ASHRAE DE-93-12-3 -Energy Requirements and Potential Savings for Heated Indoor Swimming Pools

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DE-93-1 2-3

ENERGY REQUIREMENTS AND POTENTIAL SAVINGS FOR HEATED iNDOOR SWiMMiNG POOLS C.C. Smith, P.E. MemberA SHRAE

R.W. Jones, P.E.

ABSTRACT In a series of extended tests, the rate of evaporation from the quiet water surface of a large indoor swimming pool has been measuredand correlated with air and water temperature and air humidity. Precise measurements of change in water level and of steam consumptionin the pool water heater were both used to determine evaporation rates. Goodagreement of the two methods was observed. The form of the evaporation rate equation published in the 1991 ASHRAEHandbook--HVAC Applications was confirmed. Actual evaporation from the quiet water surface varied from O. 020 to O. 055 lb/(h.ft2). These rates are 76% of those obtained by use of the published equation at the measuredconditions. It is recommended that a 73 % factor be used as a multiplier in the ASHRAE equation for evaporation from quiet indoor pools at elevations less than 1,000 feet above sea level iNTRODUCTION The design and operation of heating and ventilating equipmentin a natatorium depend on accurate knowledgeof the rate of water evaporation from the swimmingpool surface. That information is also necessary for predicting water-heating requirements and for the design of energy conservationfacilities. Energy analysts frequently employ the evaporation equation presented in the 1991 ASHRAEHandbook--HVAC Applications for calculating pool energy loads. This equation was developed by Carrier in 1918. Other equations have also been proposed. However, there is substantial disagreementof 50 %to 100 %in the application and results of these equations. ’riffs disagreementlikely occurs because equations have been based on the results of tests with small evaporating pans rather than on direct measurement of water loss in swimmingpools. The disparity in evaporation equation results causes wide differences in predicted energy savings from pool efficiency and renewable energy measures. Because of this uncertainty in predicted energy savings, the U.S. Department of Energy has sponsored a series of tests to measure evaporation rates in swimmingpools. The procedures and results of tests to measureevaporation rates from a quiet,

G.O.G. LSf, Ph.D. Member ASHRAE indoor pool and their application to prediction of energy savings by use of pool covers are presented. Evaporation rates were determined by precise measurements of water level in an unoccupiedpool over sufficient time intervals (18 to 68 hours) to achieve evaporation errors no larger than 2%. Rates determined by level change measurements were closely confirmed by simultaneous measurementsof rates of heat supply to the pool water. The results confirm the form of the ASHRAE equation and the dependenceof evaporation rate on the difference in vapor pressure of water at pool temperature and at the dew point of air in the natatorium. The rate of evaporation from an undisturbed water surface was found to be 76 %of the rate obtained by use of the ASHRAE equation, with a standard deviation of 4.5%. Measurementand correlation of evaporation rates from a pool in active use, conditions under which considerably higher rates are expected, are planned. The U.S. Departmentof Energy’s Institutional Conservation Program has launched a nationwide campaign to Reduce SwimmingPool Energy C_osts, or RSPEC. The initiative will focus awareness on the energy consumption and operating costs of the nation’s 5.9 million pools and spas. Market-ready energy efficiency and renewable energy products will be supported through information and technology transfer to institutional and commercialpool owners. Programgoals are to reduce pool owners’ operating costs, conserve our nation’s precious resources, and protect the environment through the use of conservation and renewable energy. ’/’he measures supported by RSPEC,including hybrid solar heating systems, pool covers, and windbreaks, must be adequately assessed before pool owners can make informed investment decisions about their use. Accurate methods to calculate pool energy loads before and after measure implementation must be available. Since evaporation is the primary source of heat loss in pools, typically accounting for 50%to 70%of the total, its prediction is particularly important. Heating and ventilation requirements in indoor swimruing pools depend heavily on the rate of evaporation of water from the pool surface. Heat must be supplied to the water at a rate equal to the loss. Maintenanceof acceptable relative humidity in the natatorium, usually about 50%, requires removalof that moisture either by ventilation or by

Charles C. Smithis a research scientist and GeorgeO.G.LiJf is professor emeritus at the Solar EnergyApplications Laboratory, ColoradoState University, Ft. Collins. RandyW.Jones is a mechanicalengineer in the Department of Energy,DenverSupportOffice, Denver, CO. 864

