SWIMMING POOL HEATING BY SOLAR ENERGY

~ I CSIRO SERIES JrJ0.3 TR 19 ' i I SWIMMING POOL HEATING BY SOLAR ENERGY J. T. CZARNECKI ' ',.. ~ DIVISION OF MECHANICAL ENGINEERING TECHNICAL REPORT No. TR 19 Highett, Victoria 1978

ISBN 0 643 000309 6 Printed by CSIRO, Melbourne 78. 156-1 750

CONTENTS Summary 1. Introduction 1 2. Heat Requirements 2.1 Convection Heat Loss 2.2 Evaporation Heat Loss 2.3 Radiation Heat Loss 1 2 2 3 3. Methods of Solar Heating 3.1 3. 2 Swimming Pool Covers and Enclosures Solar Collectors 5 5 7 4. Other Design Considerations 4.1 4. 2 Heat Loss Coefficient Thermal Time Constant 4.3 Combination of Pool and Shower Water Heating 4.4 4. 5 4.6 Water Circulation in Collectors Plastic Tube Collector Economic Considerations 8 8 9 10 10 11 11 Acknowledgement 12 References 12 Tables 1-2 Figures 1-7

SUMMARY Work on solar heating of swirroriing pools performed in the CSIRO Division of Mechanical Engineering since 1960 is reviewed and updated. Methods of solar heating are discussed and data necessary for the design of suitable systems are presented together with typical examples.

1 1. INTRODUCTION The conditions for comfortable swinnning are determined mainly by the water temperature, ambient air temperature, relative humidity and wind velocity with water temperature being the most important factor. Although the minimum water temperature acceptable for swimming is about 20 C, the desired level seems to be 25 C as shown, for example, by Sheridan [l]. The water temperature in an unheated swimming pool in relation to the ambient air temperature depends on the amount of solar radiation absorbed in the water and on the rate of heat loss from the water. In an open pool. exposed to sunshine, the water temperature is normally close to the mean air temperature. In a shaded pool the water tends to be below the mean air temperature. In temperate climate zones of Australia the swinnning season in open swimming pools is relatively short. It is estimated to last about three months per year in Canberra, Hobart and Melbourne and five months in Perth and Sydney. Since outside this swimming season there are lengthy periods when the outside air temperatures during the day are high enough for comfortable swimming, the swimming season can be extended simply by increasing water temperature to a suitable level. This can be done using conventional fuel burning heaters or solar energy. Solar energy is particularly suitable for this application because heating to a relatively low temperature results in a high efficiency of solar energy collection and also in low-cost collection devices. The potential for the use of solar energy in swimming pool heating was recognized in the CSIRO Division of Mechanical Engineering as early as 1960. Work at that time resulted in the development and testing of two methods of solar heating of swimming pools. One method consisted of an inflated clear plastic cover applied to the pool when it was not in use, and the other of a corrugated iron roof used as a solar energy collector by trickling water down the corrugations. The results of this work have been described by Czarnecki [2,3]. Work was resumed in 1976 and consisted mainly of testing the suitability of pool covers and commercially produced solar collectors for solar heating of swimming pools (Czarnecki [4]). This report provides basic information needed for the design of a solar heating system for any type of swimming pool in Australia. 2. HEAT REQUIREMENTS The heat requirement to maintain a swimming pool at an elevated temperature is equal to the heat loss at this temperature less the heat gain due to dire~t absorption of the incident radiation in the water. Hence a knowledge of the heat loss rate is essential for the design of any type of swimming pool heating system.

A swimming pool loses heat to the environment by convection, evaporation, radiation to the atmosphere, and conduction to the ground. The heat loss due to conduction is normally small in both in-ground and aboveground pools and can be neglected for most practical purposes. Above-ground pools are subject to an additional heat loss by convection from the sides. Tests described by Czarnecki [4] showed, however, that this loss was largely compensated by the solar radiation absorbed in the sides of the pool. Czarnecki presented a method of calculating the heat loss [2,3], and this was later verified independently on an actual swimming pool by Prior and Boadle [5]. The method is repeated below with the equations converted to SI units and with climatic data allowing for the evaluation of loss rates in all Australian capital cities. 2 2.1 Convection heat loss The rate of heat loss due to convection to ambient air can be expressed by the equation where qc h c T w T a h (T - T ) c w a -2 heat transfer by convection, W m -2-1 convective heat transfer coefficient, Wm K, water temperature, C, ambient air temperature, C. (1) The convective heat transfer coefficient depends on the wind velocity and the following relation is used after Sheridan [l]: h c where V 3.1 + 4.1 v wind velocity, m s- 1 (2) Hence, from (1) and (2), (3.1 + 4.1 V) (T - T ). w a (3) 2.2 Evaporation heat loss The rate of heat loss due to the evaporation of the water from an open swimming pool is usually the highest of all losses. It can conveniently be evaluated using the expression given in Czarnecki [2], which, converted to SI units, is: 16.3 (3.1 + 4.1 V) (p - p ) w a -2 heat loss by evaporation, W m water vapour pressure at temperature T, kpa, w partial water vapour pressure in air, kpa. (4) The constant of 16.3 in the above equation has the dimension Km s 2 kg- 1 resulting from the relation between the coefficients of heat and mass transfer. The water vapour pressure p depends on the water temperature in the manner shown in Fig. 1. w

