Engineers do take showers

and save £410/year!

Even as I have taken successive steps to reduce my bills and my carbon footprint, a remaining guilty pleasure is my good long soak in the shower every morning. Somehow it’s essential to wake up slowly. So I have tried various low-flow shower-heads, and after a couple of appalling “cold mist” experiences, finally found an aerating shower head (the EcoCamel) that still felt good and claimed to reduce flow substantially. But just how much was it really saving us?

The first step of my analysis was to measure the water flow – and that gave me a big surprise. The original head was a standard Aqualisa shower head fitted by the plumber at install, so I put that back on. I borrowed a measuring-jug from the kitchen, put it under the shower, turned it on and … it was full in a fraction of a second, far too fast to measure. Wow, that’s a lot of flow. Our hot water system uses mains water pressure, so I guess our showers are similar to a power shower experience.

So I went and got a bucket, which held 11 litres. The old shower head filled the bucket in 35 seconds. The new head in 94 seconds. So that’s 37% of the flow. Sounds good, but is it really significant for our household budget?

The above calculation shows that the old head uses 18.8L/minute. Or 188L for a 10 minute shower. Clearly my costs are going to be a combination of the water bill, and then the energy bill to heat it up, so let’s work each out separately.

Water Cost

Referring to my latest Anglia Water bill, I see that I am charged £0.81 for every cubic metre (m3). Doesn’t sound too bad – that’s a lot of water for less than a pound. But then I noticed that sewerage is ALSO charged on that – Anglia Water assume that 90% of what they supply as fresh water is then flushed down the drain again. And they charge £1.42/m3 for sewerage, so every cubic metre of water is deemed to cost me £1.28 in sewerage too, in other words I am charged a total cost of £2.09/m3. There are 1000 litres in a m3, so this is 0.209 pence per litre. Sounds pretty cheap compared to bottled water!

Energy Cost

Our gas boiler was installed pre-1998, so is the less efficient non-condensing type. Our heating system is of the “conventional” type, meaning that a big loop of water piping runs through the boiler and then around the house, heating the radiators and heating the hot water tank. A 3-way valve determines whether the heat goes to the radiators, the hot water tank or both.

On our last bill, gas cost us 3.6p per kWh (“unit”).

The specific heat capacity of water is 4186 Joules per (kg °C). A watt is a joule per second. So a watt-second is a joule. So a watt-hour is 3600 joules. So a kilowatt-hour is 3,600,000 joules.

Heat Added = specific_heat x mass x delta_temp

Comfortable shower water temp is 40°C (just above body temp)
Incoming water temp is 10°C. So delta is 30°C

1L of water weighs 1kg
So 1L of water raised 1°C takes 4186 Joules which is 0.00116kWh
So raising it 30°C takes 0.0349kWh
So every litre of water costs 0.126p to heat.

Aha, but when I consulted our wise friends in the Data Analytics team at AlertMe they pointed-out that this doesn’t take into account all the inefficiencies in my heating system. BRE’s BREDEM-8 model for our heating system type estimates its year-round average efficiency at 70%, plus a 15% of distribution loss (all that piping between the boiler and the tank gets warmed-up too, even in summer), plus an average storage loss in the hot water tank of 30%. This makes the net efficiency around 48%, so in fact my water is costing around twice as much to heat as I first calculated.

This puts the true cost of heating every litre of water at 0.263p.

Putting it all together

So every litre of water costs 0.209p to buy and 0.263p to heat = 0.472p total. A 10 minute shower with the old head consumed 188L and cost £0.89 per shower. So two such showers (me and my wife) taken every day for a year costs an amazing £650/year. And our Eco Camel head, by reducing the flow to 37% (i.e. by 63%), is saving us £410/year.

One thought on “Engineers do take showers

  1. Well, I’ve checked your calculations very carefully, and I can’t find an error. I was thinking that you’d perhaps turned 0.01p into £0.01 at some point (easy to do), but I can’t find it if you have. All the figures stack up, so that result is truly amazing!

    A few things are probably making it big / seem big:

    * I measured my shower, which like yours is mains fed but not pumped. I’m using 13 l/min vs your nearly 19, so you must have had a hell of a shower head on there.

    * The EcoCamel quotes a maximum of 8 l/min, whereas you’re measuring only 7. So overall you’re getting a bigger delta (nearly 12 l/min) than I might (maybe 5-6 l/min).

    * The headline £400 a year figure initially sounds like it’s coming off your energy bill, which would be truly startling. But actually half of it is coming off your water bill (still money though of course!). £200 off your energy bill feels more reasonable. Mine would be about £100 = a bit less than 10% of the total annual cost. Still a pretty good saving for one intervention costing £30!

    The funny thing is, I’m still not convinced I’m going to rush out and spend £30. The psychology of money is very odd. That £30 would come from my pocket now, whereas the £100 would come “off” my bill in a year’s time. We really do discount future savings far too heavily.

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