But consider what happens when you take a shower. The incoming water might be 10 degrees Celsius (50 F). The temperature is then raised to say, 43 degrees Celsius (110 F). The water cascades over your body and then goes down the drain.

It is estimated that about 95% of the energy used to heat the water to a comfortable temperature is simply going down the plughole.

If you have an electric shower unit, you could actually recover some of that energy.
An electric shower connects directly to the cold water supply. A very powerful heating element (typically 8 or 9 kW) then rapidly heats the water to produce an almost instant supply of hot water.
In the winter time, incoming water may be colder than in the summer time, so you need to use more energy to heat the water to the required temperature.

So how can we recover the wasted energy?
The answer is a simple heat exchanger, which transfers the heat from the waste water to the incoming water supply.

Basically what happens is this: the cold water supply runs through a pipe that either coils around the waste pipe, or runs through the inside of the waste pipe.
As the shower starts to flow and hot water goes down the waste pipe, it starts to heat up the cold water inlet pipe. Heat has been transferred from the waste to the cold supply.
The supply water is now several degrees warmer than it was before, so the shower unit needs to use less electricity to heat the water up.

Heat exchangers of this type are commercially available, but it wouldn’t be beyond the capabililties of a competent DIY enthusiast to make one for himself.

You would need to ensure that the cold water supply had a check-valve to stop warmed water going back to the cold supply.

Your shower unit would also need to be thermostatically controlled. A standard shower unit would simply apply the same amount of energy to the warmer water, resulting in scaldingly hot water output. You might end up having to adjust the temperature manually several times during a shower to compensate for the changes in temperature.