7708d_c07_384-441 - Flow past a circular cylinder with The...

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Unformatted text preview: Flow past a circular cylinder with The pathlines of flow past any circular cylinder 1 regardless of size, velocity, or fluid 2 are as shown provided that the dimensionless parameter called the Reynolds number, Re, is equal to 2000. For other values of Re, the flow pattern will be different 1 air bubbles in water 2 . 1 Photograph courtesy of ONERA, France. 2 Re 5 2000: Although many practical engineering problems involving fluid mechanics can be solved by using the equations and analytical procedures described in the preceding chapters, there re- main a large number of problems that rely on experimentally obtained data for their solu- tion. In fact, it is probably fair to say that very few problems involving real fluids can be solved by analysis alone. The solution to many problems is achieved through the use of a combination of analysis and experimental data. Thus, engineers working on fluid mechanics problems should be familiar with the experimental approach to these problems so that they can interpret and make use of data obtained by others, such as might appear in handbooks, or be able to plan and execute the necessary experiments in their own laboratories. In this chapter we consider some techniques and ideas that are important in the planning and exe- cution of experiments, as well as in understanding and correlating data that may have been obtained by other experimenters. An obvious goal of any experiment is to make the results as widely applicable as pos- sible. To achieve this end, the concept of similitude is often used so that measurements made on one system 1 for example, in the laboratory 2 can be used to describe the behavior of other similar systems 1 outside the laboratory 2 . The laboratory systems are usually thought of as models and are used to study the phenomenon of interest under carefully controlled condi- tions. From these model studies, empirical formulations can be developed, or specific pre- dictions of one or more characteristics of some other similar system can be made. To do this, it is necessary to establish the relationship between the laboratory model and the other sys- tem. In the following sections, we find out how this can be accomplished in a systematic manner. 385 7 S imilitude, Dimensional Analysis, and Modeling 7.1 Dimensional Analysis To illustrate a typical fluid mechanics problem in which experimentation is required, con- sider the steady flow of an incompressible Newtonian fluid through a long, smooth-walled, horizontal, circular pipe. An important characteristic of this system, which would be of interest Experimentation and modeling are widely used tech- niques in fluid mechanics. to an engineer designing a pipeline, is the pressure drop per unit length that develops along the pipe as a result of friction. Although this would appear to be a relatively simple flow problem, it cannot generally be solved analytically 1 even with the aid of large computers 2 without the use of experimental data....
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7708d_c07_384-441 - Flow past a circular cylinder with The...

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