# Calculation of the real cost of a shower or bath with water and heating

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

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

Price = price of water + price of water heating.

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

To simplify, 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 around 20%.

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

a) Price of 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 a little less than 3 euros to 4 euros in 4 years without anyone really talking about it ... in short, it's not the debate)

It is said that a shower consumes around 50L.

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

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

A long shower, say 15 minutes with the head open, will therefore consume around 150L. We are approaching 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 therefore have from 50/1000 * 4 to 150/1000 * 4 = 0.2 to 0.6 euros!

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

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

Energy = X * T * Delta Pc

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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. 10 ° C is retained. The delta is therefore 38-10 = 28 ° C.

We therefore have the formula: Energy = X * 28 * 4.18 = X * 117 in kJ we go 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, which is the price of a tumble dryer cycle which we say is very energy intensive!

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 € / electric kWh (Belgium): around 1 € / shower (0.5 € / economy shower and 1.5 € / long shower)

Price = price of water + price of water heating = 0.4 + 3 * 0.2 = 1 € / full shower.

The ventilation is also interesting: 40% of the price for water and 60% for water heating. I thought that the part of the heating would be higher… especially since I took the electric energy, ie the most expensive.

For oil heating, we cost around 0.1 € / kWh, for an oil shower, we are therefore at 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 costs more than exhaustible oil? Bigre ...

In the end, for a family of 4 people, the “shower” price alone (1 shower / day per person) can amount to 4 € / day and therefore 120 € / month, in short, it is starting to make money, especially at the moment! !

By being thrifty, we 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 would be perhaps interesting to pass the price with the variable "duration" in the shower to obtain a value of the price in € / minute of shower ... I would do it if asked after your remarks or suggestions.

Following the reasoning