I hope you can answer this if you're an engineer!!!?

Question

You have been asked to design a solar water heating system for a family of four. The family uses 100 gallons per day of hot water at 50 degrees Celcius. The cold water enters the house at 5 degrees Celcius. The solar collector heats the cold water to 75 degrees Celcius and stores it in an insulated storage tank until the family needs it. The sun shines for an average of 7 hours per day and provides 235 Watts per meter squared. Determine the size of the storage tank and the size of the collector.

Answer 1

Sattra has it dead on.

The hot water will be mixed with cold to give you 50 degrees. Simply set up:

75(X) + 5(100-X) = 50(100)
X = 64.28 gallons
Where X is the amount of hot water added to the mix

Now calculate your heat duty required per day
deltaH = (1cal/g*C)(243375.5 g)(70 C)
delta H = 17036285 calories/day

Do a conversion of the power to get your energy output from the solar panels

(235W/m^2)(.01433kCal/min*W)(60min/hr)(1000g/kg)
output = 202053 cal/m^2*hr

Multiply by your daily ration of sunshine
(202053 cal/m^2*hr)*(7hr/day) = 1414371 cal/m^2*day

And divide into your required heat duty
(17036285 cal/day)/1414371 (cal/m^2*day)

Total size of collector = 12.05m^2

Answer 2

storage tank = usage
storage tank = 100 gal

but 75 deg in and 50 deg out - assuming no temp loss in the tank - which is something cool you can do as an engineer

starting with a standard dilution
what you have/what you want = 75/50 = 1.5
volume/dilution factor = 100 gal/1.5 = 66.7 gal of 75

but the water diluted with 5 deg water so you need less
66.7 gal of 75 deg and 33.3 gal of 5 = 51.7 degree water

too high - switch to fractions because of 100 gal it makes this easier
0.64 x 75 + 0.36 x 5 = 49.8 degree

slowly increase to 64.3 gal tank - this is iteration - Bigsky uses an equation - both work

yeah you should have a larger storage tank than daily usage for rainy days but....

size of the collector...
first - how much power from 7 hrs of sunlight
235 W/m^2 = 235 J/s*m^2
235 J/s*m^2 x 7 hr x 3600 s/hr
5922000 J/m^2

second how much power is needed to increase
water temp from 5 to 75 deg C
eqn: Q = mc(Tf - Ti)

m = mass, 64.3 gal = 243.4 L
and water specific weight of water is approx. 1 kg/L
m = 243.4 kg

c = water heat capacity
c = 4184 J/kg K

Tf-Ti = 75 - 5 = 70 deg C
but because this is a delta the deg C difference = kelvin difference

all together
Q = 243.4 kg x 4184 J/ K kg x 70K
Q = 71279816.4 J

divide Q by J from the sun for the size of the solar collector
71279816.4 J/ 5922000J/m^2
= 12.04 m^2

so you think a larger storage tank is needed because where you live it is sunny 1 day in 8 = then recalc....

hope this helps

Answer 3

It depends when the family uses the water and how well insulated the tank is. Worst case, while still being able to achieve the objective, they use all the water just before the sun comes up and by that time you have only been able to keep it at 50C. You'd also need to know the mass of the tank and its specific heat capacity, but we can assume 0 and 0 for this lame example, and we have to assume we have to hold the whole 100 gallons.

As engineers, that means people from the practical world, you can't assume perfect insulation.

378.5l of water heated 70C in 7 hours.

4.18J/g/K, a liter is a kilogram of water, at least near enough within a percent or so.

4180x378.5x70 = 110,749,100J

7 hours is 25,200 so you need 4394.8W so you need 18.7 square meters.

Answer 4

I think,
the size of the storage tank has to hold at least 64.3 gallons, and the size of the solar panel has to be at least 12.03 meters squared.

Someone else should double check my answers.

Answer 5

OK. Let us assume we have an auto-tracking parabolic mirror. Let us assume the system will automatically drain if it gets too cold.

I am interested in a source of super heated steam to inject/boil beer wort.
Thanks.

Answer 6

Dude,
Solar panels for hot water are out.
The water freezes at night if the temperature drops much below freezing.
All the solar panels I've heard of in the past fifteen years are photovoltaics, which generate electricity, not hot water.