ASHRAE Transactions: Symposia

operation of dehumidification exluipment. If ventilation is used, the incoming air must be heated during most of the year at rates dependenton air quantity, prevailing temperature, and humidity conditions. Moisture removed by dehumidification requires electric energy for compressor operation. The cost of energy for an indoor pool is a large componentof its operating budget, and the potential for savings by use of effective conservation measures is substantial. The design of heating and ventilating equipment, the prediction of energy requirements, and decisions on energy conservation proposals require reliable information on pool evaporation rates. In numerousinvestigations, the specific rate of evaporation has been found to be directly proportional to the difference in vapor pressure of water at pool temperature and at the air dewpoint. The rate also increases with surface air velocity. The widely used evaporation formula of Carrier has been published in manyeditions of the ASHRAE Applications Handbook. Most of the published equations, including Carrier’s, are based on measurementsof evaporation from undisturbed water surfaces in small shallow pans exposedto streams of air at knowntemperature, humidity, and velocity. Evaporation from large water surfaces such as lakes occurs at a lower rate than from small test pans, but the same variables have been found to apply. Although the ASHRAEHandbookhas long stated that the Carrier equation is applicable to swimmingpools, measurements of evaporation in an actual pool under controlled and monitored conditions have not been published. Reports of rates of heat supply to pool water and of condensate collection from dehumidifiers have been published, but variation in operating conditions and lack of conformity of heat supply and condensate recovery with actual evaporation rates maketheir use unreliable. Lack of accurate data on evaporation from an actual pool has resulted in ambiguity and disagreement on the applicability of the Carrier equation. There are, for example, discrepancies in the 1987 and 1991 ASHRAE Applications as to whetherthe equation should be applied to pools in use or to undisturbed water surfaces. Thesediscrepancies need to be resolved, both for reliable heating and ventilating

specifications and for predicting the reduction in energy use to be realized by covering the pool. Energy costs can be substantially reduced by the placement of floating covers on the water surface whenthe pool is not in use. Evaporation is prevented and water heating is not needed during those periods. Ventilation and air heating can also be curtailed whenthe pool is covered. The prediction of energy savings that can be achieved by coveting pools is an important factor in determining whetherthe use of pool covers is cost-effective in specific instances. Evaporation rates have been estimated by using equations based on data obtained in manysmall-scale evaooration experiments reported in the technical literature. The Carrier equation, published in ASHRAE Applications, is W = (95 + .425v)(Pw -pa)/Y

(1)

where W = v = Pw = Pa Y

evaporationrate, lb/0a-ft2); air velocity at water surface, fpm; saturation vapor pressure at water temperature, in.

Hg;

= saturation vapor pressure at the air dew point, in. Hg (also partial pressure of water in pool atmosphere); = latent heat at pool temperature, Btu/lb.

Other investigators have obtained data that conform reasonably well with the earlier work and the ASHRAE equation, but in someinstances, substantially higher rates have been reported. With few exceptions, previous investigators have correlated their evaporation measurementswith equations similar to Carrier’s, differing only in the values of the coefficients A and B in the relationship W= (A Bv)(pw - pa)/Y. Table 1 is a summaryof several reported coefficients, converted to uniformunits. Table 1 shows that although there is agreement on the factors affecting evaporation rate and on the form of the equation, the measured rates differ as muchas twofold. Someof the differences are apparently due to variation in the shape and size of the evaporating surface, factors receiving only limited quantitative evaluation.

TABLE1 EvaporationRate Equations Investiqator Carrier Rohwer Himus & Hinchley Lurie & Michailoff Meyer (tanks) Meyer (reservoirs)

~ear 1918 1931 1924 1936 1931 1931

~ 95 90 165 117 ii0 81

~ .425 .277 °376 .468 .253 .185

Notes (I) (2)

(3) (3)

NOTES: (I) Equation also in ASHRAE Handbooks, (2) Based on several hundred measurements in wind tunnel and outdoor test pans, (3) Meyer’s e~*atlons based on air velocity at 30 ft. height. Values of B in table are computed by asstn~ing surface velocity is one-half the velocity at 30 ft.