3 The partial water vapour pressure in the air, pa' can be evaluated if the relative humidity is known as follows: p x RH s 100 (5) where ps RH saturation water vapour pressure, kpa, relative humidity, %. The saturation water vapour pressure in the air can be found from Fig. 1 with p p for T T. s w a w 2.3 Radiation heat loss The heat loss by radiation from the surf ace of the water may be evaluated by means of the simplified equation shown below. where qr h r T s 0.95 h (T - T ) r w s heat transfer by radiation, W m- 2, radiation heat transfer coefficient, as defined in -2-1 Czarnecki [2], Wm K, sky temperature, C. (6) In the derivation of equation (6) the emittance of the water has been taken as 0.95. Normally, the sky can be assumed to be a black body at temperature T T - 11 C as used, for example, by Cooper [6]. s a The variation of the radiation heat transfer coefficient h with the mean temperature of water and sky is shown in Fi~ 2. It is bas~d on the approximation. h ~ 2.268 x 10-7 3 ttw + Ts+ r 273.15 which is accurate only 2 for a small temperature difference, say T - T < 20 C. w s The factors necessary for calculating the heat losses are ambient air temperature, wind velocity, and partial pressure of water vapour in the air. Monthly means of these quantities based on data published by the Bureau of Meteorology [7] are given in Table 1 for all Australian capital cities. Also shown in this Table are the values of solar radiation incident on a horizontal surf ace, and on a surface facing north inclined at an angle equal to the latitude as predicted by Paltridge and Proctor [8]. It must be noted that the latter figures are approximations and should be used only in the absence of measured values. The daily heat requirements of a swinuning pool to be maintained at a predetermined temperature T can now be calculated by means of the heat balance equation w Qr AP (0.0864 qt - 0.9 Qh) where Qr heat input required, MJ day- 1, -2 total rate of heat loss, W m

4 A p swinuning pool surface area, m 2 Q h solar radiation on horizontal surface, MJ m- 2 day- 1 In equation (7) it is assumed that 90% of the incident solar r adiation is absorbed in the water and contributes to heating. This assumption is based on data given by Robinson [9]. The above method of calculating the heat requirements i s illustrat ed by the following two examples. Example 1. Calculate the heat requirements for an open swinuning pool of 10 m x 5 m, located in Melbourne, to maintain the water temperature at 25 C during the month of March. From Table 1: T = 18.3 C, p = 1.32 kpa, V = 3. 3 ms, Qh = 16. 7 MJ a a m- 2 day- 1, and from Figs. 1 and 2: p = 3. 1 kpa and h = 5. 5 W m- 2 K- 1 w r 0-1 Since a home swinuning pool is normally well sheltered f r om wi nds, a. - 1 wind velocity equal to one third of that in Table 1, i.e. V = 1.1 m s, will be used for the calculation of heat losses. Justification of this assumption is given later in this report The heat losses, calculated using equations (3), (4) and (6), are as follows: qc qe qr qt 51. 0 W m- 2 220.8 W m- 2 92.5 W m- 2 364.3 W m- 2 The daily input can now be calculated by means of equation (7): Q r 822 MJ day- 1 This daily heat requirement of 822 MJ means that a 10 kw heater would have to operate almost continuously to satisfy the load. Example 2. Calculate the heat requirements for an indoor swinuning pool of 50 m x 21 m (Olympic size) to maintain the water temperature at 24 C when T 26 C, RH= 60%, V = 0.5 m s- 1, T T = 26 C, and the pool is not a s a exposed to solar radiation, i.e. Qh = 0. From Figs. 1 and equation (5): p = 3.0 kpa, p Fig. 2: h = 6.0 W m- 2 K- 1 w a r 2.0 kpa, and from

