical expressions for the first and second derivatives of the energy can derived, so enabling geometry optimisations to be performed efficiently. For these cavil it is necessary to define their size. In the case of a spherical cavity a value for the rad can be calculated from the molecular volume ... 

Current Efficiency. Current efficiency for caustic production in diaphragm and membrane cells can be estimated from collection of a known amount of caustic over a period of time and from a knowledge of the number of coulombs of electricity passed during that time period. An alternative method involves analysis of the gases evolved during electrolysis and determining the anolyte composition. Material balance considerations (7) show the expression for the caustic efficiency for membrane cells to be... 

For estimating CI2 efficiency (Tlcb) term Cl2(a) in equation 14 should be dropped. The corresponding expression for caustic efficiency for diaphragm cells is... 

Equation 16 is the correct material balance expression for calculating the chlorine efficiency of diaphragm cells. Whereas many approximate versions are used (8), the one closest to equation 16 is the "six equation" ... 

For sieve trays, Chan and Fair [Ind. Eng. Chem. Pioc. Des. Dev., 23, 814 (1983)] used a data bank of larger-scale distillation column efficiencies to deduce the following expression for the product kcCi ... 

Detention efficiency. Conversion from the ideal basin sized by detention-time procedures to an actual clarifier requires the inclusion of an efficiency factor to account for the effects of turbulence and nonuniform flow. Efficiencies vaiy greatly, being dependent not only on the relative dimensions of the clarifier and the means of feeding but also on the characteristics of the particles. The cui ve shown in Fig. 18-83 can be used to scale up laboratoiy data in sizing circular clarifiers. The static detention time determined from a test to produce a specific effluent sohds concentration is divided by the efficiency (expressed as a fraction) to determine the nominal detention time, which represents the volume of the clarifier above the settled pulp interface divided by the overflow rate. Different diameter-depth combinations are considered by using the corresponding efficiency factor. In most cases, area may be determined by factors other than the bulksettling rate, such as practical tank-depth limitations. 

Equation (12-17) is called the photostationary state expression for ozone. Upon examination, one sees that the concentration of ozone is dependent on the ratio NO2/NO for any value of k. The maximum value of k is dependent on the latitude, time of year, and time of day. In the United States, the range of k is from 0 to 0.55 min T Table 12-5 illustrates the importance of the NO2/NO ratio with respect to how much ozone is required for the photostationary state to exist. The conclusion to be drawn from this table is that most of the NO must be converted to NO2 before O3 will build up in the atmosphere. This is also seen in the diurnal ambient air patterns shown in Fig. 12-2 and the smog chamber simulations shown in Fig. 12-3. It is apparent that without hydrocarbons, the NO is not converted to NO2 efficiently enough to permit the buildup of O3 to levels observed in urban areas. 

This equation, although originating from the plate theory, must again be considered as largely empirical when employed for TLC. This is because, in its derivation, the distribution coefficient of the solute between the two phases is considered constant throughout the development process. In practice, due to the nature of the development as already discussed for TLC, the distribution coefficient does not remain constant and, thus, the expression for column efficiency must be considered, at best, only approximate. The same errors would be involved if the equation was used to calculate the efficiency of a GC column when the solute was eluted by temperature programming or in LC where the solute was eluted by gradient elution. If the solute could be eluted by a pure solvent such as n-heptane on a plate that had been presaturated with the solvent vapor, then the distribution coefficient would remain sensibly constant over the development process. Under such circumstances the efficiency value would be more accurate and more likely to represent a true plate efficiency. 

Fractional efficiency The efficiency of a device expressed for different fractions, e.g., the efficiency of a filter for particles of different sizes. 

For the (CICBT)iXr, (CBCBT)iXr and (CICBTBT)iXr cycles, with equal pressure ratios across the split compressors and turbines, it may be shown that the corresponding expressions for efficiency are... 

A problem often encountered in practice is to determine what is the most efficient method for removing a substance quantitatively from solution. It can be shown that if V mL of, say, an aqueous solution containing x0 g of a solute be extracted n times with u-mL portions of a given solvent, then the weight of solute xn remaining in the water layer is given by the expression ... 

The only physical difference is that here the current, I, is not directly measurable and thus the dimensionless current density, J, is not directly computable. This difficulty can, however, be overcome if the ratio of the reactivities, A, of normally adsorbed and backspillover oxygen is known (e.g. from electrochemical promotion experiments, where A, as already noted, also expresses the Faradaic efficiency). Thus in this case upon combining the definition of A with equation (11.23) one obtains the following expression for J ... 

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