Influence coefficient balancing

Practical applications of the influence coefficient method to multiplane, multispeed balancing are presented by Badgley and the author. The separate problem of choosing balancing planes is discussed at some length by Den Hartog, Kellenberger, and Miwa for the (N + 2)-plane method, and by Bishop and Parkinson in the V-plane method. 

Using the influence coefficient technique for multiplane balancing is simply an extension of the logic, which is hardwired into the standard balancing machine. This extension has been made possible by the availability of better electronics and easier access to computers. 

Tessarzik, J.M., Badgley, R.H., and Anderson, W.J., Flexible Rotor Balancing by the Exact-Point Speed Influence Coefficient Method, Transactions... 

In this section we will consider the energetics of exopolysaccharide production in some detail. We will see how chemostat (substrate limited) derived yield coefficients and slfbstrate elemental balances can be used to determine how the nature of the substrate influences... 

In another review, Hoffert discussed the social motivations for modeling air quality for predictive purposes and elucidated the components of a model. Meteorologic factors were summarized in terms of windfields and atmospheric stability as they are traditionally represented mathematically. The species-balance equation was discussed, and several solutions of the equation for constant-diffusion coefficient and concentrated sources were suggested. Gaussian plume and puff results were related to the problems of developing multiple-source urban-dispersion models. Numerical solutions and box models were then considered. The review concluded with a brief outline of the atmospheric chemical effects that influence the concentration of pollutants by transformation. 

The five-year Parde coefficients (Fig. 4a) exemplify the way in which the typical glacionival runoff regime [24] has developed a balanced, uimatural pattern. Now, because of the influence exerted by power plants, more water is discharged in the winter half-year and less in the summer half-year than in the decades where such influence was absent. 

A very simple type of a bubble column, which was not mentioned above is a gas-wash bottle. This very small-scale system (VL = 0.2-1.0 L) may be used for basic studies, in which general effects (e. g. influence of pH and/or buffer solutions specific ozone dose) are to be assessed. Its use is not recommended for detailed studies, because the mass-transfer coefficient is often low and its dependency on the gas flow rate is unknown or difficult to measure. Often there is no possibility to insert sensors or establish a reliable measuring system for exact balancing of the ozone consumption. An optimal mode of operation would comprise treatment of the (waste-)water for a certain period of time, preferably without withdrawal of solution during the ozonation. In this way different ozonation conditions can be tested by varying the ozonation time or the ozone gas concentration. A variation of the gas flow rate is not recommended. 

Maintenance of proper temperature is a major aspect of reactor operation. The illustrations of several reactors in this chapter depict a number of provisions for heat transfer. The magnitude of required heat transfer is determined by heat and material balances as described in Section 17.3. The data needed are thermal conductivities and coefficients of heat transfer. Some of the factors influencing these quantities are associated in the usual groups for heat transfer namely, the Nusselt, Stanton, Prandtl, and Reynolds dimensionless groups. Other characteristics of particular kinds of reactors also are brought into correlations. A selection of practical results from the abundant literature will be assembled here. Some modes of heat transfer to stirred and fixed bed reactors are represented in Figures 17.33 and 17.18, and temperature profiles in... 

The balance between conduction and diffusion still operates for a much larger isolated wet object, provided radiation is excluded. This is the basis of the wet bulb thermometer method for measuring humidity. The actual rate of evaporation now is not as simply determined and is influenced by wind. The wet bulb temperature is almost independent of wind condition, owing to a convenient accident. Heat conduction is a diffusion process, and the diffusion coefficient for water vapor in air (0.24 sq. cm./sec.) is numerically close to the diffusion coefficient of temperature in air (thermal conductivity/specific heat = 0.20 sq. cm./sec.). Hence, the exact way in which each molecular diffusion process merges into the more rapid eddy diffusion process is not important because no matter how complex the transition is, it must be quantitatively similar for the two processes. 

This relationship shows that if the flux of an irreversible process i is affected by thermodynamic force Xj of another irreversible process j through the mediation of coefficient Ly, then the flux of process j is also influenced by thermodynamic force Xj through the mediation of the same coefficient Lj = Ly In the case of interacting chemical processes, this statement reflects the principles of detailed (intimate) equihbrium and mass balance of the reactants that underlie the concepts of chemical kinetics. 

Cybulski and Moulijn [27] proposed an experimental method for simultaneous determination of kinetic parameters and mass transfer coefficients in washcoated square channels. The model parameters are estimated by nonlinear regression, where the objective function is calculated by numerical solution of balance equations. However, the method is applicable only if the structure of the mathematical model has been identified (e.g., based on literature data) and the model parameters to be estimated are not too numerous. Otherwise the estimates might have a limited physical meaning. The method was tested for the catalytic oxidation of CO. The estimate of effective diffusivity falls into the range that is typical for the washcoat material (y-alumina) and reacting species. The Sherwood number estimated was in between those theoretically predicted for square and circular ducts, and this clearly indicates the influence of rounding the comers on the external mass transfer. 

In this section we will consider the energetics of exopolysaccharide production in some detail. We will see how chemostat (substrate limited) derived yield coefficients and elemental balances can be used to determine how the nature of the substrate influences rates of metabolite production, and to give an indication of the scc for improvement of the producing micro-organism. You should note that for most industrial bioprocesses, the unavailability of data in the primary literature would prevent such an andysis. Further aspects of exopolysaccharide production are covered in Chapter 7 of flus text. 

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