5 Equations (3), (4) and (6) again are used for the evaluation of heat losses. qc -10.3 w m -2 qe = 83.9 w m -2 qr -11.4 w m -2 qt = 62. 2 w m -2 It may be noted that the heat losses by convection and radiation are negative, which means that there is heat transfer to the water from the surroundings. Using equation (7) the heat requirements are evaluated to be: Q r 5643 MJ day- 1 It is of interest to note that by a suitable choice of relative humidity and air temperature in the enclosure it is possible to make the total heat loss and, therefore, the heat requirements equal to zero. In the above example, this is the case if either the relative humidity is increased to about 82% or the air temperature to 29 C. If desired, this effect can be used in the design of an enclosed swinnning pool to obviate the need for a water heater, provided that the air temperature and relative humidity can be kept within comfort limits. 3. METHODS OF SOLAR HEATING Before attempting to heat a swinnning pool by any method, means of reducing its heat losses should be considered. Heating an open swimming pool can be compared with heating a home while all doors and windows are open and, therefore, should be regarded as wasteful. A substantial reduction in the heat loss rate can be achieved by using pool covers or enclosures. By sheltering the pool from high winds while exposing it to maximum sunshine, an increase of water temperature can be achieved as heat losses by convection and evaporation are thus reduced. There are two basic methods of heating swinnning pools by solar energy:- (i) Avoiding waste of the solar radiation incident on the swinnning pool by using pool covers, and (ii) Heating of water in solar collectors located outside the swimming pool. 3.1 Swimming pool covers and enclosures When a single layer clear plastic cover is placed on the water surface, the heat loss due to evaporation will cease while most of the incident solar radiation will be transmitted through the cover and absor bed in the water, thus increasing the water temperature.

6 A double layer cover with an air space between the layers has an advantage over a single layer cover in that it also reduces the convection and radiation heat losses. A cover developed in 1960 in collaboration with Plaspiline Industries was tested on a typical open home swimming pool in Melbourne (Czarnecki [2]). It was made by welding two sheets of weatherable PVC film together to form inflatable sections, which were clipped together to form a continuous cover. Fig. 3 shows the cover on a home swimming pool. From several months of testing the cover in Melbourne, the following correlation was found between the mean monthly temperature rise of the water above the mean air temperature, and the monthly incident solar radiation: where 6T 0.406 Qh - 1.8 (8) mean water temperature rise above the mean air temperature, oc, Q. d -2-1 h = inci ent solar radiation, MJ m day The correlation coefficient for this relation is r = 0.952 and the standard deviation 0 = 0.7 C. Experience has shown that the covers made of weatherable PVC film can last more than five years under normal conditions of use. Since that time, air-bubble plastic packaging material made of clear polyethylene film has become available and a cover was made of this material and tested. It consisted of four sections floating on the water, the airbubbles facing down. To prevent the cover from being blown off the pool by wind, it was cut around the edges across the air-bubbles. The opened bubbles filled with water thus holding the cover down. During tests conducted in 1976-77, two similar above-ground swimming pools were used. One was equipped with the air-bubble cover while the other was left uncovered. In this way a direct comparison of the water temperature in both pools could be made. The tests indicated that under steady state conditions the mean temperature increase of the water in the covered pool is directly proportional to the incident solar radiation and can be expressed by the empirical equation 6T w where 6T w 0 25 Q +_1 c. h (9) temperature difference between covered and uncovered pool, C. The cover material is now manufactured out of UV-stabilised polyethylene film which is likely to last two to three years when exposed to sunshine. An above ground swimming pool equipped with this cover is shown in Fig. 4. The heat gain from the solar radiation depends on the transmittance of the cover material to the solar radiation. For the cover used in the experiments, the transmittance has been estimated to be ~bout 80%.

7 This is derived using a measured value of 83% for solar radiation transmitted through the cover at normal incidence during bright sunshine, and allowing 3% loss due to varying angle of incidence and contamination of the cover. It should be noted that with an opaque cover the heat gain is expected to be small because only the top layer of the water would be heated by conduction from the cover. Adequate mixing of the water would improve this situation. Swimming pool enclosures offer an alternative to covers for reducing heat losses. They also provide means for year-round swimming if the air inside is suitably conditioned. To keep the evaporative heat loss low, the relative humidity inside should be maintained as high as possible but without causing condensation and discomfort to swimmers. Generally, a relative humidity of up to 60% appears to be acceptable for comfort, and the problem of condensation can be resolved by suitable design of the enclosure. 3.2 Solar collectors Once the heat requirements of a swimming pool are established, a suitable heating system can be designed. The conventional fuel burning heaters are expensive to run because large amounts of heat are involved. Utilization of solar energy by means of solar collectors provides an alternative practical means of heating. Various types of solar collectors especially designed for swimming pool heating are now commercially available. They are constructed of metal or plastic and are not glazed. The performance of some of these collectors was measured by Proctor [10] using the method described by Pott and Cooper [11]. Ranges of performance of glazed and unglazed collectors are shown in Fig. 5. An efficiency of solar energy collection of about 70% can be expected from both types when they operate near ambient air temperature. The efficiency of the unglazed collector, however, drops rapidly with increasing temperature difference, making this type unsuitable for winter heating. Glazed collectors must then be used. A description of the factors affecting the performance of glazed and unglazed solar collectors for swimming pool heating can also be found in a report by de Winter [12]. Knowing collector can A c the heat requirements of a swimming be calculated using the expression Qr. n Qi pool, the area of the solar (10) where A c area of solar collector, m 2 efficiency of solar energy collection, solar radiation incident on the collector, MJ m- 2 day- 1 Using the data from Example 1 and assuming n 0.65 and Qi= 20.6 MJ- 2 day- 1 (taken from Table 1 for March in Melbourne), the collector area is calculated to be A c 60.9 2 m.

