I had no accurate concept of how much water ran through a shower, so I measured one to try and get a picture of how much it costs to heat water for a shower. Now, this is a MAINS pressure system, so if you have a water header tank, you have a low pressure system and the results will not be comparable. The results also depend on:
I set the shower to the preferred temperature, which in my case is 40 degrees C (104 deg F), put the mixer to full and let it run for a minute into a bucket. After 1 minute, the bucket had 15 litres of water.
The position of the mixer and the proportion of hot water in the mix depend on the temperature of your cold water AND the temperature of your hot water. Sounds sensible. My cold water was coming in at 16 deg C (61F) and the hot was coming in at 56 deg C(133F), so if the mixer was set at half, assuming equal pressures, then the water would come out at 36 deg C (97F); which is a little cool. Since I want 40 degree water temperature, the mixer is set to 60% hot and 40% cold, so in my case, I am using 9 litres per minute of hot water. Is this typical? It seems reasonable. The NZ energy conservation authority does state 9 litres per minute for a shower. My hot water of 56 degrees is a little higher than the recommended 54 degrees but is in the ball-park. The bathroom is very near the hot water cylinder. Water pressure here is 480kPa (~70psi). Generally you will have lower pressure if you are high on a hill and higher pressure if you are low down, but that does depend on where the authority has located the mains header tanks.
This house has a 180 litre hot water cylinder, which is a common size for a smaller household. In this case, the shower will run the cylinder out of hot water in 20 minutes. (For larger families, 250 litre and 300 litre cylinder sizes are available.)
With a 180 litre tank, two people need to have showers less than 10 minutes each in length. One good option of course, is to throttle back the mixer (if the mixer is of this type). At half setting, the mixer did indeed produce half the flow, and the shower pressure is still good enough.
Let's assume two people each have 5 minute showers at full blast. In the ten minutes, they will have used 90 litres of hot water. Cold water at 16 degrees (in this case) replaces the 90 litres, which was initially at 60 degrees in the tank. The nett temperature after the cylinder stabilises would be 38 degrees.
(In practice, cold water enters at the bottom of the cylinder, which is where the thermostat AND the heater element are located. The thermostats in these cylinders usually have 8 degree Celsius differential (some are 10 degrees), so as soon as the water near the thermostat goes below 52 degrees, the heater element comes on. Although the water does not mix immediately, due to stratification, the following calculations remain correct.)
When nobody is drawing any hot water, the cylinder water will slowly cool anyway, due to heat losses. Just how much loss you have depends on how well insulated the cylinder is from the surrounding cool air as well as the temperature of that air. In summer the rate of heat loss will be lower than in winter.
Clearly there could be a wide variety of scenarios. Industry assumed rates of energy loss (standing loss) from cylinders varies from 1.4kWh per day to 4kWh/day. However, wider ranges are possible with higher losses in cold climates. Using 2.0kWh per day loss, the water in an 180 litre cylinder will drop by 10 degrees Celsius in the day; just enough to trigger the thermostat on. A 2kW element will run for slightly over an hour to boost the temperature in the 180 litre cylinder by 10 degrees, costing just 56 cents.
If you turned the power off to the cylinder, the water temperature in our tank will drop to ambient over a period of time, again depending on the losses. The rate is an exponential curve, adhering to Newtons' law of cooling. The rate of heat loss reduces as the tank cools. After 2 days off, the cylinder water will be around 42 degrees, costing some 99c to heat. Had you left it on, it will cost about $1.12. In fact, water in our notional tank takes over 11 days to drop to 20 degrees C if the surrounding air was at 18 degrees. If you returned from holiday after 11 days and switched on the tank, it will take 4 hours and 10 minutes to heat, costing $2.25. Had you not turned it off, it will cycle on and off eleven times, resulting in 11.5 hours running in total, which costs $6.16.
So, you will save money by switching off for a holiday but it saves little money unless you are away for a few days or more and you do have to wait longer for the cylinder to heat up. Of course, this situation varies a little depending on cylinder size, losses and ambient temperatures, but the rough rule will be that it is worth turning off if you are to be away more than a few days.
As noted earlier, it takes the same amount of energy to raise a given amount of water by a given number of degrees. So, if you had a timer which disconnected power at a time when the thermostat is trying to turn on, then when eventually your timer activates, the heater will have to be on for longer. So, the use of a timer will not save any power. If you are going away for more than a few days, then turn off the cylinder completely. If you are away less than a few days, a timer will not help save power.
The only scenario where a timer might be useful is if you can pay an off-peak or night rate. Allowing the cylinder to switch on only at off-peak times then becomes sensible, but of course you have to be aware then of the reduced availability of your hot water. If you needed a shower at say 7am, then you need to ensure the timer lets the cylinder switch on by say 5am each day.
My hot water cylinder management guides go like this:
I have built a heat extractor for my shower that recovers the heat from the water going down the drain and preheats the cold water entering the shower mixer, this works extremely well and saves about 30% off our hot water, especially in the winter when the electric backup element is turned on. The hot water is essentially free as I have 8 sqm solar heating panels on the roof that I built 5 years ago. Heat exchanger is 6 meters of 15mm soft copper tube wound in a spiral inside a big piece of plastic drain pipe, this is mounted vertically under the floor, the shower waste drains on to the top of the spiral, exits the bottom; cold water to the mixer runs inside the copper tube, works very well, however the thing needs cleaning every 6 months, so have made it to be easily removed. Water pressure is 120 kpa, as I got an all copper HWC made to my spec (for fittings) by SuperHeat in CCH for the solar, stainless cylinders were not readily available at the time, which can run at mains pressure. I have been playing around building heat pipes filled with refrigerant gas as a means of moving heat from the shower grey water to the cold water, they work very well and would provide a double barrier isolation to be strictly legal, however tricky to make. Would also be good to use on a power amp etc to move heat from power transistors to an external heat sink.
Make a comment using the form on the contact page