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1. |
Identify
variables governing the problem. (Critical
and essential first step) Set up a
table
listing each of the variables along with the dimensions of each variable. |
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2. |
Determine
the number of Pi terms by subtracting the number of dimensions involved
in
the variables from the total number of variables. |
|
3. |
Select
the number of repeating variables equal to the number of basic dimensions
involved
in the application. Use them to form
dimensionless products. |
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4. |
Form
the Pi terms by multiplying the dependent variable and each of the non-repeating
variables by the product of repeating variables each raised to an exponent
that will make
the
combination dimensionless. i.e. ui u1a
u2b u3c where ui
is a non-repeating variable, u1,u2,u3 are
the repeating variables. |
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5. |
Repeat
step 4 for each of the remaining non-repeating variables. |
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6. |
Check
all the resulting Pi terms to verify they are dimensionless and
independent. |
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7. |
The
result is a set of linear algebraic equations involving a, b, and c with
one equation
for
each dimension such as: a + b ˗
c = 0, (for F), ˗3 + a + b
˗4c = 0 (for L) and
˗b
+ 2c = 0 (for T). Solve for a, b,
and c giving the dimensionless product ui
u1a u2b u3c . |
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8. |
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 dependent term.
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