8 Thus, to maintain a swimming pool of area 50 m 2 at an average temperature of 25 C in Melbourne during March, a solar collector with an area of about 61 m 2 is needed. To avoid overdesign, the size of the solar collector in Example 2 is calculated for the month of highest solar radiation. Table 1 shows that, in - 2-1 Melbourne, this month is January, when Qi 25.5 MJ m day. Substituting this value in Equation (10) and using n = 0.6 the collector becomes A c 368.8 m 2 In Table 2, the expected mean water temperature in outdoor swimming pools exposed to sunshine are shown for each month of the year in Australian capital cities for pools: (A) (B) (C) uncovered and unheated, covered with clear plastic cover, uncovered and heated using unglazed solar collector of an area equal to the swimming pool area, facing north and of inclination equal to the latitude. These temperatures were obtained by means of a computer pr ogram using equations (3), (4), (6), (7), (9) and (10), and the climatic data from Table 1, but wind velocity was taken to be equal to one third of that shown in the Table. This is due to the natural wind velocity reduction near the ground and also to the wind breaks normally present around the pool in the form of buildings, fences, trees and shrubs. The basis for this assumption was established during tests described earlier [4]. The mean water temperature in the unheated pool recorded during these tests was 21.5 C compared with the 21.7 C calculated on this basis. The a verage wind velocity recorded by the Bureau of Meteorology during t he time of testing was 2. 37 m s- 1 From Table 2 it can be seen that the effect on the water temperature of an unglazed solar collector of an area equal to the swimming pool area is about the same as that of a clear plastic cover. From Czarnecki [2] and Table 2 it is evident that by either of these means the swimming season in open swimming pools can be extended by about three months. For instance, in Melbourne the swimming season is increased in this way from the normal three months to six months of the year. 4. OTHER DESIGN CONSIDERATIONS 4.1 Heat loss coefficient For certain calculations it is convenient to use the heat loss coefficient of a swimming pool. It is defined from the following expression : (11) where qt UL T w T eq total rate of heat loss, W m- 2 heat loss coefficient, W m- 2 K- 1, water temperature, C, equivalent heat loss temperature, C.

9 The temperature Teq in the above equation depends on the ambient air temperature, water vapour pressure difference defined in equation (4), and sky temperature shown in equation (6). The following relation fits well the actual observations: T eq T - 5. a Combining equations (11) and (12) the heat loss coefficient can be written (12) T - T + 5 w a (13) Since the rate of heat loss from a swimming pool depends on a number of variables, the heat loss coefficient is not a constant but varies within. the limits determined by these variables. Its value is estimated to vary between 30 and 50 W m- 2 K- 1 for open swimming pools and between 15 and 25 W m- 2 K- 1 for covered or enclosed pools. For certain applications, however, an average constant value of UL may be assumed without introducing a great error, particularly if the conditions remain fairly steady. One practical application of the heat loss coefficient is the evaluation of heat requirements when data for calculating the individual heat losses are not available. This can be done assuming an average value of UL by means of modified equation (7) as follows: where 6.T r required water temperature increase, K. Using the above equation, the heat loss coefficient of the swimming pool s~ecified in Example 1 can be calculated. It is found to be 31.44 W m- 2 K- with 6.T = 6 K, being the difference between the required water temperature of r25 C and the temperature of an open and unheated pool of 19 C taken from Table 2 for Melbourne in March. When the heat loss coefficient has been determined, the equivalent heat loss temperature Teq can be evaluated for the conditions used in Example 1. With help of Equation (11) and qt= 364.3 W m- 2, T = 25 C, its value is found to be 13.4 C, which checks quite well with the v~lue of 13.3 C found from expression (12) with T = 18.3 C. a 4.2 Thermal time constant The transient temperature increase when heat is applied to a swimming pool can be expressed by the following equation: UL 6.T(t) 6.Te [l - exp (-t ~)] (15) (14) where 6.T(t) 6.T e t transient temperature change of the water at time t, C, final temperature change of the water after a step change of heating, C, time, s, heat loss coefficient of the pool, W m- 2 K- 1, heat storage capacity of the water per unit surface area, J m-2 K-1.

