Fri Jan 24, 2003 I switched on the hot water heater at 8:03:48pm.

It kicked in at 8:04:30, showing 48degF, beyond which I made the following table by noting the time and temperature:

time temp 806 50 807 52 808 55 809 58 810 60 811 61 812 64 813 68 814 70 815 73 816 76 817 79 818 81 819 84 820 87 821 89 822 92 823 95 824 97 825 100 826 102 827 105 828 107 829 109 830 112 831 115 832 118 833 120 834 123 835 125 836 128 837 1308:37:30 it just shut off. At the instant it shut off the temperature indicator was reading 132F.

8:38 it's still off, but rose to 133F

octave:7> A=[sum(x.*x) sum(x); sum(x) length(x)] A = 21598320 26288 26288 32 octave:8> b=[sum(x.*y); sum(y)] b = 2377163 2885 octave:9> A\b ans = 2.6157 -2058.6023Slope of graph is 2.6157 deg F/minute.

1 BTU is 1 pound 1 degree.

There are 10 pounds in a gallon, and the tank is 100 gallons, so the tank holds 1000 pounds of water that is being raised 2.6157 deg F/minute, 2.6157*60*1000BTH/hour = 156,942 BTU/hour.

The unit is rated at 200,000 (199,000) BTU/hour, so it's running around 79% of its rating.

To put this into perspective, if we have 52 deg F water (the temperature
it's coming out of the ground), and want a 105F shower, we mix hot and cold,
but that's equiv. to running hot water heater up to 105F only, so it's
105-52 = 53 deg F difference,

53/2.6157 = 20.262 minutes to heat the whole tank, e.g. therefore produces
4.9353 gallons per minute, therefore we get approximately enough to run
two showers for an infinitely long duration without ever running out of
hot water.

The tank of course serves as a "buffer", so, for example, it can run the firehose through the Navigator (25GPM) for only 4 minutes on a full tank if at 105F but if at higher temperature, it stores more energy, and can then run the firehose for longer and still recover.

Another interesting question: what's the cost (dollars per minute) to keep the firehose running with 105 deg F water?

I did google search: 61.18 cents per 100,000 BTU natural gas;

$1.07 per 100,000 BTU propane

$2.43 per 100,000BTU electric.

That means our 200,000 btu /h unit costs 122.36 cents (i presume per hour) to run continuously.

A full tank to goto showering temp (or equiv. that portion of a tank that would be used for showering temp if mixed from a higher temp) is therefore 40.786cents

That means for less than 41 cents worth of natural gas, a person can be decontaminated with 100 gallons of comfortably warm water dumped onto their body through a firehose (which takes 4 minutes at 25 GPM).

Cold water costs approx. 1.2317$/cubic meter approx. .4662491960 cents per gallon, e.g. approx. 47 cents for a full (100 gallon) tank.

Thus the true cost to decon someone is approximately 87 cents.