Proposed Problems

The first nine problems are simple and meant to help you familiarize yourself with most of the units used throughout the book. They are not representative of all units that you will be using as a chemical and bioprocess engineer, but they will allow you to handle unit conversions and in addition become familiar with some dimensions in process engineering and in other systems. 

Then the rest of problems are presented to test your ability in more difficult situations where the main subject is the handling of unit conversions. 

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The proposed problem also could be solved by integrating Equation (7.57) for one mole,... 

In this first chapter, we seek to reinforce this perspective by including a series of case studies. We will propose problems in various areas of investigation and include specific examples of environmental remediation and advanced medical research issues addressed by polyurethanes in one form or another. While each example deals with a specific discipline, it is important to recognize that we have chosen all the examples in this chapter as surrogates with much broader applicabilities beyond the specific fields cited in the examples. 

Let us return to the proposed problem of calculating the displacement of a viscoelastic thin hollow sphere after a sudden internal pressurization. According to Eq. (16.66a), the determination of the displacement u requires to obtain an expression for (1 — v)/E in the viscoelastic system. From the differential operators of a standard solid and the equations for the tensile modulus and the Poisson ratio developed, respectively, in Problems 16.2 and 16.4 at the end of this chapter, the following expression for (1 —v)/E is obtained ... 

Indeed, there are further important aspects such as controllability, operability, costs, safety, reliability, etc. which impose constraints on process design. However, they are secondary objectives always related to the functional representation. Hence, they can be characterized as supplementary layers linked to the proposed problem space (tabs at the top of Fig. 5.42). 

Solving the proposed problem by employing Green s function, we can obtain... 

The chemical instrumentation discussed in the preceding chapters of this text can all be utilized in automated systems. The choice is largely dictated by economics and the applicability of the instrument to the proposed problem. Three groups of instruments have been widely automated spectrometers, electrochemical instruments, and chromatographs. Some of the many techniques commonly used and a few others are listed in Table 24.1. A review of all the instruments used in automated control systems cannot be given in the space allotted here. Additional reading is found in the bibliography at the end of this chapter. 

The proposed problem with equal consumption and production rates can be seen as a special case of the classic ELSP by assuming constant pumping rates for aU products, i.e. ps = p and no set>up times. Additionally, in this case the cost function has to be adjusted according to the total stock level in the entire supply system (provider, pipeline, and consumer stock). Hence, (3.7) changes to... 

The proposed algorithm is not only helpful to the decision makers to solve the problems of emergency evacuation route optimization, but also to propose problems based on the two trend curves of objective functions by applying the algorithm. 

Each entry in the following table represents a proposed problem concerning a two-phase, VLB situation. For each problem, answer these four questions ... 

These characteristics of theory building from case study seem to fit well with the proposed problem stated in this book as the main objective is to develop a framework for assessing and guiding companies progress towards a Demand Driven Supply Chain concept, which is not clearly defined yet in the academic literature and not fully executed in practice by supply chain professionals. 

The solution of (28) which fulfills the initial conditions is sought. Equation (28) is of the form of equation (25), and thus it is understood how to solve the proposed problem. 

From a methodological point of view, we will first solve some problems from each class in order of increasing level of difficulty. The idea is to demonstrate that with an appropriate method, even the most difficult problems can be solved without much trouble. To be crmsistent with our predicament, for both solved and proposed problems, we have considered a variety of problems, from very basic to very difficult. We hope that after completing this section, you will agree with us that, yes, you can You will also discover that the key to success is the strategy and method. Initially, perhaps always, it will be critical to work hard, but you will be rewarded. Here, our goal is to get you to the point where you can finally say to yourself, Yes I can and so can eveiymie else ... 

As stated at the beginning, all the concepts required in the solved- and proposed-problem sections were learned (or should have been learned) in high school. Assuming that it is necessary to review certain concepts, we will take the opportunity to do an exhaustive review in the solved-problem section. Some of the concepts to be reviewed include, for example, ideal gas mixtures, Dalton s law, and Amagat s law. But we will also keep it simple the focus will be, as in previous chapters, on tackling problem formulation ... 

If a number of substances is being maintained in fixed proportions in the process, it is better to consider them all together, enclosing them in one variable (see proposed problem 13 in Sect. 7.10). For example, if a food material (e.g., tomato juice) is to be concentrated by removing water, then all components (e.g., carbohydrates, proteins, fats) will remain together in the concentrated stream then it would be most efficient to call all of them solids and use just one variable for it all. 

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