Nondimensional representation of the boundary-value problem

Abstract

Given that an experiment can be considered to represent a physically realizable boundary value (bv) problem and given that the derived measurements are to represent aspects of the solution to the bv problem, it is rational to extend this understanding such that a maximum amount of information can be obtained from a given experiment. The first portion Sect. 2.2.1 establishes the bases for obtaining information regarding the flow associated with a prototype (the object/flow of actual interest) from measurements made in a model study. This section focuses on the large class of flows for which a Newtonian fluid and its governing equations establish the model-to-prototype information exchange. Dimensional analysis Sect. 2.2.2 provides a complement to Section 2.1 with a less structured - and therefore a more flexible - approach to problems that extend beyond those readily addressed by the Sect. 2.2.1 material. The important issue of collecting experimental results in non-dimensional groups is addressed in Sect. 2.2.2. The discussion of self-similarity Sect. 2.2.3 addresses the immense compaction of experimental data that is made possible for those flows that exhibit this property. The bases for, and utilization of, self-similarity are explored in detail.