Heat transfer in water heater 1

[brightonbill]

I have an interesting problem that I am struggling to solve.

I am working on a residential project in which the client would like to install a 100L water storage heater to provide hot water to a shower. The hot water heater has 2No. 6kW elements and the water flow required is 0.15 L/s to the shower. Assuming the mains cold water supply is at 10 degrees C and stored water is at 60 degrees C with a mix at the shower head of 38 degrees C how do I work out the amount of time the hot water will last at 38 deg C and what will be the steady state temperature of the hot water supply when the tank is exhausted?

Please humour me.

Bill

 

[moon161]

Write and solve the equation of state for the water tank. It's more complicated if you consider heat loss in the pipe run.

 

[racookpe1978]

Please write down what YOU think the answer to this problem should be.

 

[IRstuff]

100L is a bit small for residential, isn't it? Typical in US is more like 190L.

Worst case scenario is where the heater doesn't do anything, which should be easy to calculate

Assuming no losses, the power divided by the specific heat divided by the flow rate gives you the best case steady state temperature.

TTFN
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[racookpe1978]

Seems like a homework problem to me, but do you read "The hot water heater has 2No. 6kW elements" as quantity two of 6 KW heater elements? 12 Kwatt total steady state heaters?

 

[brightonbill]

Thanks for the replies.

I know the water heater has a small capacity, but this is what the Client has suggested (for a one bed holiday lodge). I need to have the facts before I go back to him and and tell him it's only going to last 20 mins (or whatever).

My calcs show that the ratio of hot to cold is 127% i.e. 127/100 = 1.27:1 does anyone else concur. So for 0.15L/s; 0.083L/s is hot and 0.66L/s is cold? Therefore the 100L should last 1204 seconds = 20 mins.

Also I have worked out from Q = mCp delta T that the steady state is approximately 20 degrees C (19.57). What I can't get my head round is what effect the constant heating of the water has on the length of time the water will last.

I've ignored all losses because it would drive me insane.

By the way I'm an electrical engineer so please bear with me. It's new territory for me.

Many thanks

 

[IRstuff]

No, your steady state is 19.57 PLUS the inlet temperature of the water, so more like 29.57.

TTFN
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[TheTick]

Never saw the need to heat hot water. Now, a cold water heater, there's an invention I would have in my house.

 

[JohnRBaker]

What are you doing, channelling George Carlin…

https://www.youtube.com/watch?v=g6xfQ7ho8BM

John R. Baker, P.E.
EX-Product 'Evangelist'
Irvine, CA
Siemens PLM:
UG/NX Museum:

To an Engineer, the glass is twice as big as it needs to be.

 

[brightonbill]

Honestly. Plumbers!

 

[Compositepro]

Tanks with two heaters typically have one set low in the tank and the other set toward the top in order to provide hot water for a longer time before before it becomes unacceptably cold. There are two thermostats and only one heater is operational at any time (so heating power is 6 kW not 12 kW). The lower heater is the main one which will get the whole tank up to temperature. The only time the top heat comes on is when the top thermostat gets cold enough to switch from bottom to top heater. At this point the bottom heater is heating cold water to warm, which is not warm enough to use. By switching heaters, the top heater will be used to heat warm water to hot, usable water. This adds about 5-10 minutes of use (depending, of course, on flow rate and tank size).
The heater manufacturer will have data on the hot water capacity (minutes of flow versus flow rate before output temperature drops), and for recovery time (time for the tank to come back to full temperature).

 

[IRstuff]

BTW, I used to live in a place with an electric water heater and hated it; it was the most expensive how water you can imagine in a residential environment. While the inherent electrical efficiency is high, the price of electricity was 15x the price of gas per unit of energy.

TTFN
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[racookpe1978]

" ... supply hot water to a shower ... "

Please confirm that there is NO "bathtub" that needs hot water. A shower requires a continuous supply of hot water, but if it turns cooler, the user will "only" get mad and turn off the water. He or she can turn down the cold water side as the supplied water runs colder and colder. A shower in a single room bathroom is probably "only" going to run for those 20-25 minutes, and there probably won't be another shower or another use for hot water while it is running. (A bathtub needs to be completely filled with hot water, and other hot water taps might be running at the same time.)

Any dishwasher or clothes washer running also?

 

[IRstuff]

If you add another heater then the steady state is about 38C.

I think your 20 minutes is pretty much it; under the worst-case scenario, the user will continually adjust their shower valve to deliver a constant number of joules to the shower head, which will deplete the heat storage according to the calculation earlier

TTFN
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[MintJulep]

The hot water in the tank is only 60C if you start your shower at exactly the instant the heaters turn off.

All other shower start times will be between the turn on and turn off temperature.

Further, whatever the starting temperature is, it won't be that for long.

As hot water leaves it is replaced with cold water. Water temperature leaving the tank will not be constant.

So the limiting point is when the water leaving the tank reaches 38C. At that time 100% hot and 0% cold is required.

My approach would be:

Pick an initial tank temperature.
Compute mix for the first liter at the shower head, or first minute under the shower head.
Compute new tank temperature.
Loop until tank temperature = 38

 

[dvd]

Look at the literature available from the heating element supplier. They usually have an easy to follow guide.

This may provide some help -

http://www.watlow.com/reference/files/powercalculations.pdf

http://www.watlow.com/reference/files/wattage.pdf

 

[gruntguru]

"As hot water leaves it is replaced with cold water. Water temperature leaving the tank will not be constant."

Hot water systems take hot water from the top of the tank and admit cold water to the bottom. With a well designed system there is surprisingly little mixing.

Steady state temperature (at the reduced flow rate of 0.084 l/s) is 44 deg with 12 kW or 27 deg with 6 kW. So if no mixing occurs and 12 kW is available at the inlet (doubtful), the shower will operate for 20 minutes as stated, at which point the hot water supply drops from 60* to 44* and the shower mix will need to be adjusted to 0.124 l/s hot - 0.026 l/s cold. The 44* water in the tank then lasts another 13.5 minutes before dropping to 34*.

je suis charlie

 

[brightonbill]

Thanks everyone.

I know that's it's a bit of a strange situation, but the Client has asked us to investigate it. Just to give you the whole story, it's a single bed holiday lodge with no kitchen. It has only a shower and WHB, hence he thinks that the load will be low. But inevitably, someone will go in the shower for 20 minutes, run the hot water supply down and the next person has a refreshingly cold shower.

I was trying to show this in actual numbers to the Client to encourage him to put an electric shower in with a small instantaneous undersink heater, so they will never run out of hot water.

When you're paying $600 per night no hot water will not be welcomed with open arms.

Many thanks for all the input, I feel confident that I can put the lid on this one now.

Thanks

 

[EdStainless]

If this is used for holidays then the inline demand heater makes even more sense, why pay to store hot water when it isn't in use.
In a home there is hot water needed every few hours, so storage isn't a big loss, but in your case it is different.

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P.E. Metallurgy, Plymouth Tube

 

[berkshire]

Brighton bill,
The inline tank-less water heaters tend to consume more than the 12KW you mentioned A 13kw tank-less heater will give will give you about 6.5 liters per minute. If this is not enough flow for your shower you would need a bigger unit, and god forbid you have a bath tub there, it would take you half an hour to fill with the 13 kw direct heater.
B.E.

You are judged not by what you know, but by what you can do.