Calculation of the actual cost of a shower or bath in water and heating

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

Try to estimate the actual cost of a shower (or a bath, only the amount of water exchange) according to the following formula:

Price = water price + price of heating water.

So more is long and it's hot, it costs more!

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

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

a) Price of water consumed: about € 0.4 / shower

The price of water depends of Commons.
It is about € 3 / m3 in France
In Belgium it is 4 € / m3 (from just under EUR 3 4 euros 4 years without anyone really talking ... well it's not the debate)

We say 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
tap is not necessarily fully open), so retain an average value of 10L / min

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

A long shower, say 15 minutes pommel opened, will therefore consume approximately 150L. We approach the capacity of a bathtub, so from a time so it is logically more interesting to take a bath than a shower!

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

b) Price of energy heating water for a shower: about 3 kWh (kWh 2 so economical) or 0.3 0.6 euros euros / shower (following price per kWh)

It is the heat balance of the amount of water consumed denoted X and converted into euros after ...

Energy = X * T * Delta Pc

Cp = 4.18 kJ / L
Delta T = T ° varies with the cold water on arrival in the housing 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.

The cold water enters the housing between 8 ° C and 13 ° C. This varies according to the year. 10 ° C is retained. The delta is to 38-10 28 = ° C.

So we have the formula: Energy = X * X = 28 4.18 * * 117 kJ kWh we go because it is what is charged 1 3600 kJ kWh =

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, consumes * 150 0.0325 4.875 = kWh or the price of a cycle of dryer is said very energy!

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 Invoice with hot water to electricity with a price of € 0.2 / kWh electric (Belgium): approximately € 1 / shower (€ 0.5 / 1.5 economic and shower € / long shower)

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

Ventilation is also interesting: 40% of the price for water and 60% for heating water. I thought from the heating would be higher ... especially since I took electric power, ie the more expensive.

Heating oil is is about 0.1 € / kWh for the oil shower so it is 0.7 € and the share of water therefore costs more expensive than energy!

There would a broader questioning to be done for this particular case: renewable water costs more expensive than the exhaustible oil? Bugger ...

In the end for a family of 4 people, just the price "shower" (1 shower / day per person) can go back to 4 € / day and therefore 120 € / month, in short it starts to do especially at this time! !

By being frugal, we can divide the bill by 2 (€ 0.5 / shower), placed at € 120 50 60 to € / month ... and 50 € / month is not nothing in the current household budget!

It might be worthwhile to spend the price with the variable "duration" in the shower for a price value in € / minute shower ... I would if asked after your remarks or suggestions.

Following the reasoning

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