Similitude, Dimensional Analysis and Modelling

Although many practical engineering problems involving momentum, heat and mass transport can be modelled and solved using the equations and procedures described in the preceding chapters, an important number of them can be solved only by relating a mathematical model to experimentally obtained data. 

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. 

One of the goals of the experimental research is to analyze the systems in order to make them as widely applicable as possible. To achieve this, the concept of similitude is often used. For example, the measurements taken on one system (for example in a laboratory unit) could be used to describe the behaviour of other similar systems (e.g. industrial units). The laboratory systems are usually thought of as models and are used to study the phenomenon of interest under carefully controlled conditions. Empirical formulations can be developed, or specific predictions of one or more characteristics of some other similar systems can be made from the study of these models. The establishment of systematic and well-defined relationships between the laboratory model and the other systems is necessary to succeed with this approach. The correlation of experimental data based on dimensional analysis and similitude produces models, which have the same qualities as the transfer based, stochastic or statistical models described in the previous chapters. However, dimensional analysis and similitude do not have a theoretical basis, as is the case for the models studied previously. 

Chemical Engineering. Tanase G. Dobre and Jose G. Sanchez Marcano Copyright 2007 WILEY-VCH Verlag GmbH Co. KGaA, Weinheim ISBN 978-3-527-30607-7 

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I 6 Similitude, Dimensional Analysis and Modelling the application of the pi theorem yields ... 

Dobre and Sanchez Marcano, 2007] T. G. Dobre and J. G. Sanchez Marcano. Chemical Engineering Modelling, Simulation and Similitude, London Wiley-VCH, 2007, chapter 6 Similitude, Dimensional Analysis and Modelling . 

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