ASHRAE Transactions: Symposia

865

Recent reports from the U.S. and Geunany show evaporation rates lower than indicated in Table 1 and large differences in the rates from active and inactive indoor pools. Equations that include additional parameters and nonlinear variation with vapor pressures have also been proposed. Evaporation was assumed to be equal to measured condensate recovery from dehumidifiers, but air leakage, condensation on building surfaces, other water losses, and variation in pool conditions adversely affect the accuracy of the results. The current ASHRAE recommendations are to assume that the equation applies to pools in active use and that evaporation from a quiet pool is about half that rate. Data supporting these recommendationshave not been published, however. The object of the present investigation has been the procurementof reliable information on evaporation rate, energy requirements, and conservation potential in indoor swimmingpools. DESCRIPTIONOF THE TEST FACILITY The facility used for the tests is a modemswimming pool with a surface area of 4,340 ft 2 in a natatorium 120 feet by 110 feet by 20 feet in height. Water temperature is normally maintained at 82°F by thermostat, air temperature at 80°F, and air humidity at approximately 60%by means of humidistat-controlledventilation. Air-to-air heat recovery is used requiring 17.5 horsepowerfor fan power. Automatic swimmingpool covers are normally used when the pool is not occupied. Pool water is circulated by conventional equipment through filters and through heat exchangers supplied with steam from a central boiler plant. Condensatefrom the pool water heaters (along with condensate from shower water heaters) is returned by pumpsto the central boiler plant. Automatic water makeupto compensate for pool evaporation is provided, but that feature can be disabled manually to ensure no change in water level other than by evaporation. Side gutters for overflow of pool water drain into the recirculation system, but maintenance of the pool level slightly belowthe gutter lip during the measurements avoids the need for returning overflow water through an open surge tank. Condensate from the steam heating system can be measured by calibrating the automatic steam trap and recording the frequency of discharge to the condensate return pumps. There are, therefore, two methods for determining evaporation rate, one being the water level change in the pool and the other being the calculation of heat supply rate by measurement of condensate from the pool water heaters. Temperature and Humidity Control ~’! Pool water temperatureis maintainedby a thermostati- ;~i cally controlled valve on a steam line entering the pool water heater. Ventilation is controlled by a humidistat to 866

supply 100% fresh outdoor air when relative humidity increases to an upper setpoint. Fans are turned off when relative humidity decreases to a level approximately 5% below the upper setpoint. During testing, humidity in the natatorium was usually within +3%of the average, occasionally reaching a maximum departure of 5 %. Exhaust fans operate simultaneously with air supply fans. Air temperature varied from the average by less than 2°F. Method and Procedure Evaporation measurementsby themselves are not useful in verifying or establishing a relationship with other variables unless they are controlled and monitored. The variables are the rate of air movementacross the water surface, water temperature, air temperature, and air humidity. Accurate measurementof those quantities and of the evaporation itself provides the information necessaryfor establishing a reliable evaporation equation. The evaporation mass. flux from a water surface cannot be measured directly by practical means. It can be measured, however, by the liquid volumeloss during the test period under consideration. At typical conditions in indoor pools, evaporation rates of about 0.04 poundsof water per hour per square foot of quiet water surface maybe expected. At this rate, the water level in a pool will decrease about one-fifth inch per day. With suitable equipment, water levels can be measured to an accuracy of :t:0.002 inch, so the evaporation over a one-day period can be measured to an accuracy of 1% to 2%. Other means of water addition or discharge are monitoredor, as in this test, prevented. In a test of 68 hours duration, the pool water level was determined by a micrometer hook gauge rigidly mountedto the pool side. This gaugeis read visually to 0.005 inch, so the 0.52-inch change in level was measured with an accuracy of about 1.5%. In tests of shorter duration, a micrometer gauge was used. This gauge has a higher precision adjustment and senses electrical contact with the water surface instead of a visual indication of contact. Level observations were repeated until two or more agreed to within .002 inch. Measurementswere made inside a small cylinder partially submergedbelow the surface to suppress any wavemotion during observations (stilling well). A second measurement method is to monitor energy input to the pool water and makecorrections for the small quantities of energy dissipated from the pool by other mechanisms(primarily radiant and convective heat losses from the pool surface. The evaporation rate is determined by applying the heat of vaporization of water at the pool temperature, which, for the testing conditions, was 1,045 Btu/lb. Pool heat input was monitored by weighing the condensate collected from a steam-to-pool water heat exchanger. Steamenters the heater as saturated vapor at 19 psi absolute pressure and 225°F. Liquid condensate leaves at 150°F. The resulting enthalpy difference is 1,038 Btu/lb. CondenASHRAE Transactions: Symposia

