Depending on where you live, the city water pressure is usually between 70 and 120 psi at the tap. I had the idea last year to use that water pressure to make compressed air. It would be silent and uses no electricity. It does use electricity at the city pumping station and it does use about 45 gallons of water every time you fill it or charge it. But, in an off grid situation and with well water, the pump would be run by solar or wind. And the pressure tank could be for your water pressure regulator. But when you need it, you would also have compressed air. In other words, you already have a pressure tank on a pump system that regulates, this would just be an add on that would give you more steady pressure without the pump kicking on. But every so often, if you need an air powered tool, you have the air already there.
Or you could use it in your shop even if you are still on grid. After all, it is silent and it takes no electricity. At 100 psi water pressure, a 50 gallon water tank would give about 6.5 gallons of compressed air.
Note that the hot and cold are capped and soldered shut. Get rid of the pressure relief valve, you can keep the valve if you like but you won't be using the heaters and city water pressure would never get that high. Even if it did, something else (probably in someone else house) will blow before your tank. Just use the drain valve and the pressure relief ports for this setup as shown in the picture above. You can't use the hot water port because as the water compresses the air, water could shoot through the tube to your air tools when it gets high enough.
Depending on the pressure, the volume changes. For instance, at 60 psi the air volume would equalize at about 10 gallons. A problem could be water vapor in the output. A simple dryer mechanism can be built out of copper and 90 degree elbows. The heavier water vaper just can't maneuver like the air around the bends and turns so it hits the copper walls and condenses.
Mainly, I see someone using this if they want to add a pressure regulation tank to their house and they would like compressed air always available. Anyway, something to think about.
Also, if you are trying to figure the math for different pressures, just use ideal pressure law P1V1=P2V2. But use absolute pressure. The tank starts at 15psi and if you pressurize it with 60 psi water, don't use 60, add 15 to the 60 and use 75 as your number. That is absolute pressure. The 60 psi is really psi gauge which means it is that number plus whatever atmosperic is. So, add atmospheric pressure to your water pressure and then use those numbers as P1 and P2.