While not strictly a water heater, this is fun nonetheless. This portable pump shower was probably brought to the United States in the 1850s by a British subject who was (rightfully) uncertain of being able to find bathing facilities here.
The way it worked was: Fill the lower tub about halfway with warm water.
Pump the water up to the overhead tank with the built-in pump. Step in shower and pull chain. This lifts a lead weight and produces a very nice shower as long as you hold the chain.
If you run out of water, pump up the slightly dirty water and repeat. (Heating water was a REAL chore!) Next in line for bathing gets to go, using the same water. And on down the line.
When all finished, open the lead tap on the side and operate the pump. This puts the dirty water into a bucket for disposal. In England, there were special oilskin cone-shaped hats for kids to prevent their hair from getting wet. Imagine!