temperature, and 56% relative humidity, are shown in Table 2 and Figure 1. Summarizedin the table are data on temperature, humidity, pool water level, water heat supply rate, and measuredand calculated evaporation rate. Figure 1 showsthe history of water temperature and air temperature and humidity during the Test III period. Goodcontrol of temperatures and humidity is evident, thereby making possible a meaningful correlation of evaporation rates with those parameters. The bottom line in Table 2 shows the measured hourly rate of evaporation averaged 0.039 pounds per square foot and the evaporation 2. based on an adjusted heat supply rate of 0.044 lb/h-ft Evaporation rates, based on measurementsover short periods (as seen in the first three intervals in Table2), are not representative because very small errors in measuring water levels can be large fractions of the actual level changes, and changes of a few tenths of a degree in pool temperature can account for sizable portions of steam Temperature and Humidity Measurement condensate (heat supplied) for only a few hours. An error of only 0.01 inch in measuring the 0.004-foot level charge So that the pool evaporation rate could be reliably during the first 3.6 hours would result in an evaporation correlated with the conditions in the pool, high-quality error of 25 %. Similarly, a pool temperature change of only instruments were used and operating conditions were 0.20F (commonlyobserved) represents about 300,000 Btu maintained at sufficiently constant levels over the test of stored heat. The average pool heat supply rate is about periods to validate the computational comparison. Air and 250,000 BtuPa, so evaporation based on steam condensate water conditions were monitored and recorded at six-minute measurementsspanning only four hours would be in error by almost 30 %. intervals using a desktop computer. Pool water and air dryErrors are minimized, however, over the long periods bulb and wet-bulb temperatures were measured with T-type used in the tests reported here. Table 2 showsthe developthermocouple welded junctions. These temperature sensors ment of constancy in evaporation rates determined by both agreed to within 0.5°F with a precision scientific mercurymethods. in-glass thermometer, and the thermocouples agreed with Figure 2 showstotal water evaporated during Test III each other to within 0.2°F. This precision includes the as measured by the change in pool level and as measuredby electronic signal conditioning and was repeatable during the steam supply to the pool heater. The difference in the two testing period. results is due to energy factors, whichare described below The primary method of humidity measurement was by in detail. Also shown in Figure 2 is total evaporation obtaining air wet-bulb and dry-bulb temperatures. These computed by use of the ASHRAE equation. temperature sensors were mountedin the draft of a small Air movement at the pool surface, shownin Table 3, (40-watt) fan, with the wet-bulb sensors located in a wick was observed three times during Test III, at 3 hours, 29 wetted with distilled water. The wet-and dry-bulb sensors hours, and 58 hours. Air movement was in random direcwere located at the pool side, 12 inches above the water tions when the ventilation fans were not operating. surface. A recording hair hygrometer and a mercury-inAn estimate of the duration of ventilation time was glass sling psychrometer were also used. All methods made from observing air humidity records (Figure 1). agreed consistently within 3 %relative humidity. Periodic Humidity rises whenthe ventilation is off and falls when measurements with a sling psychrometer showed relative the fans are running. It appears that the on and off periods humidity variation of about 3 %around the 13001perimeter. are nearly equivalent, and air movement was equally Pool water temperature was monitored by a single divided between the two conditions. At air velocities in this thermocouple probe with the sensor tip submerged four range, the ASHRAE equation shows ah almost negligible inches below the pool surface. Prior to testing and twice effect on evaporation (a 2% increase for a doubling of during the test period, a mercury-in-glass maximum/minivelocity), so an average air velocity of 5.3 fpmwas used as mumthermometer was moved throughout the pool water a constant value in the ASHRAE calculation. volumeto determine temperature variation. The thermomeTests at four other pool operating conditions were ter indicated constancyof temperature within 1 °F. conducted for varying periods of time. Table 4 contains a summaryof the conditions and results of all five evaporaRESULTS tion tests. All conditions for these tests were identical Detailed results of Test III, conducted for 68 hours except for air temperature and relative humidity. As under conditions averaging 82°F pool temperature, 78 °F air described above, outdoor air was automatically supplied sate is discharged from a receiver tank by a pump in response to a level switch. Five condensatedischarge cycles were measured and averaged at 88.6 pounds per cycle. A digital readout counter was connected to the pumpswitching contacts, which totaled the discharge cycles during the test period. Testing began and ended with the condensate receiver empty. Since the hot water heaters serving showers had been turned off, only pool-heating condensate was admitted to the receiver during the test period. Air velocity across the pool surface is another variable that must be determined. Since the vdocity is low, a sensitive methodof measurementwas required. Periodically, air velocity at the pool surface was measured by releasing balloons of neutral buoyancy(helium-filled and counterweighted) over the center of the pool and timing their movement.Measurementswere made when ventilation fans were operating and when they were shut down.

