Empirical correction factors

Harkins and Jordan [43] found, however, that Eq. 11-26 was generally in serious error and worked out an empirical correction factor in much the same way as was done for the drop weight method. Here, however, there is one additional variable so that the correction factor/ now depends on two dimensionless ratios. Thus... 

The flow in a heat exchanger will clearly not be isothermal, and this is allowed for by including an empirical correction factor to account for the change in physical properties with temperature. Normally only the change in viscosity is considered ... 

The equations for estimating nucleate boiling coefficients given in Section 12.11.1 can be used for close boiling mixtures, say less than 5°C, but will overestimate the coefficient if used for mixtures with a wide boiling range. Palen and Small (1964) give an empirical correction factor for mixtures which can be used to estimate the heat-transfer coefficient in the absence of experimental data ... 

Internal mixing air-assist atomizer. Derived from wax spray data in Ref. 461 using NOTE atomizer Good agreement with fuel-air or fiiel-steam spray data 11031 Discrepant with water-air spray data 179114621 MMD is to be multiplied by an empirical correction factor for conditions of droplet coalescence. 

Nagaoka s equation (Nagaoka et al, 1955) is an extension of Plank s model and takes into account the time required to reduce the temperature from an initial temperature T, above the freezing poinf. The lafenf heat of fusion in equafion 3.3 is replaced by the total enthalpy change A/i which includes the sensible heat which must be removed in reducing the temperature from an initial T and in addition an empirical correction factor is included. Thus... 

Approximate derivation o Tobwg)- Given values of and the basic BWG treatment also leads to explicit equations for the ordering temperature, T ", but the omission of sro inevitably leads to calculated values that are appreciably higher than shown by experiment. If the simplicity of the BWG method is to be retained, an empirical correction factor (x) has to be included, where X = Typical equations for various structural transitions are given... 

The empirical correction factors 4> (calculated on assumption that for all networks swollen in pure water % from Eq. (6) should be 0.48) change between 0.05 and 0.3 (see Ref. [48] for salt I the data are in Fig. 8). Generally, we can say that the effect of the positive charge on the formation and extent of transition is 5 to 10 times smaller than the effect of MNa. There are probably several reasons for the low value of (a) positive charges are localized at a larger distance from the main chain (smaller influence on the chain conformation) (b) due to the... 

This chapter will first provide some basics on ozone mass transfer, including theoretical background on the (two-) film theory of gas absorption and the definition of over-all mass transfer coefficients KLa (Section B 3.1) as well as an overview of the main parameters of influence (Section B 3.2). Empirical correction factors for mass transfer coefficients will also be presented in Section B 3.2. These basics will be followed by a description of the common methods for the determination of ozone mass transfer coefficients (Section B 3.3) including practical advice for the performance of the appropriate experiments. Emphasis is laid on the design of the experiments so that true mass transfer coefficients are obtained. 

The disadvantages of using empirical correction factors, which lump many parameters together, becomes clear when one considers that a and 0 have been found to change depending on not only the concentration and type of contaminants, but also on the hydrodynamics of the system. Clearly, a better understanding of the relationship between physical properties and kLa and the quantification of these physical properties in (waste-)water is necessary, so that correlations based on dimensional analysis can be made. However, from the practical point of view, the empirical correction factors have proven their worth, when measured and used appropriately. 

The empirical correction factors are developed from comparing two mass transfer coefficients, thus, it is essential that both are measured correctly. Brown and Baillod (1982) point out that the a value from the ratio of two incorrectly measured mass transfer coefficients, apparent mass transfer coefficients, is different from the a of true mass transfer coefficients. 

Tooker [2] then used this approach to formulate a means of calculating the extract air requirements for enclosures, such as conveyor transfer stations. The equations of Hemeon [1] and Tooker [2], and variations thereon, are used widely in industry. However, they generally grossly over-predict the rate of air entrainment unless empirical correction factors... 

If we express EM in terms of free energies we obtain Equation 10.13 and we can recognise that RTIn (EM) is an empirical correction factor when an intermolecular process is replaced by an intramolecular one. If we substitute into Equation 10.13 the separate enthalpy and entropy terms and recognise that in a strain free ring AE/ nter = AHintm we get Equation 10.14. 

Fortunately for us, we wish only to calculate IR spectra that resemble, or would resemble, experimental ones, and for this there is a simple expedient. Calculated and observed frequencies differ by a fairly constant factor, and ab initio (and other theoretically-calculated) frequencies can be brought into reasonable agreement with experiment by multiplying them by a correction factor. An extensive comparison by Scott and Radom of calculated and experimental frequencies [80] has provided empirical correction factors for frequencies calculated by a variety of methods. A few of the correction factors from this compilation are ... 

In the authors opinion the outstanding questions to be examined now and in future work include the following, (i) Can use of an effective n be justified If so, does it provide a useful predictive empirical correction factor (ii) Many environments in which the donor and acceptor reside are complex in structure. These include proteins and nanostructured materials, for example. To what extent can a polarizable continuum model be applied in these situations (iii) Extending such arguments, there can be a... 

The empirical correction factors networks swollen in pure water x from Eq. (6) should be 0.48) change between... 

In this context, a frankly empirical approach was adopted by earlier workers not yet blessed by Debye and Huckel s light. Solutions that obeyed Eq. (3.52) were characterized as ideal solutions since this equation applies to systems ofnoninteracting solute particles, i.e., ideal particles. Electrolytic solutions that do not obey the equation were said to be nonideal. In order to use an equation of the form of Eq. (3.52) to treat nonideal electrolytic solutions, an empirical correction factor was introduced by Lewis as a modifier of the concentration term ... 

This equation is also a consequence of Eqs. 9.19 and 9.20. The distance between the piezotransducers, d, can be determined from measurements of (f - f i) for the resonator filled with a liquid of known ultrasonic velocity, c. Based on the simple model for an ideal resonator, Eqs. 9.21 and 9.22 work surprisingly well in real resonators at frequencies that are close to the resonance frequency of the piezotransducer. These equations have been widely used with high-resolution measurements of ultrasonic velocity in liquids. The scope of these equations has been expanded by including empirical correction factors [70]. 

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