1 Introduction

Two flows having different values of length scales, flow speeds, or fluid properties can apparently be different but still "dynamically similar". Exactly what is meant by dynamic similarity will be explained later in this chapter. At this point it is only necessary to know that in a class of dynamically similar flows we can predict flow properties if we have experimental data on one of them. In this chapter, we shall determine circumstances under which two flows can be dynamically similar to one another. We shall see that equality of certain relevant nondimensional parameters is a requirement for dynamic similarity. What these nondimensional parameters should be depends on the nature of the problem. For example, one nondimensional parameter must involve the fluid viscosity if the viscous effects are important in the problem.

The principle of dynamic similarity is at the heart of experimental fluid mechanics, in which the data should be unified and presented in terms of nondi-mensional parameters. The concept of similarity is also indispensable for designing models in which tests can be conducted for predicting flow properties of full-scale objects such as aircraft, submarines, and dams. An understanding of dynamic simi-larity is also important in theoretical fluid mechanics, especially when simplifications are to be made. Under various limiting situations certain variables can be eliminated from our consideration, resulting in very useful relationships in which only the constants need to be determined from experiments. Such a procedure is used extensively in turbulence theory, and leads, for example,...