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