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Question for the mathemagicians
Ok, I'm looking into the circle-in-circle problem (for sizing sleeves for linesets). It seems that it's basically an open ended problem, but I'm wondering if the limits of my application will make it solvable. What I want to know is something like the minimum % fill of a circle that will allow my linsets to fit. As an example, I have three copper lines (two 1-1/8" & one 3/4" with 1" insulation around each, so 2x dia 3-1/8" & 1x 2-3/4" ) and one raceway for control wires, c. 1" OD. What is the approximate minimum % fill that will allow them to enter the sleeve without interfering with each other? That's the maximum number of pipes that I'm interested in, but they are various sizes, generally 1 or 2 big, and 1 or 2 smaller.
Would I be better served by looking at this as a diameter problem, vs an area problem? The application is an Excel workbook, so I can easily math it, once I figure out exactly what I want to math.