How to calculate the size of solar hot water systems?

Calculating Daily Energy Requirement

To calculate the daily energy requirement of a solar hot water system, you need to consider the temperature increase required, the volume of water to be heated, and the specific heat capacity of water. The specific heat capacity of water is 1 Btu/lb-°F, which is equivalent to 4.184 kJ/kg-°C. Let’s assume a temperature increase of 30°F (16.7°C) and a water volume of 50 gallons (189 liters) per day. Using the formula Q = mcΔT, where Q is the energy required, m is the mass of water, c is the specific heat capacity, and ΔT is the temperature increase, we can calculate the daily energy requirement. For example, if the water mass is approximately 400 pounds (182 kilograms) per day, the daily energy requirement would be Q = 400 lb/day * 1 Btu/lb-°F * 30°F = 12,000 Btu/day. To convert this to kilowatt-hours (kWh), we can divide by 3,412 Btu/kWh, resulting in approximately 3.5 kWh/day.

Selecting System Size

When selecting a solar hot water system size, consider the daily energy requirement calculated above and the available solar radiation in your area. A general rule of thumb is to select a system with a capacity of 30-50 gallons per day for a small cabin. This will typically require a system with a tank size of 50-100 gallons (189-378 liters) and a collector area of 2-4 square meters (21-43 square feet). For example, if you want to heat 50 gallons (189 liters) of water per day with a temperature increase of 30°F (16.7°C), you would need a system with a capacity of approximately 40 kWh/day. This would require a collector area of at least 2.5 square meters (27 square feet) with a heat exchanger efficiency of 0.8 and a temperature increase of 30°F (16.7°C).