Hey Zookie, if you want to get into stoichiometry....give me your best shot!
Here is what 5L/min of gas generation does (this is more than most of the units I have seen do):
PV=nRT P=1, V=5L, R=0.0821, T=~300
0.203004466 moles/min
0.022556052 moles H2/min
0.045112104 g H2/min
20MPG at 50MPH
1 hour 50 miles
2.5 gallons
9.45 Liters
8.0325 kg's
8032.5 g's
133.875 g's diesel/min
The top calculates how many grams of hydrogen 5L/min would generate....about 0.045g. The bottom calculates how much diesel fuel you consume per minute assuming 20MPG and a 50MPH speed, and arrives at about 134g/min.
That works to a factor of almost 3000 (2968 to be exact)! So, people think that by adding 1 part in 3000, they will have an impact on fuel efficiency? Give me a break. More like an impurity level.
To make enough hydrogen to make a difference, here is what you need (and once again, I will assume the hydrogen comes for free, because we already know you can't make electrolysis "generate" energy):
To get a 10% increase in fuel efficiency, I will assume you need 10% more fuel heat. We know hydrogen has 3x the heat content per gram when combusted, so we need to add 3.33% by weight hydrogen to the fuel stream. In the example above, if we are using 134g/min of diesel, we would need to supplement with 0.03333*134=4.46g/min hydrogen. 4.46 grams of hydrogen works to 495 Liters/min of electrolysis gas! If you had a 1" ID hose from the electrolysis vessel to the air intake, the gases would be flowing at 53 feet/sec = 36MPH.
So, unless the hydrogen is acting in some catalytic fashion (which, trust me, it does not), 5L/min of brown gas won't do a thing. To generate enough to have about a 10% increase in fuel efficiency, one would need closer to 100x that volume, which corresponds to about 22g of water a minute being electolyzed. That works to 5-6 gallons of water per tankful of diesel (assumes 40 gallon tank).
Again, the energy needed to make the hydrogen will exceed the gain in the engine (since all you do in the engine is combust it back into water), so the above is moot anyway. I was just doing it to show you the magnitude of what you will need to generate to even be in the ball park, assuming you got the hydrogen for free (no energy input).
The manufacturers of these products never go into the real science because if they did, they would not be able to fool people. The bottom line is 2 main points:
1. From a purely energy perspective, you can't make more energy than you have. If you use the vehicles stored energy (electrical system) to drive the electrolysis, those systems will need to be re-topped and that ultimately comes from burning a little more diesel.
2. Assuming the electrical draw (to run the electrolysis) is small compared to what is wasted all the time just running the electrical system (I'm just guessing these devices are inefficient since the belts are always turning), which means you get your hydrogen for free (as I have stated in assumptions before), the systems everyone I have ever heard discussed produce NO WHERE NEAR the amount of gas you would need.
Two major holes in the side of the ship if you ask me.
Ralph