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Chapt05

# Chapt05 - Wind tunnel test of an F-18 fighter plane model...

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Wind tunnel test of an F-18 fighter plane model. Testing of models is imperative in the design of complex, expensive fluids-engineering devices. Such tests use the principles of dimensional analysis and modeling from this chapter. (Courtesy of Mark E. Gibson/Visuals Unlimited) 276

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5.1 Introduction Motivation. In this chapter we discuss the planning, presentation, and interpretation of experimental data. We shall try to convince you that such data are best presented in dimensionless form. Experiments which might result in tables of output, or even mul- tiple volumes of tables, might be reduced to a single set of curves—or even a single curve—when suitably nondimensionalized. The technique for doing this is dimensional analysis . Chapter 3 presented gross control-volume balances of mass, momentum, and en- ergy which led to estimates of global parameters: mass flow, force, torque, total heat transfer. Chapter 4 presented infinitesimal balances which led to the basic partial dif- ferential equations of fluid flow and some particular solutions. These two chapters cov- ered analytical techniques, which are limited to fairly simple geometries and well- defined boundary conditions. Probably one-third of fluid-flow problems can be attacked in this analytical or theoretical manner. The other two-thirds of all fluid problems are too complex, both geometrically and physically, to be solved analytically. They must be tested by experiment. Their behav- ior is reported as experimental data. Such data are much more useful if they are ex- pressed in compact, economic form. Graphs are especially useful, since tabulated data cannot be absorbed, nor can the trends and rates of change be observed, by most en- gineering eyes. These are the motivations for dimensional analysis. The technique is traditional in fluid mechanics and is useful in all engineering and physical sciences, with notable uses also seen in the biological and social sciences. Dimensional analysis can also be useful in theories, as a compact way to present an analytical solution or output from a computer model. Here we concentrate on the pre- sentation of experimental fluid-mechanics data. Basically, dimensional analysis is a method for reducing the number and complexity of experimental variables which affect a given physical phenomenon, by using a sort of compacting technique. If a phenomenon depends upon n dimensional variables, di- mensional analysis will reduce the problem to only k dimensionless variables, where the reduction n k 1, 2, 3, or 4, depending upon the problem complexity. Gener- ally n k equals the number of different dimensions (sometimes called basic or pri- Chapter 5 Dimensional Analysis and Similarity 277
mary or fundamental dimensions) which govern the problem. In fluid mechanics, the four basic dimensions are usually taken to be mass M , length L , time T , and tempera- ture , or an MLT system for short. Sometimes one uses an FLT system, with force F replacing mass.

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Chapt05 - Wind tunnel test of an F-18 fighter plane model...

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