How many showers can we dish out until the sun shines again?

Until we get real and install some better solar hot-water heating — with a 1500 gallon unpressurized drainback tank (we’ll see!) — we will have a 105 gallon Rheem Marathon electric hot water heater being heated by a Geyser heat pump hot water heater.

My question is how many showers can be had when the sun isn’t shining (due to nighttime or clouds) without having to turn on the heat pump and use non PV electricity. Time for some algebra!

First the assumptions. And let’s make some guess at a usage pattern rather than really doing algebra and solving for n (when n=number of showers)
1. Hot water temp on the hot water heater set to 130F
2. Showers will have H20 Kinetic 1.5 gallon/minute shower heads
3. There will be some mixing with cold water since 130F is too hot for a shower. But let’s just be conservative and say we use a full 1.5 gallons per minute.
4. Pretend like we know the incoming well-water temp (let’s say it’s 50F)
5. Pretend there is no heat loss thru the tank walls and no significant temp stratification. (The Marathon is pretty well insulated…)
6. Timer that switches the HW heater off during night-time hours to prevent slipping into non-solar usage.

Ok so, let’s see what the tank temp (assuming no stratification) is after 2 10-minute long showers is (as a guess of what the tank might be able to handle)

So that’s… 1.5 gallon/minute * 2 * 10 = 30 gallons of outgoing 130F water getting replaced by 50F
So in the tank we will now have
30gallons * 50F
75gallons * 130F
which is an average of (30*50+75*130)/105 = 107.14F

And I think that’s still warm enough for a short shower, so given my conservative numbers, we could have several people taking showers before the sun comes up on our PV array without having to pay for a full-priced KWh from our currently non-net-metering electric company.

I think. And we will have to try to run things like dishwashers and washing machines during the day probably/ideally.

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