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## Homework Statement

Hi. I have a function that contains 4 variables: Q, R, [itex]\mu[/itex],

^{dp}/_{dx}I wish to choose 3 of them, such that they

**cannot**be combined into a dimensionless product.

I have chosen (correctly) R, [itex]\mu[/itex],

*and I would like to know if my method sounds correct:*

^{dp}/_{dx}If we know the dimensions: [R]=[L] [[itex]\mu[/itex]]=[ML

^{-2}T

^{-2}] and [

*]=[ML*

^{dp}/_{dx}^{-1}T

^{-1}]

and I know that in order for them to be dimensionless, their power product must equal zero:

[L]

^{a}[ML

^{-1}T

^{-1}]

^{b}[ML

^{-2}T

^{-2}]

^{c}=[MLT]

^{0}

or the system

a-b-2c=0

b+c=0

-b-2c=0

By inspection, this system can only be satisfied if a=0 but that does not make any sense since R is a physical quantity.

Hence I have reasoned that these 3 variable cannot form a non-dimensional parameter by themselves.

Does this work? Thanks!