Does dimensional analysis require a dependent variable with units?

Question

In a dimensional analysis of a=f(b,c,d), is it possible for a to be unitless?

I know that there are limitations on dimensionless parameters, such as the inability to represent a non-linear relationship. I want to know if any similar limitations are placed on the dependent variable.

For example, $bc/d$ with a speed, time & length. – J.G. Jul 14 '22 at 17:45 — J.G., Jul 14 '22 at 17:45

score 0 · Accepted Answer · answered Jul 14 '22 at 18:15

0

it possible for a to be unitless?

Yes; prominent examples are the fine structure constant α or the Reynolds number.

answered Jul 14 '22 at 18:15

emacs drives me nuts

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I had not considered that the Reynolds number could be the dependent variable in a dimensional analysis; I have only seen it as one of the PI groups. – Reid Johnson Jul 14 '22 at 20:07

Does dimensional analysis require a dependent variable with units?

1 Answers1