# Thread: Relationship between diameter and length

1. Hi

I'm looking to solve a problem and thought I would call on your help to point me in the right direction.

This is related to a 3D printing filament. It's starts it's life being 10m long and with a diameter of 1.75mm. A printing process alters the diameter to 0.4mm. I would like to determine what length this will correspond to?
I know it will be longer than 10m as it will 'stretch' if you like via this process.
I just can't yet see how I can work this out. I know there's an equation or two out there that I can use to solve for this.

Kind regards

Anthony

2.

3. You need to work out the volume of the filament, this will be . The volume won't change so use this calculated volume and the new "r" to find the new "l".

4. of course! Thanks Mr PhDemon! Much appreciated. I knew there was a simple equation and relationship out there!

All the best

Anthony

5. No problem.

6. That equation works IF, in the process of reducing the diameter, the filament isn't compressed into being denser.
(I don't know if it is, but it's a possibility).

7. Originally Posted by Dywyddyr
That equation works IF, in the process of reducing the diameter, the filament isn't compressed into being denser.
(I don't know if it is, but it's a possibility).
I thought PhDemon’s solution was spot on; although afterwards I did wonder if some other variable would come into play. How would a change in density change the mathematical relationship between the length and volume?

8. Originally Posted by Vexspits
How would a change in density change the mathematical relationship between the length and volume?
It would mean that the reduction in diameter was "invalid" for the calculation, e.g. if it came out of the nozzle at twice the start density then it would be using 0.8mm "worth" of filament rather than the 0.4 expected.

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