Quote:
Originally Posted by jgourd
Suppose I have a 48" length of hose with an inside diameter of 3/16". The hose's supply end is 21.5" below its dispense end. Also suppose that the average flow resistance of such a hose is 2.25 lbs/ft. At the supply end, a pressure of 9.02 PSI is pushing liquid through the hose (assume the liquid is beer with a specific gravity of 1.010 g/cm^3).
1) What is the flow rate of the liquid at the dispense end?

This is a practical problem rather than a theoretical one. As you probably know the rate of flow of viscous fluid through a tube depends on the viscosity of the fluid, the diameter and length of the tube and the friction of the fluid with the tube walls. The details are in many physics and fluid mechanics textbooks. The practical approach is to take measurements on actual beverage tubing and it is from these that the various dispense tables are derived. The tables all assume a flow of 2 Oz per second at the faucet (i.e you can fill a 12 Oz glass in 6. Second.)
Quote:
Originally Posted by jgourd
2) What is the pressure (in PSI) at the dispense end?

Clearly, the pressure at the dispense end is 1 atmosphere (14.7 psia).
Quote:
Originally Posted by jgourd
3) Perhaps the more important question is, what pressure (in PSI) must be present at the dispense end in order to have a desired flow rate of 0.78 gal/min (with all of the specifics of the hose as described above)?

You'll need enough pressure to overcome the flow resistance (found in tables or from online calculators). Example:
http://www.kegworks.com/blog/2007/05...tbeersystem/. Just multiply the total length of the line, including the vertical run, times the resistance figure. e.g. 2 ft 1/4" ID stainless steel: (2)*(1.2) = 2.4 psi; 3 ft 3/16 ID vinyl: (3)*(2.2) = 6.6 psi.
You'll also need the gas to do the work of lifting the beer. The pressure difference at 2 points h apart in a fluid column is simply density*gravitational_constant*h. It works out quite simply here as an atmosphere is 30 feet of water and 14.7 psia. So it takes about 0.5 psi per foot to nullify the hydrostatic pressure. So the overall formula is
P = sum[i=1,N](resistance_of_hose_i*length_of_hose_i) + 0.5*h
for a system with N bits of hose of different lengths and resistance coefficients.
Note that 0.5*h is for water. For another fluid it would be 0.5*h*SG but as beer has SG so close to 1 and there are so many other approximations (viscosity, for example) it's not worth worrying about. Even with the most accurate formula you will find you have to "tune" the system by tweaking gas pressure (bearing in mind that eventually this will translate into more or less gassy beer), adding "chokers", changing hose diameter or type etc.
I would prefer formulas as opposed to just, "here's the answer." That way I can learn. Thanks![/QUOTE]