What happens if a cylinder filled with propane gas is connected to an empty one of the same size Let's say I have $2 100$ lb propane cylinders. One of the cylinders is filled to its maximum capacity while the others are empty. If I connect them to each other via a high pressure hose in an upright position and open the valves on both, will the propane gas go over to the empty tank from the full tank until both are EQUALLY filled? 
What I am trying to do is connect $5$ propane tanks to each other standing upright; $4$ full, $1$ empty. I'm wondering if the propane will transfer equally amongst the $5$ cylinders until there is an equilibrium in the amount of propane that each cylinder contains. 
If this is not possible, will connecting them in an upside down position so that propane is released in liquid form result in an equal amount of propane in each of the five cylinders due to hydrostatic equilibrium? 
 A: Okay, so you asked specifically about "a cylinder filled with propane gas", and if it's really filled with the gaseous form then that will distribute evenly.
However you probably meant that the cylinder was filled with liquid propane, and that is a lot harder to deal with. If the system could handle the pressures you might try a bunch of successive runs where you try to boil some of the liquid evenly and then condense it evenly within the tank, otherwise you have to wait for natural processes of condensation to eventually spread out the liquid, and there's a good chance that they might not.
There is a nice effect called the siphon effect, it says that if you have two open-air tanks filled with different amounts of water, and you fill a tube completely with water and it arcs over the edges of the tanks to connect them, then if you leave them for a while you will discover that they have the same water level. I do not mean that they will be filled evenly because they might have different shapes and one could be lower or higher than the other; I just mean that if you took the water level from the one as a 2D plane extending across the space outside the tank and eventually intersecting the other tank, you would see that this plane also intersects the other tank. What happens can simply be described as "the water seeks its minimum-energy configuration, some of the water from over here can have a lower energy over there, and because the tube is 100% full of water it does not form a potential energy barrier to this sharing of water."
Now this is a very suggestive result for your purposes, but it comes with a lot of stipulations, too. The tanks are open-air, but why? It's so that I don't need to consider in my energy calculations "okay this tank has more water in it, but also its air is pressurized and that contains some energy too." In your case you would like two tubes connecting the cylinders, one that could equalize pressures while one could allow fluid to flow, and then they could come to the same fluid-levels via siphon. But in order to be very sturdy usually these tanks only have a valve on one side and that's it.
So if you want to do the same thing you probably need to cycle the same valve from "equalizing pressures" to "equalizing water levels" back and forth over-and-over again.
The easiest way to do this would be to stably fix the 5 cylinders side-by-side in a big rack that can rotate slowly, so that when the valves are all upside-down then they share some propane-liquid, and when the valves come right-side-up then they equalize their propane-gas amounts.  This will still take a while to equalize all of the propane, but it should eventually do it and it could probably solve the problem over the course of several hours while being left to itself. What you really want to increase the speed is to find a regime where the tube is consistently half-full of fluid, so that it really acts as "two tubes" and allows free flow between the tanks.
A: First and foremost. What you are suggesting is both very dangerous and for that reason prohibited by law in most countries in the world.
That being said, here's how you do it:
Just connecting the tanks standing upright will eventually spread the gas over both of them, but you may celebrate a number of birthdays before they are done doing that. Turning the full one upside down and lifting it over the empty one will make things go considerably faster, but keep an eye on the weight of the tanks to prevent overfilling.
Which brings us to the one and only reason you might ever want to do something like this. It is a method to release LPG from an overfilled tank. Overfilling LPG tanks may cause the tank to tear open, rapidly releasing all its content looking like smokey water. I once opened a car trunk half filled with it. That's the kind of sight that makes your blood freeze. Don't go there.
Another reason to not do this unless you absolutely have to is the risk of seriously damaging the valves. There is all sorts of nonsense laying on the bottom of most any gas tank, like sand, welding chips, metal shards, you name it. Besides that, LPG being odorless by itself is mixed with a substance that reeks awful, but looses that smell completely at burning. If you get any of that on your 50.000 Dollar three piece suit, you're gonna want to throw it away, because the only way to ever get that smell out is by burning it.
A: If the propane in the tanks are under pressure,then on connecting them, both tanks will be full of propane as it is a gas. Had it been water, or in a liquid form, then both the tanks will have the same level no matter how you arrange them. 
