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In this chapter, we first review the concepts of dimensions and units. We
then review the fundamental principle of dimensional homogeneity, and
show how it is applied to equations in order to nondimensionalize them
and to identify dimensionless groups. We discuss the concept of similarity
between a model and a prototype. We also describe a powerful tool for engineers
and scientists called dimensional analysis, in which the combination
of dimensional variables, nondimensional variables, and dimensional constants
into nondimensional parameters reduces the number of necessary
independent parameters in a problem. We present a step-by-step method for
obtaining these nondimensional parameters, called the method of repeating
variables, which is based solely on the dimensions of the variables and constants.
Finally, we apply this technique to several practical problems to illustrate
both its utility and its limitations.
