This theorem is one method of determining appropriate dimensionless groups, from a number of
It states that:
in a physical problem involving “n” quantities / variables
in which there are “m” fundamental dimensions (M,L,T)
the quantities may be arranged in (n-m) independent dimensionless groups or parameters
These are called
group is formed from the product of 3 repeating variables raised to a power and one of the
remaining non-repeating variables raised to the power of unity.
The choice of repeating variables is guided by the following considerations:
Each repeating variable must contain between them all the fundamental dimensions.
The repeating variables should describe a size characteristic, a fluid property characteristic
and kinematic characteristic, d,
and v respectively.
The repeating set must contain three variables that cannot themselves be formed into a
both l and d cannot be chosen as they can be formed into the dimensionless
and v cannot be used since