How are water heaters sized? That's a good question. When I started out in the plumbing design business I asked this question to a lot of engineers before I got a good answer. Many of them just specify what they think will work from experience and others just send the parameters to water heater reps and let them do the calculations. The size is determined by this formula.
Demand in gallons x 8.33 x ΔT
1 btu is defined as the amount of energy required to raise one pound of water 1 degree. So since one gallon of water weighs approximately 8.33 pounds we use this number.
The Greek letter delta is used to represent the change in temperature, known as delta T. So if we want the water to be 120 degrees we need to know what the temperature of the ground water is to find the delta T. Let's use 60 degrees for the incoming water temperature. So we need to raise the temperature by 60 degrees to achieve our 120 degree water temperature.
40gal. x 8.33lbs/gal = 333.2
333.2 x 60( ΔT) = 19,992btu's
So it will take 19,992 btu's to raise 40 gallons of water by 60 degrees. So what does this tell us? This tells us that we would need at least a 20,000btu rated water heater for this application. You will find the btu rating on gas water heaters. What if the water heater is electric? In order to convert the btu's to kilowatts simply divide the btu's by 3413.
19,992 ÷ 3413 = 5.85 kilowatts
What does all of this means in terms of solar hot water? Knowing the basics of hot water design enables us to apply this to determining how many collectors are necessary for a given hot water demand.