ASHRAE Transactions: Symposia

867

TABLE2 Resultsof PoolEvaporation, Test III ELAPSED TIME HRS

TEMPERATURES AIR DB AIR

2.4 3.6 8.7 20.9 26.8 28.9 32.4 45.4 52.2 56.4 68.4

78 78 79 76 77 78 80 77 77 78 76

.LEVEL

67 68 67 67 65 66 68 67 68 66 66

CUM EVAP* LBS

0.686 0.683 0.682 0.680 0 ¯ 672 0 ¯ 669 0. 667 0.666 0. 658 0.654 0.650 0.643

- DEG F WB WATER

813 1084 1626 3794 4607 5149 5420 7588 8672 9756 11696

AIR

83 83 83 83 83 83 83 83 83 83 83

RH

,EVAP RATE* 2 LB_L_~HR-FT

59 61 57 64 55 55 57 61 65 55 59 CUM

~APOR WATER i. I. I. i. I. i. i. i. i. I. I,

HEAT**

241 321 642 1231 1633 1753 1954 2623 2804 2829 3480

0,078 0.069 0.043 0.042 0.040 0.041 0.039 0.039 0.038 0.040 0.039***

PRESSURE-IN AIR

14 14 14 14 14 14 14 14 14 14 14

0.57 0.60 0.55 0.58 0.52 0.54 0.58 O. 58 0.61 ,0.54 0.52

MM HG DIFF 0.57 0.54 0.59 0.56 0.62 0.60 0.56 0.56 0.53 0.60 0.62

HEAT EVAP** 2BTU/__~T

EVAP RATE** 2 LBS/HR-F~T

231 306 605 1141 1518 1629 1815 2428 2580 2586 3186

0.092 0.081 0.066 0.052 0.054 0.054 0.053 0.051 0.047 0.044 O.044*ee

~_o~/~: Determined by water level change Determined by adjusted heat supply rate Final results of test

’--

Air

Pool

1oo # 9O I

8 8o ~ 7o ~ 6o ~ ~o

~ 3o

10 I

I

J

I

8

16

24

32

_.J.~_m.L__

40

Hours From Start Figure 868

48

I

56

64

72

of Test

The recorded trends of temperature and relative humidity during a 68-hour test period (Test III). ASHRAE Transactions:Syrnposia

--

Heat Input to Pool

Level Change of Pool

......

---

ASHRAE Calculation

2 0 6

12

18

30

24

36

42

48

60

54

66

72

Hours From Start of Test

Figure 2

Total evaporation (pounds of water) trends during a 68-hour testing period (Test III in Table 4*). (*Adjusted for pumpenergy and heat losses other than evaporation.)

TABLE3 Observations of Air Movement OverPool Surface (fpmair velocity) Space Time of Observation 3 Hrs. 29 Hrs. 58 Hrs.

Ventilation Fans Off

Status

3 1 2

Fans O__n_ 9 I0 7

TABLE4 AverageTest ConditionsandResults Test No. Temperatures [Hrs Air Air WB Pool Duration] (°F) I II III IV V

[18] [18] [68] [24] [20]

82 82 78 73 71

ASHRAE Transactions: Symposia

76 74 66 61 59

83 83 83 83 83

Rel. H~n~idity (%) 72 73 57 53 51

Vapor Pres. Difference (In-Hg)

