Fluid Mechanics-Similitude, Dimensional Analysis, and Modeling

Although many practical engineering problems involving fluid mechanics can be solved by
using the equations and analytical procedures described in the preceding chapters, there remain
a large number of problems that rely on experimentally obtained data for their solution.
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 execution
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 possible.
To achieve this end, the concept of similitude is often used so that measurements made
on one system 1for example, in the laboratory2 can be used to describe the behavior of other
similar systems 1outside the laboratory2. The laboratory systems are usually thought of as
models and are used to study the phenomenon of interest under carefully controlled conditions.
From these model studies, empirical formulations can be developed, or specific predictions
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” system.
In the following sections, we find out how this can be accomplished in a systematic
manner.