Design equation summary

In principle, one can carry out a four-dimensional optimization in which the four parameters are varied subject to constraints (< 1 and P4 < 1 ), to minimize the deposition time with the non-uniformity bounded e.g., MN < 3. However, objective function evaluations involve solutions of the Navier-Stokes and species balance equations and are computationally expensive. Instead, Brass and Lee carry out successive unidirectional optimizations, which show the key trends and lead to excellent designs. A summary of the observed trends is shown in Table 10.4-1. Both the deposition rate and the non-uniformity are monotonic functions of the geometric parameters within the bounds considered, with the exception that the non-uniformity goes through a minimum at optimal values of P3 and P4. 

Summary of design equations for ideal reactors (continued)... 

The necessary wall thickness for metal vessels is a function of (1) the ultimate tensile strength or the yield point of the metal at the operating temperature, (2) the operating pressure, (3) the diameter of the tank, and (4) the joint or welding efficiencies. Table 4 presents a summary of design equations and data for use in the design of tanks and pressure vessels based on the ASME Boiler and Pressure Vessel Code as specified in Section VIII of Division 1. 

Determination of appropriate coefficients of heat transfer is required for design calculations on heat-transfer operations. These coefficients can sometimes be estimated on the basis of past experience, or they can be calculated from empirical or theoretical equations developed by other workers in the field. Many semiempirical equations for the evaluation of heat-transfer coefficients have been published. Each of these equations has its limitations, and the engineer must recognize the fact that these limitations exist. A summary of useful and reliable design equations for estimating heat-transfer coefficients under various conditions is presented in this chapter. Additional relations and discussion of special types of heat-transfer equipment and calculation methods are presented in the numerous books and articles that have been published on the general subject of heat transfer. 

Table 8.1 Summary of Design Equations Given that V = Vq 1 + 8 )...

Detailed mathematical models and design equations for predicting the grade penetration and systan pressure drop have been developed [2,18,29,52,56,57,59]. Summaries of some of these models are shown in Tables 53.11 and 53.12. Pressure drop equations for other scrubbers can be found in standard Chemical and Environmental Engineering texts or handbooks [11-16]. 

X. This equation is found in a summary of various design equations in Figure 4.5 of the reference of Endnote V. The equations for calculating the wall thicknesses of non-cylindrical vessel shapes are considerably more complicated and outside the scope of this book. 

If mass transfer resistances are important then the actual mass of catalyst needed to get the same conversion is W =W/n.In summary, with a given amount of catalyst the conversion at the outlet can be calculated through the so-called "design equations" extended below to the case where we have strong diffusion effects ... 

Alternative equations and graphical techniques have been developed to calculate Nqg for other design conditions (Colburn, 1941 White, 1940). A summary of useful design equations for transfer-unit calculations is presented by Sherwood et al. (1975). 

Appendix 3 Summary of Design Equations 61 n. Ideal continuous stirred-tank reactor (CSTR)... 

The third solution to Schrodinger s equation produces the magnetic quantum number, usually designated as m. Allowable values of this quantum number range from -f to +f. A summary of... 

Boiling and condensation phenomena are very complicated, as we have shown in the preceding sections. The equations presented in these sections may be used to calculate heat-transfer coefficients for various geometries and fluid-surface combinations. For many preliminary design applications only approximate values of heat flux or heat-transfer coefficient are required, and Tables 9-4 to 9-6 give summaries of such information. Of course, more accurate values should be obtained for the final design of heat-transfer equipment. 

To appreciate the refinements that this thermodynamic treatment introduces into the customary expression describing the osmotic responses of cells and organelles, we compare Equation 2.18 with Equation 2.15, the conventional Boyle-Van t Hoff relation. The volume of water inside the chloroplast is VM,n because n v is the number of moles of internal water and Vw is the volume per mole of water. This factor in Equation 2.18 can be identified with V — b in Equation 2.15. Instead of being designated the nonosmotic volume, b is more appropriately called the nonwater volume, as it includes the volume of the internal solutes, colloids, and membranes. In other words, the total volume (V) minus the nonwater volume (b) equals the volume of internal water (Ew ). We also note that the possible hydrostatic and matric contributions included in Equation 2.18 are neglected in the usual Boyle-Van t Hoff relation. In summary, although certain approximations and assumptions are incorporated into Equation 2.18 (e.g., that solutes do not cross the limiting membranes and that the... 

In this section we present a number of examples designed to illustrate the use of a nonequilibrium model as a design tool. In view of the large number of equations that must be solved it is impossible to present illustrative examples of the application of the nonequilibrium model that are as detailed as the examples in prior chapters. In the examples that follow we confine ourselves to a brief summary of the problem specifications and the results obtained from a computer solution of the model equations. In most cases several different column configurations were simulated before the results presented below were obtained. 

Although it is an unfair summary of this elegant work, it is obvious that a chemist interested in designing a better substrate for this enzyme would prefer to use the first equation listed since this equation fits the data the best and the parameters are easy to obtain. 

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