## Exercises

5.1 Repeat Example 5.1 for an indoor swimming pool.

5.2 A 100 m2 light-colored swimming pool is located in a well-sheltered site, where the measured wind speed at 10 m height is 4 m/s. The water temperature is 23°C, the ambient air temperature is 15°C, and relative humidity is 55%. There are no swimmers in the pool, the temperature of the make-up water is 20.2°C, and the solar irradiation on a horizontal surface for the day is 19.3 MJ/m2-d. If this pool is to be heated by solar energy, how many square meters of collectors would be required if their efficiency is 45%?

5.3 A water storage tank needs to be designed to hold enough energy to meet a load of 11 kW for 2 days. If the maximum storage temperature is 95°C and the supply water must have at least a temperature of 60°C, what size of tank is required?

5.4 A fully mixed water storage tank contains 1000 kg of water, has a UA product equal to 10 W/°C, and is located in a room that is at a constant 20°C temperature. The tank is examined in a 10 h period starting from 7 am, where the Qu is equal to 0, 8, 20, 31, 41, 54, 64, 53, 39, 29 MJ. The load is constant and equal to 13 MJ in the first 3 h, 17 MJ in the next 3 h, 25 MJ in the next 2 h, and 20 MJ the rest of time. Find the final storage tank temperature if the initial temperature is 43°C.

5.5 A storage tank needs to be designed to meet a load of 1.2 GJ. The temperature of the storage tank can vary by 30°C. Determine the storage material volume if the material is water and concrete.

5.6 Repeat Example 5.3 by considering a storage tank of 150 kg and compare the results.

5.7 Repeat Example 5.3 for September 15, considering that the weather conditions are the same.

5.8 A solar water heating system with a fully mixed tank has a capacity of 300 L and a UA value of 5.6 W/°C. The ambient temperature at the place where the tank is located is 21°C. The solar system has a total area of 6 m2, Fr(to) = 0.82, and FRUL = 6.1 W/m2-°C. At the hour of estimation, the ambient temperature is 13.5°C and the radiation on the collector plane is 16.9 MJ/m2. If the temperature of the water in the tank is 41°C, estimate the new tank temperature at the end of the hour.

5.9 A liquid-based solar heating system uses a heat exchanger to separate the collector loop from the storage loop. The collector overall heat loss coefficient is 6.3 W/m2-°C, the heat removal factor is 0.91, and the collector area is 25 m2. The heat capacity rate of the collector loop is 3150 W/°C and, for the storage loop, is 4950 W/°C. Estimate the thermal performance penalty that occurs because of the use of the heat exchanger if its effectiveness is 0.65 and 0.95.

5.10 A liquid-based solar heating system uses a heat exchanger to separate the collector loop from the storage loop. The flow rate of the water is 0.65 kg/s and that of the antifreeze is 0.85 kg/s. The heat capacity of the antifreeze solution is 3150 J/kg-°C and the UA value of the heat exchanger is 5500 W/°C. The collector has an area of 60 m2 and an FRUL = 3.25 W/m2-°C. Estimate the factor FR /FR.

5.11 A family of seven people lives in a house. Two of them take a bath every day and the rest take showers. Estimate the daily hot water consumption of the family by considering two meal preparations, two hand dish washings, and two face or hand washings.

5.12 Determine the solar collector area required to supply all the hot water needs of a residence of a family of six people in June, where the total insolation is 25700 kJ/m2-d, assuming a 45% collector efficiency. The demanded hot water temperature is 60°C, the cold water make-up temperature is 16°C, and the consumption per person is 35 L/day. Estimate also the percentage of coverage (also called solar fraction) for heating the water in January, where the total insolation is 10550 kJ/m2-d.

5.13 A commercial building water heating system uses a recirculation loop, which circulates hot water, to have hot water quickly available. If the temperature of hot water is 45°C, the pipe UA is 32.5 W/°C, the tank UA is 15.2 W/°C, the make-up water temperature is 17°C, and ambient temperature is 20°C, estimate the weekly energy required to heat the water with continuous recirculation. The demand is 550 L/d for weekdays (Monday through Friday) and 150 L/d in weekends.

5.14 A solar collector system has a total area of 10 m2, FR = 0.82, and UL = 7.8 W/m2-°C. The collector is connected to a water storage tank of 500 L, which is initially at 40°C. The storage tank loss coefficient-area product is 1.75 W/°C and the tank is located in a room at 22°C. Assuming a load flow of 20 kg/h and a make-up water of 18°C, calculate the performance of this system for the period shown in the following table and check the energy balance of the tank.

 Hour S (MJ/m2) Ta (°C) 7-8 0 12.1 8-9 0.35 13.2 9-10 0.65 14.1 10-11 2.51 13.2 11-12 3.22 14.6 12-13 3.56 15.7 13-14 3.12 13.9 14-15 2.61 12.1 15-16 1.53 11.2 16-17 0.66 10.1 17-18 0 9.2 