I have just had a bath

[SteamyTea]

Recently we have had a few people talking about domestic hot water (DHW) and how large the storage cylinder should be, and how long it will take to reheat.

So in the best tradition of the scientific methods, I got a 2 litre jug, a thermometer and started the stopwatch on my phone.

Then I measured the flow rate from my tap.

Now I have a combined tap that mixes the hot and cold.  As it is an old fashion one, it does not a thermostatic mixer, I put my hand in the water and see if it sensible temperature.  Today I actually measured it at 38°C.  A bit colder than I like (once my feet have got used to it), but perfectly good for a relatively quick morning bath.

My two litre jug filled up in 8 seconds, so a flow rate of 15 litres per minute.

After 3.5 minutes the bath was half full, which is fine for a quick morning bath, so it took 52.5 litres, which is actually less than I thought.

I also measured the temperature of my incoming water, 9°C.

 

The energy needed

 

4.18 [kJ.kg^-1.K^-1] x 52.5 [kg] x (38 - 9) [ΔT, temperature difference] = 6,364.05 kJ, or, 1.77 kWh

So allowing for standing losses from the cylinder, that can be called 2 kWh.

 

As I have not check the flow rate of my shower since I fitted it nearly 20 years ago, and I checked it when it did not have a shower head fitted, I thought I would do it again, properly.

8 litres per minute.  Now this does not seem very high, but to be honest, it is better than most showers I have used recently, so I have no complaints.

Now when I get home from work and want to wash the blood, sweat and tears off, I usually spend about 3 minutes in the shower.  It actually runs for about 4 minutes to get the cold water out the pipes, and gives me a chance to get my buff body out of my clothes.

So that is 32 litres of water.

 

The energy needed

 

4.18 [kJ.kg^-1.K^-1] x 32 [kg] x (38 - 9) [ΔT, temperature difference] = 3,879.04 kJ, or, 1.08 kWh

 

That is 1 kWh less, another 3 minutes and it is the same as a bath.

 

To reheat with my bog standard Economy 7 2.8 kW heating element takes

 

1.77 [kWh] / 2.8 kW = 0.63 h or 38 minutes for the bath

 

1.08 [kWh] / 2.8 [kW] = 0.39 h or 23.2 minutes.

 

As I have E7, I obviously have to wait until the early morning for heating.

 

I currently pay about 16p/kWh so a bath costs me 28p.

 

 

Now to take a stab at how large a cylinder is needed.

My cylinder is 200 litres, but the top temperature is generally 48°C and the bottom temperature is 20°C (about house ambient temperature).

That gives the top 100 litres, which is two bath fulls, a mean temperature of 42°.

That is enough for 2 baths, or 3 showers.

You could probably squeeze an extra shower out of that without raising the temperature, or raise the temperature and easily get 3 baths and 5 showers.

The reheat times will obviously go up, but not drastically.

 

To heat 150 litres of water

 

4.18 [kJ.kg^-1.K^-1] x 150 [kg] x (38 - 9) [ΔT, temperature difference] = 18,183 kJ, or, 5.05 kWh

 

Reheating at 2.8 kW

 

5.05 [kWh] / 2.8 [kW] =1.8 hours or 108 minutes.

 

 

Edited February 23 by SteamyTea

[ToughButterCup]

Too much detail @SteamyTea, too much detail. 🤨

[SteamyTea]

5 minutes ago, ToughButterCup said:

Too much detail @SteamyTea, too much detail. 🤨

Here is a picture before the blood, seat and tears are removed.

 

[ToughButterCup]

The thing about that scene is that any single one of the blows exchanged at that time could easily have killed either opponent.

 

 

[ProDave]

1 hour ago, SteamyTea said:

My two litre jug filled up in 8 seconds, so a flow rate of 15 litres per minute.

After 3.5 minutes the bath was half full, which is fine for a quick morning bath, so it took 52.5 litres, which is actually less than I thought.

I also measured the temperature of my incoming water, 9°C.

Interesting.  At full tilt our showers will deliver 17 litres per minute.  My daughter can easily spend 15 minutes in a shower.  If your 3.5 minute shower half filled the bath, then a 15 minute shower would have been 2 bath fulls.  Thus the myth that a shower uses less water than a bath is completely dismissed.  Even my usual 5 minute shower would be very close to a full bath full.

[SteamyTea]

Just now, ProDave said:

Interesting.  At full tilt our showers will deliver 17 litres per minute.  My daughter can easily spend 15 minutes in a shower.  If your 3.5 minute shower half filled the bath, then a 15 minute shower would have been 2 bath fulls.  Thus the myth that a shower uses less water than a bath is completely dismissed.  Even my usual 5 minute shower would be very close to a full bath full.

Yes.

It is why I don't feel too bad having regular baths.  They also help the aches and pains from years of youthful exuberance.

 

Do you really need a shower that can deliver 17 litres a minute?

[ToughButterCup]

5 minutes ago, SteamyTea said:

...

Do you really need a shower that can deliver 17 litres a minute?

 

Our Hansgrohe (Raindance) showerhead delivers 18 litres a minute. When I ordered it, I paid no attention to the flow rate: and so got a bit of a shock. But on the other hand it does deliver a gentle shoulder massage.

There's a hand unit that delivers about 9 litres a minute. Frankly sometimes I prefer that to the large static shower head. I have come to appreciate the luxury of 18 litres a minute - especially on sunny days where the PV generates enough to recharge the SunAmp. 

 

I often shower three times a day (morning, evening and after sport) - that means at least £1.50 - and makes me wince a bit because up to now I'd never given the overall cost a second thought. 

 

As usual, @SteamyTea your posts make me think. Thanks.

[marshian]

1 hour ago, SteamyTea said:

Recently we have had a few people talking about domestic hot water (DHW) and how large the storage cylinder should be, and how long it will take to reheat.

So in the best tradition of the scientific methods, I got a 2 litre jug, a thermometer and started the stopwatch on my phone.

<snip>

 

To heat 150 litres of water

 

4.18 [kJ.kg^-1.K^-1] x 150 [kg] x (38 - 9) [ΔT, temperature difference] = 18,183 kJ, or, 5.05 kWh

 

Reheating at 2.8 kW

 

5.05 [kWh] / 2.8 [kW] =1.8 hours or 108 minutes.

 

 

Bravo claps hands - nice detail (in some case a smidge too much) but Thank you for showing your workings