We have a Hot Water Recirculation Pump. It does not save any energy in the heating of the water. It may make a small difference in the amount of water used, but I didn't notice a big difference in our bill. I love it, though, because now hot water arrives to the shower in about 30 seconds instead of 2 or 3 minutes (which does save a little water).
Basically the water that sits in the pipes between your water heater and your tap eventually cools down. The pump moves that water back to the heater, and fresh hot water to your tap, so that you get hot water much quicker when you turn on the tap, especially for taps that are farthest from the heater. A friend of mine argues that it's wasteful because you're turning all your pipes into a big radiator, but again, it can't be a big effect because it had minimal impact on our utility bills.
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financial checklist:
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