The way an external reactor works best is for the downward flowing water to be moving fast enough to hold a lot of the CO2 bubbles in suspension, so they don't just shoot to the top of the reactor and collect there. But, not so fast that the water flow sweeps the CO2 bubbles out the exit at the bottom of the reactor. Since the speed of the flowing water in the reactor goes down as the reactor diameter goes up, you can have too big a diameter, or too small a diameter, for the specific flow rate of water going through the reactor. I haven't seen any testing data that shows what diameter is best for what flow rate. My 2 inch diameter pipe, which is actually bigger than 2 inches in diameter, works pretty well with my Filstar XP3.
I'm not sure if the length of the pipe is critical at all. Generally I think people make them about 2 feet in total length, but shorter or longer may be just as good. Obviously a 2 inch length would be much too short, and a 4 foot length would be absurdly long, but the best length doesn't seem to have been determined.