Thanks guys for the answers. You're right, I didn't account for flow and just blindly used the equations on the net... That being said most of my confusion stems from the carbonation levels I used when bottling. I kept using around 2.2 volumes of CO2. I found that anything above 2.5 would feel a bit overcarbed to my taste.
At 16 psi I should get about 2.5 vol in the keg. Now if I understand what you guys are saying, when dispensing from a keg a considerable amount of CO2 comes out of solution immediately at serving. To avoid that and maintain a dissolution closer to the 2.5 vol I should increase the length of the tube or slow the flowrate. Since I can't do much about controlling my flowrate, I need to get a longer tube.
It's very difficult to determine exact carb levels when bottling because it's near impossible to accurately estimate residual carbonation left in the beer. It's easy to determine how much is left before you start the bottling process, but impossible to know how much is lost during the transfer to the bottling bucket and to the bottles, as well as during the process of stirring the sugar solution in. It's quite possible that your bottled beers had a higher carb level than you think. In a properly set up draft system you shouldn't lose much carbonation at all during the pour. Another factor could be that you're not accounting for check valves in your serving system. If your primary regulator is set at 16 psi, but you have 2 spring type check valves between your regulator and the beer, the beer might only be seeing 12-14 psi as they reduce the pressure by 1-2 psi each.
When I find some time, I'll try dusting off my fluid mechanics textbook and figure a formula to calculate my required length, see if it is a feasible length at my current temperature/pressure. Just to make sure I understand this; the basic idea is to find the length of tube at which the flow is fully developed (ie laminar and not turbulent).
Unfortunately it's not nearly that easy. In order to keep things a bit more simple, I left out the fact that with all else being equal, higher carbonation also requires slower flow to prevent foaming. Laminar flow is not enough to guarantee a good pour, and colder beer doesn't even require laminar flow. There's no one flow rate that works, it varies depending on temp and carb level, and there's no existing mathematical model to determine what the flow rate should be for a specific combination.
I did lie a bit above, and there is one line length calculator that doesn't ignore the basic laws of fluid dynamics. You can input your system parameters, and choose a flow rate (they have it in terms of time it takes to fill a pint), and it will calculate the length of line required to achieve that flow rate. Unfortunately this does nothing to help you determine the required flow rate for a specific temperature and carbonation level.
The good news is that extra long line doesn't have any negative side effects other than a very slightly slower pour. As I mentioned earlier, line resistance decreases exponentially as flow rate decreases. I have a 30' long line that I intended to use for soda, but in a pinch I've used it for beer pushed at 12psi, and it only takes a few seconds longer to fill a pint than my 14' lines.
Anyways, that was probably more long winded than you wanted, but here's the calculator. It used to be an excel file which also allowed you edit the roughness of the tubing, which is important for folks like myself using barrier line instead of vinyl. I can probably find the excel and e-mail it to you if you really want it.
http://www.mikesoltys.com/2012/09/17/determining-proper-hose-length-for-your-kegerator/#calc
While the guy who created this calculator is the only one who got the fluid mechanics right, he still doesn't fully understand the variables involved in a good pour, so take his suggestions in the text with a grain of salt. And FWIW for a carb level of 2.5 vol, a pint fill time of 10 seconds seems to work pretty well for temps up to 40F. At your serving temp my rough guess is that you'll need something closer to 15 seconds, which would likely result in ~30' or so.
. The actual reason I would like to make the calculations is to get a ballpark figure. As stated above line length can increase exponentially. So if I want to serve a Weizen at a warmer temperature (I know makes no sense, but hey), will I need close to 40'? That would not be very feasible.