10 Expressing H as function of water depth and t in days, the above equation becomes UL fit (t) fit e Il - exp (-t 48. 5 d)] (16) where d average depth of the water, m. Similarly, the temperature drop after the heating ceases can be expressed : fit(t) fit e UL exp (-t 48.5d) (17) ""l The thermal time constant of a swimming pool, i.e. when the temperature change will reach 63.2% of its final value after a step change in heating, is derived from equation (16) or (17) to be t c 48.5d (18) where t c thermal time constant, days. For instance, the thermal time constant of an open swimming pool of average depth d = 1.5 m and UL= 45 W m- 2 K- 1 is tc = 1.6 days. The diurnal temperature swing of the water depends mainly on the thermal time constant and on the prevailing climatic conditions. An average swing of 2 to 3 C was observed by Czarnecki [4] in both open and covered above-ground swimming pools, 1.2 m deep, during testing in Melbourne. 4.3 Combination of pool and shower water heating When large amounts of hot water are used for showers in public swimming pools it may be an advantage to combine solar heating of this water with the pool water heating. A more efficient collection of solar energy will be achieved if the combined collector is used for swimming pool heating first, in preference to shower water. In this way the collector will normally operate at a lower temperature during the early, cooler part of the day, resulting in a higher performance. To ensure sufficient heating during periods of low solar radiation, an auxiliary heater must be used. An example of this combination is given in Figs. 6 and 7, which show schematics of the hydraulic and control circuits respectively. 4.4 Water circulation in collectors The efficiency of solar energy collection in solar collectors depends largely on the rate of water flow and on the mode of circulating pump operation. A minimum rate of water flow of 20 ml s- 1 per square metre of solar collector area is recommended to ensure a low operating temperature of the collector. The circulation of the water should take place only when heat can be gained in the collector. For this reason a suitable pump controller must be used. It may be in the form of a differential temperature controller with a low differential, preferably lower than 2 C, or the electronic controller developed in che CSIRO Division of Mechanical Engineering [13].

11 4.5 Plastic tube collector Black polyethylene or PVC tube laid on the roof is often suggested as a solar collector for swimming pool heating. As reported in the American periodical Sunset [14], this was first tried by Lynn Sutton of Las Gatos, California, using about 600 m of 12.7 mm diameter polyethylene hose in 30 m long sections attached to 50.8 mm diameter feeder and return lines. From that experiment it appears that the performance of such an arrangement is equivalent to that of an unglazed solar collector of area equal to the projected area of the plastic tube. A somewhat different arrangement was tested in the CSIRO Division of Mechanical Engineering in 1977. It consisted of a coil made of 40.5 m of 28.6 mm O.D. black polyethylene tube laid on white painted asbestos cement panel. The instantaneous efficiency of solar energy collection was calculated from the following measurements: Ambient air temperature Wind velocity Incident solar radiation Water flow Inlet water temperature Water temperature rise across collector 23.0 C -1 1.8 m s 841 W m- 2 47.1 mi s- 1 22.5 C 4.5 C The efficiency amounted to 90.8, 52.7 and 31.4% based on projected area of the tube, annulus area, and the area occupied by the entire panel respectively. The efficiency of collection of three types of unglazed, connnercially available collectors operating under similar conditions at the same time averaged 69.0%. A practical arrangement of a plastic pipe heater is shown by the State Electricity Commission of Victoria in their sketch No. VX21/910. In this arrangement one coil of about 200 m of 25 mm diameter plastic pipe is reconnnended for every 15 m 2 of pool surface area. Coils can be located on the roof fixed by ties to light steel mesh or by nails in timber support, leaving a gap of about 30 mm between coils. A minimum roof area of 6 m x 3 m is required to acconnnodate a coil. It appears that two such coils for every 15 m 2 of pool area would have about the same heating effect as use of the clear plastic cover. Although the plastic pipe collector may be suitable for a handyman to build, it does not appear to be a practical proposition for commercial exploitation mainly because its economics do not appear to be favourable and also because its efficiency of collection based on the area it occupies is quite low. 4.6 Economic considerations ~ e economics of solar heating may be judged by comparing the cost of solar heating with the cost of alternative methods of heating. This, however, is not straightforward since, as pointed out by Proctor [15], different economic factors apply in the assessment of the costs, depending on whether the systems are domestic, connnercial or industrial.

