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# A math problem :)

Member Posts: 284
Hi everyone..

I have a guy that has a 20 gallon electric water heater.  The WH has a 3KW element in it,,  The guy says that the water takes about 2 hours or more to heat up...  I did some calculations and it shouldn't take that long..

Here's my calculations:

*If a BTU is the amount of energy needed to raise 1 lb of water 1 degF

then -

*1LB of water = about 1 pint... (actually 1.04 LBS)

*20 gallons = 160 pints = +- 160 LBS actually closer to 166.4 LBS

*160 BTU's = the amount of energy needed to raise 160 pints of water 1

degF

If the water temp is 50 degF and we want to raise it to120 degF that's

70 degF  a difference.

*So ---  70(deg) X 160(pints)  = 11,200 BTU's

You have a 3KW element.  About 10,000 BTU's

*So...  11,200 / 10,000 = 1.12 hrs ( 1hour 8 minutes)

1.12 hours to heat the water to 120 degF

There are a few assumptions but it should have taken a bit over an

hour...

What does everyone think?

• Member Posts: 7,265

Too many assumptions.

1.000 watts equals 3423(+) BTU's.

A 3.000 watt rated element may give you the 3,000 watts at 240 volts IF the voltage is 240 volts. Unlikely.

If you are in a building that has 208 volt three phase, and 110 volt single phase, the water heater element could be as low as 190 volts or lower.

The rule of thumb that many of us use is a water heater with 4500 watt elements will recover 18+ gallons per hour if the voltage is 240 volts.

If there is a DOE sticker on the heater, it may show a first hour rating. It will be more than 20 gallons. Subtract the 20 gallons from the first hour total and the result will give you the first hour recovery with a fudge thrown in because the heater element is on and heating water.

If the element or heater is old, the element could be limed up and it won't heat as fast. If it has two elements, only one runs at a time.

A 20 gallon electric water heater is sort of a point of use heater. It hasn't enough nuts to do a good job.

The lower the voltage, the lower the output.
• Member Posts: 902
Calculation schmalulation

The only sensible thing too do with a water thats not working well is replace it.
• Member Posts: 3,056
edited February 2013
HMM...

1 KW = 3,438 Btu/hr x 3 = 10,314 Btu/hr

10,314 Btu/hr / (Temp Rise x 500) = GPM

We will use 50 degree incoming 120 Setpoint, so our rise is 70 Degrees

10,314 Btu/hr / (70 x500) = .2946 gpm

.2946 x 60 = 17.67 GPH

Add in the storage of 19 gallons and you have a 1st hour rating of 36.68 gallons. Enough for about a 6 minute shower with 3.5 gpm heads.. It should take with nothing running

19 Gallons/.2946 = 64.5 minutes from dead bang cold to full recovery..

I hate math!

Now the question is are you giving 3KW off the element. How about scale or any other issues that will prevent the btu/hr out of the element.
"The bitter taste of a poor installation remains much longer than the sweet taste of the lowest price."
• Member Posts: 284
edited February 2013
So ..

Chris....You came up with 1 hour 4 minutes and I had 1 hour 8 minutes...

Actually it takes almost 2 hours 15 minutes..

By the way...  It is 110V

So why does it take that long...  Is my math wrong?

Assumptions might make up 10%

Any ideas?

:-)
• Member Posts: 3,056
edited February 2013

1500 Watts = 1.5KW

3,348 x 1.5 = 5,022 Btu/hr

5,022/ 35,000 = .143gpm

19/.143 = 132.86 minutes or 2 Hours 12 minutes..

I ask because elements are duel marked. Rating at 120 and rating at 240 - You sure your looking at the right rating on the element
"The bitter taste of a poor installation remains much longer than the sweet taste of the lowest price."
• Member Posts: 284
edited February 2013
Yes I'm sure

The guy called yesterday asking for help....  Bought the heater himself

& turned it on without filling it first...  I repiped it...  (was all piped with Black Iron) and put in a new element...  3000W @ 120V

My heart went out to him so I didn't charge him...

But....  Yep...  I'm sure..  3KW

I hate things like this because they will keep me up at night...  Lol..
• Member Posts: 3,056
edited February 2013
Well The Math Doesn't Lie

Leak, dripping faucets or he keeps turning the water on and slowing recovery. I take it you were not there for 2 hours watching. The only other thing would be our rise is off. Is the incoming 50 and set point 120? Would also be on a 35amp fuse...At least according to the Bradford White manual...Hot setting is 120 very hot is around 140..
"The bitter taste of a poor installation remains much longer than the sweet taste of the lowest price."
• Member Posts: 284
I hung around for

about 20 minutes...  I figured that the water would be warmer by then...  But

Noooooooo....  (an old Steve Martin laugh)

I'll keep looking into it...

Thanks for all the reply's...  I very much appreciate it..

• Member Posts: 3,474
edited February 2013
Meter

Put an Amp meter on it. It should be pulling 25amps at 120 volt. You may have a mislabeled or defective element.

A 3KW 120 volt element is an odd one. You would have to run 10 gauge wire.

Carl
"If you can't explain it simply, you don't understand it well enough"
Albert Einstein
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