How should you run PTFE (Teflon) Tubes? I bought a modern machine, and it comes with PTFE tubes.  I need to relocate the spool, so I bought some longer PTFE tubes.  I bent the tub by hand, and my first test run actually had too much friction, so the extruder was unable to pull the filament through the tube.  I cut it a few inches and it seems to be fine.
What are the rules of thumb that one should use when redesigning a filament path though a PTFE tube?  For example, these are some things I can think of based on how I would teach someone about running wires in a high- or low- voltage commercial application (with or without conduit):

Bend radius.
Number of bends.
Length of tube.
Diameter of tube relevant to diameter of filament (link).
Expected friction coefficient (teflon appears to be slick, but will still have some friction)
How to secure the slippery tube (clips, zip ties, glue, etc.).
How much compression is too much for the tube (ie zip ties)?
Constriction
PTFE-Tubes usually have enough stiffness to not require additional support and constriction from anything but the two end fittings and the stiffness the filament in them provides. In fact, they make great guides for cable management to the heater block! You might want to add some constricting clamps on very long tubes. To do so, zip ties and cable guide clamps are common. Don't make them too tight as they shall not cut into the tube!
You also shouldn't constrict them too tight: A bend diameter of about 12 cm is where I would pull the line for 1.75 mm PLA: anything lower and you might get problems. For 2.85 or 3 mm filament, you should use a somewhat larger diameter - I have seen good flow with about 20 cm bends. A very simple test can be done: Fix one end, load filament, pull at the other end while holding the second fixture close to the planned position. If you have an easy way, you're good.
Length
Length is tricky: you should not be too long, as that could add too much friction, but on a direct drive or when you pull filament from a dry box, there's little to no length limit on the tube through which you pull, there's only a maximum length you can push through effectively.
Diameter
The diameter of a tube on the pushing end of the extruder motor should be somewhat snug: 1.9 and 2 mm inner diameter are common for 1.75 mm filament, and 2.85 mm does work well in a 3 mm tube. 3 mm filament needs about 3.25 mm inner diameter. As a rule of thumb: add 0.15 to 0.25 mm to the diameter of the filament and get the closest available diameter to that.
On the pulling end of the extruder, a larger size can be used. Though don't go too large, like 10 mm ID, as at some point, as you might experience backlash and rattling in the tube, resulting in noise, and for very hygroscopic filaments (PVA or Nylon), the extra air in such a large tube could reduce the effect of printing from a dry box:

3.25 mm works well for both 2.85 and 3 mm and might still work for 1.75 mm filament on the intake side (Thank you for the insight FarO!)
a 4 mm ID on the intake-side can still work for 1.75 mm and mitigate extrusion problems on a Bowden-extruder (thanks @0scar)

In either case, you have to keep in mind the bending radii - don't overconstrain! Also, remember that you need to have a fitting coupling on the delivering and the receiving end.