.31 .35 .59 .70 .75

2) Evap. (Lb/Hr-Ft Level Heat Change Supply .020 .024 .039 .050 .055

.022 .028 .044 .057 .059

869

Evaporation Determination by Pool Heat inputs and Losses

wheneverthe humidity reached a high limit and switched off whenthe humidity reached a low limit. Air temperature was not controlled, but it remainednearly constant throughout each test period. Also shownin Table 4 are evaporation rates determined by measurementof pool-level changes and by measurement (and adjustment) of heat supply rates. A nearly threefold variation is observed, corresponding to a similar range in vapor pressure differences. Also evident is satisfactory agreement between these two completely different methods for determining evaporation rates. Relative humidity and air temperatures in Table 4 cover a comparatively wide range of vapor pressure differences. Figure 3 is a presentation of measuredevaporation rates as a function of the vapor pressure differences. Evaporation results based on pool level change and on heat supply rate in the five tests are shownas data points. Also presented in Figure 3 is the straight-line ASHRAE relationship. Alinear fit to the level measurement data (cross points) is shown in Figure 3; the correlating equation is W = 74(pw - pa)/Y. The difference in slope of the two lines indicates that the ~active pool evaporation rate is 76 %of the ASHRAE prediction. At the low air velocities in an indoor pool, the influence of the velocity term is almost negligible. Insufficient velocity variation preventedits evaluation in this investigation, but in subsequent measurements on an outdoor pool (Jones et al. 1993), the coefficient of the velocity term was found to be 0.36. Using that value and an average air velocity of 5.3 fpmduring the indoor tests, the evaporation rate equation is W = (72 + o36V)

+

(Pw-Pa)

Evaporation rates calculated by the use of measured heating energy input to the pool are shownin Figure 3 by circled points. These measurementsserved as useful checks on the accuracy of the water-loss measurements. Corrections for heat transfer by convection and radiation and for pumpenergy addition and pool water temperature change were made. 11ae steam condensate measurement required prior calibration of the steam trap discharge quantity and the measurement of the temperatures of entering steam and leaving condensate. The condensate discharge was weighed on a beambalance scale five times. Quantities ranged from 87 to 90.5 lbs, with an average of 88.6 lbs. This range indicates a potential error of 3.5 lbs, or 3.9 %. The accuracy of a scientific mercury-in-glass thermometer for measuring steam and condensate temperatures was :hl°F, resulting in a potential overall enthalpy error of 0.19 %. The combined maximumerror in the heat supply measurements was thus 4.1%. Other heat losses (and gains) contribute to the small difference between the results of the two measurement methods. For the conditions in the pool and natatorium, the following heat-transfer equations were used. Radiation from pool to natatorium surfaces: qr = 0.173 × Io-SA~F(T~- 714w) where qr = radiant heat-transfer rate (Btu/h.ft2);

/Y"

Level Measurement

0

Energy Input Measurement *

---

ASHRAE Calculation

0.08 0.07 0.06 0.05 0.04 0.03 0.02

0.00 0.00

Toot polnto from Table IV

~.~’

0.01 0.I0

0.20

0.30

Vapor Pressure

Figure 3

’

870

0.40

0.50

Difference-In

0.60

0.70

0.80

Hg

Evaporation rate test results from level (water loss) and energy input measurementscomparedwith ASHRAE equation as a function of water vapor pressure difference.* (*Adjusted for pumpenergy and heat losses other than evaporation.) ASHRAE Transactions: Symposia

surface area of pool water (ft2); water surface emissivity, 0.9; radiation shape factor from pool surface to surroundings, 1.0; pool water temperature (R); temperature of walls and ceiling (R). The computedradiation loss term ranged from 1 to 11 Btu/h.ft 2, corresponding to 4%to 15%of the total heat supply rate. Convection from pool surface to air over pool: qc = hh(tp - ta), 1/ h 3, = 0.22(tp-ta) where qc h tp ta

= = = =

convectiveheat-transfer rate (BtuPa.ft2), convectionheat-transfer coefficient (Btu/h.ft 2. °F), pool water temperature (°F), air temperature over pool (°F).

In addition to the above losses, there is an estimated 2. loss from the heat exchangerand pipeworkof 0.1 Btu/h.ft Finally, there is an energy gain resulting from recirculation pumpwork equal to 3.9 BtuPa.fi 2. The combined energy adjustments for each test condition are reflected in the values shown in Table 4 and Figure 3. An example of calculated losses and gain is represented in Table 5. The small difference between evaporation rates determined by water level change and heat supply rate, ranging between8 %and 15 %, provides confidence in their validity. Inaccuracies in estimating radiation, convection, and the fractional degree variation in temperatureof a large massof pool water are considered principal sources of the differences. For example, a pool temperature rise of only 0.2°F from the start to the end of a 24-hour test represents more than 300,000 Btu, corresponding to 12,500 BtuPa. This quantity is almost 6 %of a typical hourly heat supply rate of 220,000 Btu.

