You may not realise it, but you're trying to make a perpetual motion machine, and it can't work.  You want to put water into the fuel tank, and get pure water out of the exhaust.

But, somehow, by turning water into water, you want to extract enough power to run a car.

The car will run until it's battery is flat, then it will stop.

When you burn hydrogen you get water... That's not a perpetual anything, that's just chemistry... 

C3H8+5O2 - > 3CO2+4H20

From this formula you can clearly see that when you burn LPG you get CO2 and water... The hydrogen burns in presence of oxygen creating water... Simple chemistry. 

Perpetual motion machine it would mean that it won't lose energy, but this one will, maybe even a lot of energy... 

The whole idea behind it, is that even if you have a small range, because water is everywhere and it doesn't really require processing it would be a lot cheaper to run... The fact that it produces water as waste it's a bonus that shouldn't be overlooked. 

When you burn hydrogen you get water... That's not a perpetual anything, that's just chemistry... 

C3H8+5O2 - > 3CO2+4H20

From this formula you can clearly see that when you burn LPG you get CO2 and water... The hydrogen burns in presence of oxygen creating water... Simple chemistry. 

Perpetual motion machine it would mean that it won't lose energy, but this one will, maybe even a lot of energy... 

The whole idea behind it, is that even if you have a small range, because water is everywhere and it doesn't really require processing it would be a lot cheaper to run... The fact that it produces water as waste it's a bonus that shouldn't be overlooked. 

That is the chemistry we all agree on, and when O2 and 2 H2 meet we get 2 2 H2O and 280kJ of energy per mol of water created (1 mol of water is 2 mols ( =2 gram) of hydrogen atoms,  and one mol = 16 grams of oxygen atoms.

Splitting the water again, takes the same energy, plus some losses.

1 mol of any sort of molecule that is a gas at room temp takes up about 22-24 litres at one atmosphere pressure

The bit that is worrying some of us is your assertion that you can use the car engine alternator to split water  back into gas again at any useful rate at all.

I'll spell out the sums that others are doing in their heads.
A typical car alternator runs out at about 1kW, though larger ones are available, and needs about 1.5kW of shaft power to do so.  That is kJ per second, so perhaps a couple of grams of hydrogen every 280 seconds, if all was loss  free. More like a few grams of hydrogen an hour would be more realistic.

In contrast a car engine is going to burn some kg of fuel per hour, as you need to be able to put 10s of kW to the wheels.

Now a system where fixed wind turbines or solar panels split water into hydrogen and water, and then you tanked this into a vehicle that burnt it would be a more realistic proposition - but of course the real source of power is the nuclear fusion in the  sun  - but that is burning to waste any way, or a from winds and tides a gentle reduction in  the moon's kinetic energy, at a rate that need not bother us.

It may well be possible to dispense with tanking the oxygen, and just take up that from the air, but the hydrogen will have to be carried on board - and as it does not liquefy at any sensible pressure, then that probably means high pressures and corresponding heavy tanks.

As I said in my first post, you need to get a decent grip on the numbers, and a far more detailed one than my coffee break analysis above.

I do not want to put you off, but I want to warn you away from things that have potential to be a huge disappointment and waste your efforts

Mike