You can imagine my glee when my good friend Andrew asked me a great fluids problem this weekend: He just built a new beer tap system converted from an old chest freezer.  He wants to have nice head on his beer, so he doesn't want it coming out of the tap to quickly.  He was also unsure about the pressure to keep his keg under.  Basically his question was How to balance your kegging system?  

So I made this calculator by combining the Bernoulli, Darcy Weisbach, and Swamee-Jain equations to help you calculate your perfect kegerator hose length. Simply plug in the parameters for the beer you'd like to serve, and it'll spit out a hose length for the perfect pour! Keep reading for more science about how to choose your CO2 pressure, or the background behind this calculator.

What an awesome problem! There are many empirical formulas out there that will give you a length... but I've had a lot of feedback that this equation gives vastly better results than other formulas out there.  I guess I'm not surprised: It's based on science and not empiricisms so read on for the perfect pour.

Carbonation: Selecting Temperature and Pressure

First: Every beer has a specific amount of carbonation that the brewer meant for it to have.  As a general rule, darker, maltier beers are usually less carbonated that lighter beers.  Here are your first decisions: What temperature will you serve your beer at?  Then, using a carbonation chart, determine what pressure to set your CO2 regulator at so the beer is properly carbonated for flavor.  Generally speaking, the colder and more pressure you put your beer under, the more CO2 it will absorb.  Also note: You'll need to add about 0.5 psi for every 1000' elevation you'll be keeping the beer at for proper carbonation.

Hose Length: Selecting Tubing and Flow Rate

You may be tempted to run any hose you have from your keg to your tap, but realize this: The beer is under a lot of pressure!  The only tool you have to lose this pressure is frictional losses along the length of the hose.  This is where the fun fluids come in!  The energy in a pipe system can be described by the Bernoulli Equation for conservation of energy with the Darcy Weisbach equation for frictional losses:

if the tube diameter does not change in the system, then the equation can be re-arranged to look like:

Here, you have two decisions to make: what diameter tubing you want to use and what flow rate you want for your beer.  For most home kegerator systems, or systems with a short (<8') distance to travel: 3/16" tubing is pretty standard.  If your beer will be traveling further, you may consider using a larger diameter tubing (1/4") but don't forget to keep your beer line chilled so the beer doesn't go bad or flat in the tubing. Next is flow rate.  It seems to me, 10 seconds is a perfect amount of time to pour a pint, although super beer snobs might have a specific pour time depending on the type of beer being served.

The friction factor is normally based on the type of pipe material, the diameter of the pipe, and the reynolds number of the flow within the pipe.  From these factors, the friction factor can be read on a Moody diagram or estimated using something like the Swamee-Jain equation.

I should note that I included a number of assumptions in this calculation:

1. There are no minor losses at the keg, the tap, or in the coil of hose (In reality there will be some minor losses, and so you can get by with a slightly shorter hose length).
2. The  viscosity of beer is an unchanging 0.00003279 lb/ft^2 sec
3. The roughness of vinyl tubing is e=0.000016 [ft]
4. The pressures are gauge pressures, so no elevation correction is needed.

Return to my, my hose-length calculator!

Alternate: Set Pressure/Temperature based on Hose Length

I should note that this whole process can easily be reversed, although the result is less optimal.  You can set your Pressure/Temperature based on a pre-existing tube length. This is less ideal, because you might be serving slightly warmer or less than ideally carbonated  beer.  However, this may be more practical if you're changing what beer you have on tap, and don't want to change your tube length or CO2 pressure with each new keg.

The Bernoulli w/ Darcy-W equation looks like:

If you decide what flow rate you want you can back out what your pressure change needs to be, and then using the carbonation table, you can determine what temperature would be a good serving temperature for the right carbonation.  On the second page of my spreadsheet, i've set it up for the reverse input:

Then, head over to the carbonation chart, and try to determine the optimal temperature to serve your beer at.