12 Solar heating appears to have a distinct economic advantage over other methods if used only ~ f or the purpose of extending the swinnning season in open swimming pools. The clear plastic cover floating on the pool while the pool is not in use is particularly attractive. Its disadvantage is, however, that the cover must be handled each time the pool is used. At the time of writing (Dec. 1977), the cost of the cover is about $2 per m 2 for the air-bubble polyethylene material and about $10 per m 2 for the heavier PVC one. For comparison, costs of solar collectors are approximately $100 and $50 per m 2 for the glazed and unglazed units respectively. For year-round swif!111ling in enclosed swimming pools, solar heating must be combined with auxiliary heating to ensure continuity of heat supply during periods of low solar radiation. In this application, solar heating is not replacing other types of heating, but is acting as a fuel saver. When selecting solar collectors, their cost per unit area, efficiency of collection, and life expectancy must be considered. ACKNOWLEDGEMENT Acknowledgement is due to Dr. D.J. Close who checked the manuscript and offered many helpful suggestions. REFERENCES [l] Sheridan, N.R. (1972) - The Heating of Swimming Pools, Solar Research Notes No. 4, University of Queensland. [2] Czarnecki, J.T. (1963) - A Method of Heating Swimming Pools by Solar Energy. Solar Energy]_ (1). [3] Czarnecki, J.T. (1964) - Solar Absorbers for Swimming Pool Heating. Aust. Refrig. Air Cond. Heat.~ 18 (9). [4] Czarnecki, J.T. (1977) - Solar Heating for Above-Ground Swinnning Pools. ISES - ANZ Section Symposium on Solar System Design, Melbourne, August 24th, 1977. [5] Prior, M. and Boadle, S. (1977) - Swimming Pool Heating Using Solar Energy. ISES - ANZ Section Symposium on Solar System Design, Melbourne, August 24th, 1977. [6] Cooper, P.I. (1970) - The Transient Analysis of Glass Covered Solar Stills. Ph.D. Thesis, University of Western Australia. [7] Bureau of Meteorology, Australia (1970) - Climate of Australia and Papua New Guinea. [8] Paltridge, G.W. and Proctor, D. (1976) - Monthly Mean Solar Radiation Statistics for Australia. Solar Energy 18 (3). [9] Robinson, N. (1966) - Solar Radiation. Elsevier Publishing Company.

13 [10] Proctor, D. - CSIRO Division of Mechanical Engineering. Personal communication. [11] Pott, P. and Cooper, P. I. (1976) - A~1 Experimental Facility to Test Flat- Plate Solar Collectors Outdoors. CSIRO Division of Mechanical Engineering, Technical Report No. TR 9. [12] De Winter, F. (1975) - How to Design and Build a Solar Swimming Pool Heater. Technical Report, Copper Development Association, N.Y. [13] Czarnecki, J. T. and Read. W.R. - Advances in Solar Water Heating for Domestic Use in Australia. Accepted for publication in Solar Energy Journal. [14] Sunset, June 1974 - Can you use the sun to heat your pool? [15] Proctor, D. (1977) - The Economics of Industrial Process Heat Derived from Solar Energy, ISES - ANZ Section Symposium on Solar System Design, Melbourne, August 24th, 1977.

