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], dp/dx and I would like to know if my method sounds correct:
If we know the dimensions: [R]=[L] [[itex]\mu[/itex]]=[ML-2T-2] and [dp/dx]=[ML-1T-1]
and I know that in order for them to be dimensionless, their power product must equal zero:
or the system
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!