|
1. |
Select
variables governing the problem. (Critical
and essential first step) Set up a
table
listing each of the variables along with the dimensions for each variable. |
|
2. |
Determine
the number of Pi terms by subtracting the number of dimensions involved in
the
variables from the total number of variables. The collection of variables may be
sorted
into three types - the dependent variable, the repeating variables, and the
non-
repeating
variables. |
|
3. |
Select
the number of repeating variables equal to the number of basic dimensions
in
the
application. Each repeating variable will be used to remove
one dimension from
the
non-repeating variables and from the dependent variable in the problem to
form a dimensionless product. |
|
4. |
Form
each Pi term by multiplying the dependent variable and each of the non-repeating
variables by the proper product of repeating variables so as to form a
dimensionless
product. |
|
5. |
Check
all the resulting Pi terms to verify they are dimensionless and
independent.
Note: Products and quotients of Pi terms are
also dimensionless. |
|
6. |
Express
the final relationship among the Pi terms as
Pi =
f( Pi|1, Pi|2,
etc)
where
the Pi term on the left hand side represents the dimensionless form of the dependent
variable and the Pi terms on the right hand side represent the
dimensionless forms of the
non-repeating
variables. |