What is happening here?

[MNM]

Good day, I'm using verion 12 (no need to upgrade) and am creating a spring calculation shhet. I ran into a curious phenomenon and can't quite understand it. I set upan equation to find the wire diameter "d" using the Symbolic Solve functionality. See attached SCS1a & SCS1b worksheets. Prior to the equation, I defined the units of "d" to be in 'mm' (yellow hightlighted regions). With this enabled, I get two (2) answers. With it disabled, I get four (4) answers, 2- complex. The funny thing is either way I get the proper units out, but the value is different. Why? TIA Mark P.S. I've also tried to difine this as a Solve Block, but I'm haveing some difficulty remembering the exact syntax (SCS1 worksheet)

[TomGutman]

You are not defining the units of d to be mm (the symbolic processor knows nothing about units anyway). You are defining d to be mm. Numerically, that makes d one millimeter (the value of mm). Symbolically it makes d equivalent to the (undefined) variable mm.

[MNM]

OK, but when it does a dimensional analysis, why is this result in the proper units? With "d" disabled, there should be a L^2 (length squared) in the results. BTW I got the Solve Block to work (too many undefined variables in the Find routine), so this is an intellectual excersise at this point. Mark

[TomGutman]

d is supposed to be a length, mm is also a length. Replacing d by mm makes no change to the dimensional analysis. There is no "disabling" of d. What is disabled is the assignment of the value mm (symbolic or numeric, note the two are different) to d. Note that if you assign (symbolically) mm to d and then attempt to solve for d you are really solving for mm (the symbolic processor replaces defined (to it) variables by their definitions. What you get is a formal exercise in solving your given expression for the variable mm (the symbolic processor has no concept of units, mm is just another undefined name).