Engineering problems probability

In fact, it is probably fair to say that very few problems involving real momentum, heat, and mass flow can be solved by mathematical analysis alone. The solution to many practical problems is achieved using a combination of theoretical analysis and experimental data. Thus engineers working on chemical and biochemical engineering problems should be familiar with the experimental approach to these problems. They have to interpret and make use of the data obtained from others and have to be able to plan and execute the strictly necessary experiments in their ovm laboratories. In this chapter, we show some techniques and ideas which are important in the planning and execution of chemical and biochemical experimental research. The basic considerations of dimensional analysis and similitude theory are also used in order to help the engineer to understand and correlate the data that have been obtained by other researchers. 

The issue is now to manufacture an emulsion with these properties, and to meet the remaining specifica tions. It has been discussed in previous sections that a dynamic process often makes the manufacturing easier or cheaper, and is able to improve upon the properties. There are probably many alternative dynamic processes that could end up at the right plaee on the map (214). The second part of the formulation engineering problem is to find those that fulfill the remaining speeifieations and that present some advantages over the direet emulsifieation under the final conditions. 

In order to describe the three-phase (Hydrate - Liquid Water - Vapor) equihbria (H-Lw-V) the theory developed by van der Waals-Platteeuw [9, 10] is traditionally used. The theory is based on Statistical Thermodynamics and according to Sloan and Koh [1] it is probably one of the best examples of using Statistical Thermodynamics to solve successfully a real engineering problem. An excellent description of the theory for the three-phase equilibrium calculations is provided in a number of publications [1,9, 10] and will not be repeated here. In addition, extensive details on the methodology for the calculation of two-phase equilibrium (H-L ) conditions can be foimd in the review papers by Holder et al. [12], and Tsimpanogiannis et al., [11]. 

This equipment is not known to have been used on an industrial scale and it probably achieves little which could not be equally well engineered by a conventional column plant controlled automatically to a fixed time cycle, using a system of multi-port valves. It has the disadvantage that a high proportion of the essential part of the plant is continually in motion, with the attendent mechanical engineering problems which this implies. 

As indirectly mentioned in Sect. 11.3, you are probably not yet familiar with the concept of derivatives, which is essential in handling maximum and minimum problems. Although we will present and solve interesting and applicable maximum and minimum engineering problems, it is not our intention to familiarize you with the concept of derivatives. Soon in your career you will be introduced by experts to this important and key mathematical concept for aU engineers. You are most probably familiar with the use of spreadsheets. In this section we will show you how to solve maximum and minimum problems using spreadsheets. 

Depending on the type of reaction desired, and the reversibility or otherwise of the overall electrode processes, separators may or may not be required between the anode and the cathode regions of the cell. However, for most preparative processes, an anode/cathode separator is desirable to minimize cross-flow of products between the +, - pair of electrodes and the consequent mutual depolarization effects with possible, or probable, contamination of the main electroorganic product desired. This is a practical factor determining product coulombic efficiency and yields. The usual engineering problems with separator properties, their design, and mounting, arise in scale-up for preparative applications. 

Finite element modeling is a technique whereby a material continuum is divided into a number of patches, or finite elements, and the appropriate engineering theory is applied to solve a variety of problems. The initial (and probably still dominant) use of finite element modeling was for the solution of structural engineering problems. The technique is currently being applied by a number of companies and research institutions in the design of plastic products. CAD/CAM systems provide the means to create a mesh of finite elements directly from a product model database, by automatic and semiautomatic means. 

Rational polynomials or variations of such polynomials are frequently used to approximate implicit functions occurring in engineering problems. For example the probability function defined as ... 

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