If the formula is flawed could I get the formula everyone uses here.The chart is great but useless without the correct formula to use it with.Yes,I ran the numbers backwards because everything is setup and connected with the 10 ft lines and I wanted to see where I was at.It came up as 29 psi.I just ran the numbers off the chart above(using my formula) and it came back 4' 3"lines .Which is basicly what the tower came with.That would in theory give me a perfectly balanced keg.So Im wondering why almost everyone runs long lines to eliminate foam when the shorter lines are what the charts call for.Every beer is different but some here are running 15 ft 3/16 lines.I cant imagine anything on the chart would call for that.Im really just curious why if the chart and fomula is for a perfect balance,why the longer lines
There is a lot of really misleading information out there about "line balancing". The first misleading thing is the name, which implies there's some sort of balance you're trying to reach, and that anything greater or less than some "balanced" line length will cause problems. This is simply not true. That equation does only one thing, it calculates the line length required to result in a flow of 1 gal/min. Why 1 gal/min? Because the formula was designed for use in commercial systems, and bars and restaurants want to be able to pour as fast as possible without excessive foaming, which for commercial serving parameters (~36°, <2.7 vol, relatively low FG) is ~1 gal/min.
The problem with the formula? Not everyone wants to use commercial parameters, and for warmer or more highly carbed beer, the flow needs to be slower/gentler to prevent the CO2 from coming out of solution and causing excessive foaming. You quoted a resistance figure for 3/16" ID line of 2.7 psi/ft, but that resistance figure is only valid at a flow rate of 1 gal/min. Line resistance changes with fluid velocity, so to decrease the flow rate slightly, much longer lines are required.
The only side effect of extra long lines is a slightly slower pour. Once again, since resistance decreases when the flow rate decreases, even doubling or tripling the line length doesn't change the time it takes to fill a pint by very much. Since most of us aren't running a bar or restaurant where the time it takes to pour a pint effects our bottom line, having extra long lines is generally a good idea. It allows you to serve beer at a wider variety of temperatures and carb levels without excessive foaming, and only adds a second or two to the time it takes to fill a pint. If I have time to drink a beer, then I usually have an extra two seconds to wait for it to pour.
FWIW there is only one "line balancing" calculator I've seen that doesn't ignore the basic laws of fluid dynamics. You input your pressure, line diameter, and desired pint fill speed, and it will tell you the length of line required-
https://docs.google.com/a/email.arizona.edu/spreadsheet/ccc?key=0ApGb-vIKLq7FdGtzN3BrY2xZSldORzQ2bHVVX0hzaEE#gid=0