Appendix - Worked Example

Consider the production of acetone from /-propyl alcohol, at a full annual rate of 100,000 tonnes, on an existing site (i.e. no land purchase cost). From previous experience, the delivered equipment cost can be expected to be 14.5 million. 

As this is a fluid-based process, the only solid material being the catalyst, the following equipment scale factors can be used. 

Loan interest accrued during construction (2 years)  

From mass balance and energy balance calculations, the raw material and energy costs are 

Fixed manufacturing cost (i.e. expenditure on operations that is independent of amount produced). 

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The A A2 X Ai, n -n system of formaldehyde (see Section 7.3.1.2) is also electronically forbidden since A2 is not a symmetry species of a translation (see Table A.l 1 in Appendix A). The main non-totally symmetric vibration which is active is Vq, the hj out-of-plane bending vibration (see Worked example 4.1, page 90) in 4q and d transitions. 

The varianee equation ean be solved direetly by using the Calculus of Partial Derivatives, or for more eomplex eases, using the Finite Difference Method. Another valuable method for solving the varianee equation is Monte Carlo Simulation. However, rather than solve the varianee equation direetly, it allows us to simulate the output of the varianee for a given funetion of many random variables. Appendix XI explains in detail eaeh of the methods to solve the varianee equation and provides worked examples. 

The varianee equation provides a valuable tool with whieh to draw sensitivity inferenees to give the eontribution of eaeh variable to the overall variability of the problem. Through its use, probabilistie methods provide a more effeetive way to determine key design parameters for an optimal solution (Comer and Kjerengtroen, 1996). From this and other information in Pareto Chart form, the designer ean quiekly foeus on the dominant variables. See Appendix XI for a worked example of sensitivity analysis in determining the varianee eontribution of eaeh of the design variables in a stress analysis problem. 

A worked example of the detrital-component correction and error propagation for the data of Figure 4 is given in Appendix 11. 

The general background of process design, flowsheets, and process control is reviewed in the introductory chapters. The major kinds of operations and equipment are treated in individual chapters. Information about peripheral and less widely employed equipment in chemical plants is concentrated in Chapter 19 with references to key works of as much practical value as possible. Because decisions often must be based on economic grounds, Chapter 20, on costs of equipment, rounds out the book. Appendixes provide examples of equipment rating forms and manufacturers questionnaires. 

In this equation, In denotes the natural logarithm, [A]0 designates the concentration of A at some initial time, arbitrarily considered to be t = 0, and [A]f is the concentration of A at any time f thereafter. (See Appendix A.2 for a review of logarithms.) The ratio [A]f/[A]0 is the fraction of A that remains at time t. Thus, the integrated rate law is a concentration-time equation that makes it possible to calculate the concentration of A at any time t or the fraction of A that remains at any time t. The integrated rate law can also be used to calculate the time required for the initial concentration of A to drop to any particular value or to any particular fraction of its initial concentration (Figure 12.6a). Worked Example 12.5 shows how to use the integrated rate law. 

Some feamres added to this second edition include an expanded number of worked examples and an appendix containing solutions to selected end-of-chapter problems. The overall goal of our second edition is, quite simply, to rectify the problems we encountered earlier, thereby producing a work that is much better suited as a tool to the working professionals, educators, and students of this fascinating field. 

The calculation of the uncertainties of individual strain components follows the same procedures, except that the details of the error propagation through the equations defining the strain components may differ and, if Equation (5) is used to fit the data, Fr is replaced in Equation (8) with the cube of the lattice parameter. A worked example is provided in the Appendix. Consideration of the form of Equations (7), (8), and (9) suggests that in general the absolute uncertainties in the calculated strains will be smallest at the pressures closest to the phase transition because both the strains and Vv,v will be smaller than at points further away (Fig. 3b). 

The aim of this chapter is to provide a brief background to Mossbauer spectroscopy within the context of phase transformations. The relevant parameters are summarised and the effect of temperature and pressure are discussed, particularly with reference to identifying phase transformations and characterising the electronic and structural environment of the Mossbauer nuclei. Instrumentation is summarised, particularly as it relates to in situ measurements of phase transformations, and a brief survey of applications is given. The appendix includes a worked example that illustrates the methodology of investigating a phase transformation using in situ Mossbauer spectroscopy. Numerous textbooks and review chapters have been written on Mossbauer spectroscopy, and a selection of the most relevant ones as well as some useful resources are listed in Table 1. 

Worked example Incommensurate-normal phase transformation in Fe-doped akermanite APPENDIX REFERENCES... 

This should serve as an introduction to understanding and designing switching power converters. More details and worked examples can be found in the next chapter (titled DC-DC Converter Design and Magnetics ). The reader can also at this point briefly scan Chapter 4 for some finer nuances of design. A full design table is also available in Appendix 2 for future reference. 

Values of AfG°(M, aq) and AfG°(X ,aq) can often be determined from standard reduction potentials (see Appendix 11) using equation 6.51, and tables giving values of AfG°(MX,s) for a wide range of salts are readily available. Equation 6.51 and its uses are discussed in detail in Chapter 7, and worked example 7.9 is especially relevant. 

There are several important differences between this edition and the earlier one. I am grateful to Professor James T. Hynes, University of Colorado, who kindly supplied the groups of questions at the end of each chapter. These are an important addition to the book. The questions range in difficulty some are relatively simple while others challenge the student to take up a line of reasoning from the chapter and apply it beyond the topics that are discussed explicitly. Many new problems have been added the total is over 750, about twice the number in the second edition. Answers to all the problems are given in Appendix VII. More worked examples are included these are now set apart from the text, while before they were sometimes hidden in the... 

Appendix F Worked Example for Calculating the Performance of a Gas Turbine 551... 

Appendix G Worked Example for the Calculation of Volt-drop in a Circuit Containing an Induction Motor... 

Appendix H Worked Example for the Calculation of Earthing Current and Electric Shock Hazard Potential Difference in a Rod and Grid Earthing System... 

The following checklist contains a number of questions which can aid in identifying inherently safer process options. The list is adapted from CCPS (1993a). Other checklists, particularly the extensive checklist in Appendix B of the Guidelines for Hazard Evaluation Procedures, Znd Edition with Worked Examples (CCPS, 1992) contain many questions which are related to inherent safety. 

At least in principle, can be calculated based on standard line shape theories (e.g., in Appendix A we calculate for our working example... 

For additional information the reader is referred to the original publications, the references to which can be found in the Key to Carotenoids and the Appendix II of this Volume. The Worked Examples describe in detail the experimental procedures for important reactions. 

Worked Examples demonstrate how to utilize the concepts in this course in problem solving. Each example is accompanied by one or more exercises (Try It) that are answered in Appendix F, thereby helping students to check their understanding. The examples and exercises, combined with the Concept Checks, are designed to help students gain confidence about smaller segments of material before they try to answer larger questions and problems at the end of each chapter. 

A worked example for a particular reaction is given in Appendix 2 which illustrates the application in practice of the approaches outlined in this section. 

It is hoped that the inclusion of these spread eets will help to reinforce and illustrate some of the mathematical developments provided in the main text of this book. Many of the worked examples can be investigated using the following files, and some of the figures used in the main text were derived using the gr hical capability of the spreadsheet package on these examples. The graphs have not, therefore, beea reproduced in this Appendix. 

Three example problems are presented in this section to illustrate the different formulas for several channel and ship types. All are for bow squat 5b. Comparisons of the different formulas with the measured laboratory values are shown for each example in Figs. 26.4-26.6, respectively. Appendix 26.B contains worked examples for at least one Concept and one Detailed Design application for each example problem. 

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