giampiero If i remember well many years ago Formula one engine use to spray water to mix with benzine to increase power,
I “think” from talking to my late father, who was a flight engineer (Lancaster’s) during WWW2…water injection (actually water/methanol mix) was to prevent preignition on the 2 stage superchargers, so they could run higher boost pressures without in supercharger detonation problems. It cooled the charge..the methanol has a lower evap point and added extra cooling.
It was used for take off when they had a full bomb load.
So it indirectly increased power, but by allowing much higher boost pressures to be used. Which is probably what the formula one was doing back in the day.