High humidity improves mileage for two reasons. The water molecule (atomic weight 18) is much lighter than nitrogen (28), oxygen (32) or carbon dioxide (44) molecules, so if there is lots of moisture in the atmosphere, it reduces the density of the air your car is plowing through. Also water molecules in the air displace some of the oxygen molecules that your engine would normally be combusting. So high humidity has the effect of reducing the amount of oxygen that your ICE can suck in, which also reduces the amount of gasoline burned and the amount of power produced by the ICE.
They used water injection in some supercharged WWII aircraft, but there is was mainly used under steady state (fixed throttle) conditions with about 80% to 90% throttle. Aircraft engines are operated very differently from the average car ICE, since aircraft engines are run closer the full power most of the time and the RPM's remain more constant. Unlike car ICE's that are run at low power settings most of the time and the RPM's are often rapidly changing.
A method to set up a constant high humidity entering the intake manifold may help to improve mileage, but a water injection (spraying jets of water into the intake) wouldn't. The peizo room humidifier may work provided it can produce enough mist to keep up with the ICE's air intake demands and if the electricity required to operate the peizo doesn't eat up your energy savings via heavier demands on your alternator. The peizo will also need to adjust its output to your ICE's air demands, otherwise if you spend some time idling in traffic with the peizo running full tilt, you may end up killing the engine with excess water.
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