Originally Posted By: paul

but it shows you can get back what you put in ,

Of course. That's called conservation of energy.

Originally Posted By: paul

and using a vacuum to generate the HHO will return even more.

No, it won't.
It will require less energy to do the electrolysis, but also you will get less energy during the recombination.

I'm still thinking about
"Michael Farraday has shown that 1 liter of HHO can be produced in 1 hour using 2.34 watts or 2.34 watt hours."

Maybe you can calculate the needed energy for electrolysis in your engine:


Faradays Law:

V = R I T t / F p z


V = volume of the gas [L],
R = ideal gas constant = 0.0820577 L*atm/(mol*K), = current [A],
T = temperature [K],
t = time [s],
F = Faradays constant = 96485.31 As/mol,
p = ambient pressure [atm],
z = number of excess electrons (2 for H2, 4 for O2).