WATER JET CONFERENCE - Waterjet Technology Association

The various parameters in these equations are: f; frequency, d: nozzle diameter,
V; mean jet velocity, V; amplitude of modulation of the jet velocity. From Figure 4 of
your paper: f = 300Hz, V = 330 ft/s, and elsewhere you cite: S/d ~1000 with d = 0.5 in.
Thus, from (2) = S d ~0.04, and hence from (1), it would seem that your modulation, V/V
is about 1 to 2 percent. Is this prediction (from Eqns. (1) and (2) consistent with your
experimental observations for jet modulation? Do you agree that such an analytical
approach should be useful in trying to understand these pulsed
ANSWER: Andy, many important problems cannot be solved by completely theoretical
or mathematical methods. Naturally, one way of attempting a problem for which no
mathematical equation can be derived is empirical experimentation. The procedure is
laborious, and difficulty is encountered in organizing or correlating the results into a
useful relationship for calculations.
Dimensional analysis is a method intermediate between formal mathematical
development and a completely empirical study. Such an approach is based on the fact that
if a theoretical equation does not exist among the variables controlling the phenomenon,
the equation must be dimensionally homogeneous. As a result, many factors can be
grouped into a smaller number of dimensionless groups of variables. A dimensional
analysis cannot be made unless enough is known about the physics of the situation to
decide what variables are important in the problem and what basic physical laws would
be involved in a mathematical solution if one were possible.
I am pleased equation (1) is useful to you. However, such an equation would
predict a poor operating point for our Percussive Jet in most cases. Certain variables very
important to the process do not appear in this equation. We operate over such a large
range of variables that "optimum bunching" is redefined for each case. For example,
sometimes surface tension is important but often it is of no concern.
You might try to do a more formal mathematical analysis using a computer for
solution. We feel we can process more variables, include more details, and generally
arrive at a more fundamental solution than by using dimensionless groupings.
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