Locality Item Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Qh 25.0 22.6 18.0 13.3 9.9 7.9 8.9 11.8 16. 9 19.6 23.3 25.1 Qi 28.1 26. 1 22.6 18.0 13. 7 12. 6 12.4 15.7 19. 1 23.3 25.3 26.5 Adelaide Ta 23.1 22.9 20.9 17.6 14.4 12. 1 11.1 12. 1 13.9 16. 5 19. 1 21.4 Pa 1.16 1.24 1.19 1.14 1.09 0.98 0.94 0.97 1.00 1.03 1.04 1.12 v 3.8 3.3 3.1 3.1 3. 1 3.3 3.2 3.5 3.6 3. 7 3.8 3.7 Qh 25.3 23.1 20.2 15.9 12. 5 11. 5 12.5 15.1 18.7 22.1 24.8 25.1 Qi 24.7 23.8 21. 7 20.7 17.2 15.9 17. 1 19.4 23. 5 23.5 26.4 24.7 Brisbane Ta 24.9 24.7 23.5 21.2 18.1 15.7 14.7 15.9 18.4 20.8 22.9 24. 3 Pa 2.17 2.20 2.09 1. 7 5 1.43 1. 21 1.11 1.17 1.38 1. 60 1.81 2.01 v 3.4 3.4 3. 3 2.9 2.8 2.8 2.7 2.8 2.9 3. 1 3. 3 3.4 Qh 25.9 23.3 18.5 14.4 11. 0 8. 6 9. 5 12.7 17.8 21.1 24.9 26.7 Qi 26.7 25.3 22.4 19. 7 14. 6 13.2 14. 0 16.1 20.2 22.4 25.2 26.4 Canberra Ta 20.3 19.6 17.5 13.1 8.7 6.4 5.3 6.7 9.2 12.4 15. 3 18.4 Pa 1.31 1.38 1.25 1.03 0. 84 0.71 0.67 0. 70 0.83 0.97 1.04 1.19 v 1.9 1. 7 1. 5 1.4 1.4 1.3 1.4 1. 7 1. 7 1. 8 2.0 1. 9 Qh 18.4 18.6 19. 6 18.4 19. 6 19. 2 19. 3 21.8 23.0 23.2 21.3 19.9 Qi 19.2 18.6 20.5 23.0 20.3 20. 8 21.3 23.4 24.3 24.2 21.2 19.8 Darwin Ta 28.6 28.4 28.6 28.7 27.3 25.7 25.1 26.1 27.9 29.3 29.6 29.3 Pa 3.11 3.11 3.07 2.70 2.18 1.87 1. 76 2.06 2.47 2. 77 2.93 3.05 v 2. 7 3. 0 2.4 2.7 2.9 2.9 2.8 2.7 2.8 2.8 2.6 2.8 Qh 23.2 19.9 15.1 10.6 6.6 5.1 5. 5 8.5 13.l 17.9 20.8 23.2 Qi 25.3 22.8 19.1 15.0 11. 2 10. 4 11. 0 13. 7 16.9 21.5 22.7 24.1 Hobart Ta 16.4 16.5 15.2 12.8 10.4 8.4 7.9 8.9 10.6 12.1 13.7 15.3 Pa 1.10 1.17 1.10 1.00 0.88 0. 79 0.76 0. 79 0.83 0.91 0. 96 1.06 v 3.4 3.1 3.0 2.9 2.8 2.8 2.9 3.0 3.4 3. 5 3. 6 3.4 Qh 24.9 21.5 16.7 11.6 7.3 6.2 6.9 9. 6 13.2 18.2 21.9 24.2 Qi 25.5 23.5 20.6 16.6 12.4 11.0 11. 5 14.1 17.2 20.7 22.8 24.3 Melbourne Ta 19.8 19.8 18.3 15.2 12.4 10.2 9.9 10.6 12.3 14.3 16.3 18. 3 Pa 1.30 1.41 1.32 1.17 1.04 0.93 0.89 0.91 0.97 1.04 1.11 1. 23 v 3.7 3.6 3.3 3.1 3.3 3.3 3.6 3.5 3.6 3.6 3.8 3. 8 Qh 27.2 25.2 20.7 14.9 10.6 9.4 10.3 13.6 17.6 22.5 26.6 28.8 Qi 29.0 27.8 24.2 17.9 16.1 12.8 14.3 17. 3 21.1 24.6 26.4 28.4 Perth Ta 23.5 23.7 22.1 19.3 16. 1 13. 9 13.0 13.4 14.7 16.2 19.2 21.6 Pa 1.48 1.47 1.47 1.34 1.24 1.14 1.09 1.07 1.16 1.17 1. 27 1.39 v 4.9 4.8 4.5 3.8 3.8 3.8 3.9 4.2 4.2 4.5 4.8 4.9 Qh 22.5 18.9 18.3 13.3 10.7 9.0 10. 4 13. 1 16.7 21.5 24.5 23.2 Qi 23.3 23.0 21.0 19. 2 15. 7 13.2 15.2 17.0 20.3 21.3 24.1 23.9 Sydney Ta 22.0 21.9 20.9 18.3 15.1 12.8 11. 8 13.1 15.2 17.6 19.4 21.1 Pa 1.88 1.93 1.83 1. 51 1.22 1.03 0.94 0.97 1.12 1. 31 1.50 1. 74 v 3.4 3.2 2.9 2.8 2.9 3.2 3.2 3.4 3.2 3. 4 3.4 3.4.I Table 1. Climatic Data for Capital Cities Qh is solar radiation on horizontal surface, Q. is solar radiation on surface facing north of inclination equal to the latit~de both in MJ m- 2 day- 1, T is mean air temperature in C, p is partial water vapour pressure in air inakpa, and Vis mean wind velocity i~ m s- 1

