When you define r (and other variables) dependent on OD in your solve block it uses the guess values and is never changed. It remains a constant.
That way you actually don't have any equation in OD in your solve block and Prime cannot fulfill your "equation"
because the value on the left hand side is constant 2.295 (which is what you get with the guess value OD=0.75 in).
There are two possible ways to solve your problem:
1) Turn every assignment like
into an equation
You would have to do this five times.
Drawback is that you now must have the solve block to solve for six variables (OD, r, t, Sig1, Sig2 and Sig.VM) even though you are only interested in OD.
2) The way I would prefer and have chosen in the attached sheet.
Turn all those assignments which depend on OD into functions of OD. I would also move these functions out of the solve block in front of it. That way all that remains in the solve block is the guess and one equation. The additional constraint OD>ID is not really necessary if the guess is large enough, but I would leave it there just to be on the safe side.
This is what it looks like now:
BTW, you could also use the "root" function to do the job
Depending on the range you provide you may also get the solution which is lower than ID
The "root" function could also used by providing a guess value in front instead of the range limits:
Prime 10 sheet attached