It is possible, also, that the consistently higher values of evaporation based on steam condensate measurement could have been the result of a small and unmeasured amountof moisture in the saturated steam supply. Error Potential in ASHRAE EvaporationDetermination Error in determiningthe coefficients in the evaporation equation is dependent on temperature sensor error and the averaging of temperatures across the entire pool area relative to the values at the sensor locations. The temperature sensors (T-type welded thermocouple junctions) were placed in a temperaturebath prior to testing and agreed to within ±0.2°F. The air dry-bulb and wetbulb temperature variation around the pool perimeter was observed to be less than 2°F. Pool water temperature variation was within I°F. Airflow movementcould be in error by 3 to 4 feet per minute, as seen from Table 3. By combining the above errors in the ASHRAE equation at a typical condition (pool temperature83 °F, air dry-bulb temperature 78 °F, air wet-bulb temperature 67 °F, and air velocity 7.5 fpm), the error in the compu~xl evaporation rate is 4.2%. DISCUSSION Evaporation rate accurately measured by water-level change in an unoccupied indoor swimmingpool has been found directly proportional to the difference in vapor pressure of water at pool temperature and at air dew point. The proportionality constant is 76 %of the value determined by Carrier in pan evaporation tests with undisturbed water. Identification of the sources of differences amongthe publishedrelationships is not within the scopeof this paper, but one major factor is evident. The size of the evaporating surface in most of the previous investigations was very small, from a few square inches to a few square feet. Edge effects, airflow instabilities, and other factors are likely to have contributed to the differences. Measurementson larger outdoor water surfaces, although not as accurate, have shown lower rates than found in pan tests. Estimates of

TABLE5 EnergyGainsandLossesunderTypical Conditions in IndoorPool Pool Temperature Air Temperature ceiling Temperature Steam Supply Pressure, psia Steam supply temperature Condensate discharge temperature Condensate rate Total heat supply Radiation Loss Convection loss Piping heat loss Recirculation pump energy gain

83°F 78°F 66°F (Estimated) 19 psia 225°F 150°F .0483 ibs/hr 50.1 Btu/hr - Sq Ft 5.7 Btu/hr - Sq Ft 2.4 Btu/hr - Sq Ft 0.I Btu/hr - Sq Ft (3.9 gain) Btu/hr - Sq

Evaporation

45.8 Btu/hr - Sq Ft

ASHRAE Transactions: Symposia

heat loss, by difference

871

natural evaporation from ponds and reservoirs have, therefore, long been based on the use of reduced values of the rates measuredin small-scale tests. Meyer(1942), for example, recommended use of a coefficient for lake evaporation of 74 %of that for standard pans. "l~ere can be no better facility for determiningevaporation rates in swimmingpools than a pool itself. Direct applicability to other pools of accurately measuredwater losses in a test pool is clear. The departure of the value of the coefficient from the value found by Carrier with small test pans is the result of the large difference in surface area of water. Whetherthere maybe a quantitative relationship betweenwater surface area and specific evaporation rate is beyondthe scope of this paper. It is recommended that the relationship for this 4,300-square-foot pool be considered applicable to all indoor pools larger than about 1,000 square feet. Logic and limited evidence indicate that evaporation from a pool in active use is higher than from a quiet water surface. Waves,water splashes, wet deck areas surrounding the pool, and wet skin of swimmersin and out of the pool all increase effective evaporating area. Averagesurface air velocity mayalso increase, but that effect, if any, is small. The principal factor is increased wetted surface, primarily deck space across whichpool users travel in and out of the pool. Althoughhighly variable, that area mayapproach half the pool water surface. At a comparable rate from such areas, evaporation could be 50 % higher than whenthe pool is not in use. Condensatewas collected from dehumidifiers in Germanpools at substantially higher rates whenthe pools were in use than whenidle, but quantifying the results is speculative. It should be recognized that the energy for evaporation that occurs outside the pool itself, as from wet deck areas, is not drawn from the pool water but rather from the ventilation air. The increase in pool water heat supply is probably the result of the greater area of turbulent water surface and possibly higher local velocities of air in contact with the water. Evaporation rates found in this investigation apply directly to requirements for energy, water, ventilation, and heating during closed periods, typically 40%to 60%of the time. If pool covers are applied to the water surface when the pool is not used, the resulting energy savings can be accurately predicted by use of the equation developedin this investigation. For design of pool heaters, air exhaust/supply/heating facilities, dehumidifiers, and heat recovery units, peak evaporation rates must be knownor estimated. Measurements are clearly needed. Until the data are available, it is recommendedthat evaporation rates from pools in typical active use be estimated 50%higher than from unoccupied pools under the same temperature and humidity conditions. Although a total pressure term is seldom included in evaporationrate equations, limited studies of its effect have been made by Rohwer(1931), Russell, Millar (1937), Sleight. Rohwer’sextensive evaporation measurementsover 872

