The resistance value of 3/16" is ~3psi/ft, simply divide the pressure by that value and it will yield the approx length of hose required to balance the system.
I'm not so sure about that.
My 5 ft line works pretty perfect at 10psi (w/o a mixer) which would mean it's closer to a 2psi per foot drop. That is the value that I've seen most oftern during my searching.
I've also read that as you get in the upper psi range like around 30 the drop is < 1. In other words the tubing resistence isn't constant with pressure.
Have you ever carbed a beer to 25psi and served it w/ 8-9' lines?
I agree, I've used lines that were much longer than necessary and it doesn't cause excessive foam, just a very slow pour. You can see the difference if you hook up a long line and a short line back to back on the same keg. The resistance of tubing is not a static value, it changes based on the flow rate. If you pour slowly at say 80 oz/min the resistance is closer to .94 psi/ft, whereas a very fast pour of 192 oz/min would be more like 4.7 psi/ft (see this guide
from the inventer of Ventmatic faucets (thanks to P-J for sharing this).
When balancing a system you need to pour slowly enough so that carbonation does not come out of solution, and have enough resistance in the line to dissipate all the pressure at the regulator. So a high carb beer hits you twice, first you need a long line to dissipate all the pressure at the regulator, and you need to pour slower so the resistance of your tubing decreases, necessitating an even longer line. To avoid having 20+ foot lines, looks like the mixing nozzle is the way to go.
Another thing that can cause foaming is a clogged dip tube or a perforated dip tube, which sometimes happens if they crack. Sounds like you got it sorted out though.