State Locality of Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Pool A 22.5 22.5 20.2 16.8 13.8 11.1 10.9 12.7 15.6 17.7 20.0 Adelaide B 28.8 28.2 24.7 20.1 16.3 13.1 13.1 15.7 19.8 22.6 25.8 c 27.8 27.8 25.3 21.5 17.7 14.9 14.7 17.0 20.3 23.0 25.2 A 27.0 26.4 25. 0 21. 9 18.2 15.7 15.3 17.1 20.3 23.0 25.1 Brisbane B 33.3 32.2 30.0 25.9 21.3 18.6 18.4 20.9 25.0 28.5 31.3 c 31.3 30.7 29.1 26.5 22.6 20.2 20. 1 22.3 25.8 27.9 30.1 A 24.6 23.9 20.9 16.2 11. 2 7.8 7. 5 10.2 14.9 18.4 21.2 Canberra B 31.1 29.7 25.5 19.8 14.0 10.0 9.9 13.4 19.4 23.7 27.4 c 30.9 30.3 27.4 22.9 17. 1 13.7 13. 7 16.4 21.6 25.0 27.7 A 29.7 29.5 30.1 28.5 26.7 25.0 24.5 26.7 28.8 30.1 30.3 Darwin B 34.3 34.2 35.0 33.1 31. 6 29.8 29.3 32.2 34. 6 35.9 35. 6 c 33.1 32.7 33.9 32.8 30.6 29.2 29.0 31.3 33.l 34.3 34.1 A 19.5 19.0 16.4 12.9 9.2 6.8 6.5 8.8 11.8 14. 8 16.7 Hobart B 25.3 24.0 20.2 15.6 10.9 8.1 7.9 10.9 15.1 19.3 21. 9 c 25.1 24.3 21.4 17.4 13.1 10.6 10.5 13.4 16.7 20.3 22.1 A 21.8 21.3 19.0 15.2 11. 3 9.1 9.0 10.7 13.3 16.3 18. 7 Melbourne B 28.0 26.7 23.2 18.1 13.1 10.7 10.7 13.1 16.6 20.9 24.2 c 26.9 26.1 23.8 19.7 15.1 12.6 12.5 14.9 17. 9 21.3 23.6 A 23.5 23.1 21.6 18.6 15.3 13. 3 13.0 14.2 16.5 18.6 21. l Perth B 30.3 29.4 26.8 22.3 18.0 15. 7 15.6 17.6 20.9 24.2 27.8 c 28.1 27.7 25.9 22.6 19.3 16.7 16.7 18.4 21.2 23.5 25.7 A 24.3 23.5 22.8 19.0 15.1 12.3 11. 9 13.7 16.9 20.2 22.6 Sydney B 29.9 28.2 27.4 22.3 17.8 14.6 14.5 17. 0 21. l 25.6 28.7 c 28.8 28.2 27.4 25.3 19.5 16.2 16.4 18.4 22.0 24.9 27.5 Dec 21.8 28.1 27.0 26.2 32.5 30.7 25.1 31.8 32.2 30.0 35.0 33.5 18.9 24.7 24.3 20.7 26.8 25.6 22.9 30.1 27.5 23.7 29.5 28.3 Table 2. Predicted average temperatures of the water in C, in open swimming pools exposed to full sunshine and wind velocity equal to 13 of the mean monthly values shown in Table 1. State of pool: A= unheated and uncovered, B = covered with double layer clear plastic cover, C = uncovered and heated with collector of area equal to the swimming pool area facing north and of inclination equal to the latitude.

10,/ v ~ ~ / I ~v I I I J I ~ 0 0 10 20 30 Tw,oC 40 50 Fig. 1. Variation of the water vapour pressure p with the water temperature T. w w... I.~ N I E ~ Tw+Ts Tm=---- 2 Fig. 2. 10 20 30 40 T. m, oc Variation of the radiation heat transfer coefficient h with the mean temperature T. r m 50

Fig. 3. A section of a home swimming pool in Melbourne equipped with the inflated clear plastic cover made of weatherable PVC film. Fig. 4. An above-ground swimming pool equipped with the air-bubble polyethylene cover.

0 8 0 6 0 5 >=' t; 0 4 z UJ u ~ 0 3 UJ 0 2 0 1 0 01 0 03 0 05 0-06 Fig. 5. Ranges of performance of commercially available single glazed and unglazed solar collectors. ~T = T - (T - 3), we c a T is the mean water temperature in the c collector. Expansion Tank Containing Antifreeze and Anticorrosive Liquid Vent Head Tank - -- Mains Water Vent Hot Water Solar Collector Storage Tank Draw Off Tank Heat Exch,.11ger 4011 Solenoid Valves Boiler Pump Swimming Pool Pool Pump Boiler Fig. 6. Hydraulic circuit schematic of a solar heating system combining swimming pool and shower water heating.

A~~~~~~~--~~~~~--~~~~~~~~~~----~--- 240 v o-+ Pool Thermostat 1 On above 26 c On below 26 "c: Draw Off Tank I Thermostat Pump Controller Thermostat 2 22 c Pool Pump Boiler Pump Collector Pump N~--------....,......,.......... 4 Off Solenoid Valves N/C Fig. 7. Control circuit schematic of a solar heating system for swimming pool and shower water shown in Fig. 6. N/O means "normally open" and N/C means "normally closed".