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Identify
the relevant variables influencing response in your application. Then pick the
dependent
variable of interest and form its dimensionless product such as Pi|1. From
dimensional
analysis form the dimensionless products of all independent variables.
i.e.
Pi|2, Pi|3, etc.
Here Pi|1
represents the dimensionless product for the dependent variable.
Pi|2 represents the second Pi term, the dimensionless product for the first
independent
variable,
Pi|3 represents the third Pi
term, the dimensionless product for
the second
independent variable, etc.
Let m represent the model and p the prototype.
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The prediction equation then is: Pi|1 m =
Pi|1 p.
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The
response of the model will equal the
response of the prototype provided that all the
Pi
terms for the independent variables, Pi|2,
Pi|3, etc are equal for the
model and prototype.
The
conditions Pi|2 m
= Pi|2 p, Pi|3
m =
Pi|3 p , etc are termed the model design
conditions
or similarity requirements. If
these relations are satisfied, then the dependent
response
expressed by Pi|1 m =
Pi|1 p can be calculated.
In
some cases not all the Pi terms
Pi|2, Pi|3, etc
can be made the same for both the model
and
the prototype. Then only partial similarity exists.
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Geometric
Similarity exists if shapes are similar
between the model and prototype. |
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Dynamic
Similarity exists if forces are similar
between the model and prototype. |
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Kinematic Similarity
exists if streamlines are similar
between the model and prototype. |
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