1gibson, water, H2O, is a lighter molecule than either nitrogen, N2, or oxygen, O2. To the extent that water vapor replaces air, the charge becomes lighter by mass. Furthermore, the replacement of an amount of air by water vapor lowers power by that exact amount.
The mechanisms by which water helps have been measured, calculated, surmised and speculated on by many authors.
From what I can tell....
The benefit of water as a VAPOR is that by replacing some air it lowers combustion pressure from charge dilution. At high enough temperatures its specific heat increases above that of the burned and unburned parts of the charge, thus reducing temperature and pressure and it also begins to dissociate, absorbing even more heat. The presence of water vapor then tends to slow the burn and reduce the peak temperatures and pressures. It is a good anti-knock agent with any and all fuels in an SI engine. It has somewhat different beneficial effects in diesel engines and jet engines.
Water introduced as a LIQUID, sprayed into the manifold or direct injected, will absorb a LOT of heat from its very high heat of vaporization. In the manifold, it will cool the charge air to the extent that it evaporates (charge air has to be hot) and will thereby increase the charge density. What water that does not evaporate in the manifold or if it is direct injected it will retard the temperature and pressure rise on the compression stroke from the heat it absorbs while evaporating and then reduce the maximum temperature and pressure during combustion from the mechanisms described above.
Water is usually measured as a percent of fuel by weight. Popular water injection systems can be set to inject water up to some low value like 25% of fuel. However, I have not seen anything that says there is a limit to how much water can be injected under high boost up to 360%, 3.6 x the amount of fuel by weight direct injected. In WWII 60% of fuel was common and 150% of fuel was documented. The combined anti-knock effects run anywhere from 1.5 to 3 octane numbers, ON, per 10%. One test gave 20 ON for 60%.
Later in the power stroke water returns the energy it has absorbed. In a turbo setup, I believe the return of energy should be greater compared to an open exhaust setup. However, water lowers the thermal efficiency of an engine overall (in terms of BSFC) even while increasing the maximum boost allowable and power output (the figures I've seen on efficiency do not account for the decrease in the required cooling power).
Also, there is a great benefit in mixing 50% Methanol with the water in terms of much better evaporation, cooling and increased charge density in the manifold and therefore more power. The merits of Methanol were discussed before.