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CHAPTER 2. DIMENSIONAL ANALYSIS
2.2.3 Forming Dimensionless Products
After determining the important variables in a problem, the next step is
to use a combination of dimensional analysis and knowledge of the process
being examined to form dimensionless products from the selected variables.
This is important for the following reasons:
1. Forming dimensionless products reduces the number of
variables that must be investigated, either experimentally,
numerically, or via field measurements.
2. Dimensionless graphs provide much more information than
when dimensions are included because it is possible to
cover a wider range of the parameters.
3. Points on dimensionless graphs can frequently be determined using models scaled in such a way that the dimensionless products are preserved at reduced scale.
4. Dimensionless products can be used as the basis for scalemodel design and interpretation of results.
5. Dimensionless products allow tests to be planned and experimental results to be presented in a condensed and systematic manner.
Although dimensionless graphs and design aids provide more information, they can hinder the engineer’s feel for the relative magnitude of the
parameters that comprise the dimensionless products. For example, numerical values of deepwater wave steepness (H/gT2) provide little feel for
the severity of the seastate until sufficient experience is gained with wave
steepness values.
Forming dimensionless products from the selected variables is somewhat
arbitrary. Often the insightful investigator will be able to recognize dimensionless products by observation or physical reasoning. Examples specific
to coastal engineering include the fall speed parameter (H fuiT} and the
breaker index (Hb/h). At other times the dimensionless parameters occur
as a result of mathematical derivation, such as the linear wave theory perturbation parameter (H/L), or the Ursell parameter (L2H/h3) that arises
from Stoke s second order finite amplitude wave theory. Whatever the case,
it is generally wise to keep the dimensionless products simple, and to try
to form dimensionless variables that will be easier to work with when conducting experiments.
In the realm of fluid physics, there are several dimensionless products
that are known to be very important in certain types of flows. These
products are listed in Table 2.2. Several of the dimensionless numbers
CHAPTER 2. DIMENSIONAL ANALYSIS
2.2.3 Forming Dimensionless Products
After determining the important variables in a problem, the next step is
to use a combination of dimensional analysis and knowledge of the process
being examined to form dimensionless products from the selected variables.
This is important for the following reasons:
1. Forming dimensionless products reduces the number of
variables that must be investigated, either experimentally,
numerically, or via field measurements.
2. Dimensionless graphs provide much more information than
when dimensions are included because it is possible to
cover a wider range of the parameters.
3. Points on dimensionless graphs can frequently be determined using models scaled in such a way that the dimensionless products are preserved at reduced scale.
4. Dimensionless products can be used as the basis for scalemodel design and interpretation of results.
5. Dimensionless products allow tests to be planned and experimental results to be presented in a condensed and systematic manner.
Although dimensionless graphs and design aids provide more information, they can hinder the engineer’s feel for the relative magnitude of the
parameters that comprise the dimensionless products. For example, numerical values of deepwater wave steepness (H/gT2) provide little feel for
the severity of the seastate until sufficient experience is gained with wave
steepness values.
Forming dimensionless products from the selected variables is somewhat
arbitrary. Often the insightful investigator will be able to recognize dimensionless products by observation or physical reasoning. Examples specific
to coastal engineering include the fall speed parameter (H fuiT} and the
breaker index (Hb/h). At other times the dimensionless parameters occur
as a result of mathematical derivation, such as the linear wave theory perturbation parameter (H/L), or the Ursell parameter (L2H/h3) that arises
from Stoke s second order finite amplitude wave theory. Whatever the case,
it is generally wise to keep the dimensionless products simple, and to try
to form dimensionless variables that will be easier to work with when conducting experiments.
In the realm of fluid physics, there are several dimensionless products
that are known to be very important in certain types of flows. These
products are listed in Table 2.2. Several of the dimensionless numbers