Calculating the real cost of a shower or bath and water heating

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What is the real price of a shower or a bath after the water consumed?

Let's try to estimate the real price of a shower (or a bath, only the amount of water changes) according to the following formula:

Price = water price + water heating price.

So the longer and the hotter, the more it costs!

For simplicity, we neglect the losses in the pipes and the domestic hot water system. Whoever wants to take them into account can increase the price of heating by about 20%.

Those calculations bored can skip steps c) and concluding in red below.

a) Price of the water consumed: around 0.4 € / shower

The price of water depends on the municipalities.
It is about € 3 / m3 in France
In Belgium it is 4 € / m3 (gone from just under 3 euros to 4 euros in 4 years without anyone really talking about it… in short, this is not the debate)

It is said that a shower consumes about 50L.

She measured by the actual flow rates of various heads

Results: of 6 L / min for a shower to misting 18 L / min for a zenith (open valve thoroughly, actually the
valve is not necessarily fully open), so let's keep an average value of 10L / min

A quick shower 5 minutes open tap consumes much 50L or the 50L announced earlier.

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A long shower, say 15 minutes with the shower head open, will therefore consume around 150L. We approach the capacity of a bathtub, so from a moment it is therefore logically more interesting to take a bath than a shower!

In euros and in Belgium, just for the price of water, we have 50/1000 * 4 to 150/1000 * 4 = 0.2 to 0.6 euros!

b) Energy price for water heating for a shower: approximately 3 kWh (2 kWh if economical) or 0.3 euros to 0.6 euros / shower (depending on price per kWh)

We make the heat balance of the quantity of water consumed noted X and we then convert it into euros…

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Energy = X * T * Delta Pc

Cp = 4.18 kJ / L
Delta T = varies according to the T ° of cold water on arrival in the accommodation and the T ° requested by the user.

Usually you take a shower between 35 and 40 ° C, from 45 ° C it begins to have a burning sensation.

Taken is the average value of 38 ° C.

Cold water arrives in the accommodation between 8 ° C and 13 ° C. It varies depending on the year. We retain 10 ° C. The delta is therefore 38-10 = 28 ° C.

We therefore have the formula: Energy = X * 28 * 4.18 = X * 117 in kJ we switch to kWh because this is what is billed 1 kWh = 3600 kJ

Energy = X * 117 / 3600 0.0325 kWh = X *

If X = L 50, so we consume * 50 0.0325 1.625 kWh =
If X = 150 L, we therefore consume 150 * 0.0325 = 4.875 kWh, the price of a dryer cycle that is said to be very energy-consuming!

For an efficient shower, we can retain an average value of 2 kWh / shower.

We take the value of 3 kWh / shower for the rest corresponding to a 90L shower or a long shower (9 minutes opened tap)

c) Average final bill with electric hot water with a price of 0.2 € / kWh electric (Belgium): around 1 € / shower (0.5 € / economic shower and 1.5 € / long shower)

Price = water price + water heating price = 0.4 + 3 * 0.2 = 1 € / shower all battery.

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The ventilation is also interesting: 40% of the price for water and 60% for water heating. I thought that the share of heating would be higher ... especially since I took electrical energy, that is to say the most expensive.

In oil heating we are around 0.1 € / kWh, for an oil shower, we are therefore 0.7 € and the share of water therefore costs more than energy!

There would be a more global questioning to be done for this particular case: renewable water is more expensive than exhaustible oil? Gee ...

In the end for a family of 4 people, just the price "shower" (1 shower / day per person) can return to 4 € / day and therefore 120 € / month, in short it starts to make money especially now! !

Being economical, you can divide this bill by 2 (0.5 € / shower) and go from 120 € to 50 to 60 € / month… and 50 € / month is not nothing in the current household budget!

It might be interesting to pass the price with the variable "duration" in the shower to get a value of the price in € / minute of shower ... I would do it if asked after your comments or suggestions.

Following the reasoning

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