Betsty uses a Launch Tube design.
At it's basic a launch tube is filled with a flamable fuel and then ejected from the tube by compressed gas. The spray of fuekl is lit by some sort of ignitor.
The very first gasoline cannon I saw was in 1997 at that thing in the desert. It was a very simple design made from 2" sch80 seamless pipe. The launch tube was about 6 feet long and held about a gallon of gasoline. The gas reservoir was made of the same pipe. The gas was controlled by a pressure operated valve and the gas was supplied from a nitrogen tank. Ignition was provided by a propane torch strapped to the end of the tube.
Thing made a good whump and produced a 20 foot diameter fire ball.
Over the next few years I heard of other designs that were similar. In 2001 while bored at work I worked on a design of my own. Typical of me it was a vastly more complicated design. The idea being that the unit should be able to fire repeatedly.
Besty contains several 'improvements' The fuel is supplied to the lunch tube from a fuel tank via a pump. The ignitor is a propane ring burner same as used by the ICP's. There is also a pressure switch to indicate to the operator when the unit is pressurized. Etc etc.
The main problem I have had is with the pumps. None of the pumps I've used have been self priming and the head is very low which results in slow filling times. Also the holly fuel pump I used the first year got a piece of teflon tape stuck in the prssure relief valve. The centrifical pump that I selected the second year worked okay but didn't fill the tube any faster.
Recently I ordered a dual diaphram air powered pump which I'm going to experiment with. It can pump to a head of 100 psig and a max flow rate of 6 GPM. That is good for 12 firings a minute. The large max head means that flow restrictions in the fuel lines, and the check valves shouldn't reduce the flow rate very much off the 6 gpm max that the pump can provide.
Another thing I've been toying with is switching the ignitor design over to a liquid fuel. The idea being that this might reduce the complexity of the settup that I have currently. Right now I have a fuel tank, propane tank, nitrogen tank, Batsy, and the control box + battery. It takes 20 minutes ot set up and take down.
Finally I've thought of putting a small nitrogen tank on Betsy instead of using an external tank.