a range of altitudes (including data for Fort Collins and for sea level), corrected for wind velocity differences in an analysis by Hickox (1944), showedagreement with Millar’s finding of evaporation rate proportional to the -0.25 power of atmospheric pressure. Applyingthis relationship to the Fort Collins data obtained at a 24.8-inch barometer yields a sea level rate 95.4% of the Fort Collins rates. The equation applicable at low elevations (below approximately 1,000 ft) is then: W = (69

+.34V)

(Pw-Pa)

/Y"

This rate is 73 % of that obtained by direct use of the unadjusted Carrier/ASHRAEequation. CONCLUSIONS 1.

At knownwater temperature, air temperature, and air humidity, the rate of evaporation from an undisturbed water surface in an indoor swimming pool can be reliably calculated using the equation W = A(C+

.35v)

(Pw-Pa)

/Y,

where W A C

= = =

v

=

Pw

=

Pa

= vapor pressure of water at air dew point, in.

lbs evaporated per hour; surface area of water, ft2; a coefficient dependent on barometric pressure, with a measuredvalue of 72 at 5,000 ft elevation and a computedvalue of 69 at sea level; air velocity at water surface, in the range of 1 to 10 fpm; vapor pressure of water at pool temperature, in. Hg;

Hg;

Y

= latent heat of vaporization at pool temperature, Btu/lb. 2. The rate of evaporation from an undisturbed water surface in an indoor pool is 76 %(73 %at sea level) the rate computed by using Equation 1, page 4.7, of the 1991 ASHRAEHandbook(and the identical equation in earlier editions of ASHRAE Applications). 3. Evaporation rates measured by precise pool-level differences at closely controlled conditions during five tests of 18 to 68 hours duration were determined with an average error of 2 %. 4. Least-squares correlation of measuredevaporation rates with vapor pressure differences shows a standard deviation of 4.5 %. ~ 5. Average departure of rateof evaporation by heat supply measurement from the rate measured by poollevel changeis 12 %. It is concludedthat the closeness of this agreementjustifies the determinationof evaporation rates from indoor pools by accurate measurement of the heat supply and water temperature change, together with estimates of other energy losses. ASHRAE Transactions: Symposia

6.

The small coefficient of the air velocity term in the developed equation was not evaluated because of inadequate meansfor achieving significant variation in that parameter. The 0.38 value shown in the equation is based on subsequent measurements in an outdoor pool where the effects of air velocity variation could be determined. 7. Minimumventilation rates necessary for maintenanceof constant natatorium humidity whenthe pool is not in use can be reliably determined by use of the evaporation rate equation developedin this investigation and by Equation 2, section 4.7, of the 1991 ASHRAEHandbook. Correspondingair-heating requirements can then be determined by use of outdoor and indoor air temperature. 8. Variation in pool conditions monitored at bsix-minute intervals throughout a test period resulted in maximum departures of 5.5% from the average vapor pressure difference. Computedand measured evaporation rates were, therefore, essentially constant in each test. 9. Measurementsof pool-level change over periods of at least 16 hours by use of micrometer gauges can provide evaporation rate results with maximum errors less than 2%. 10. The equations developed in this investigation maybe used with confidence in predicting reductions in waterheating and air-heating requirements by use of covers on indoor swimmingpools. REFERENCES ASHRAE.1991. 1991 ASHRAEhandbook--HVAC applications, p. 4.7. Atlanta: AmericanSociety of Heating, Refrigerating and Air-Conditioning Engineers, Inc. Biasin, V.K., and W. Krumme.1974. Evaporation in an indoor swimmingpool. Electrowarme International, May, pp. al15-a129 (Germany). Brambley, M.R., and S.E. Wells. 1983. Energy conservation measures for indoor swimmingpools. Energy8(6): 403. Carrier, W.H. 1918. The temperature of evaporation. ASHVETransactions 24: 25. Hickox, G.H. 1944. Evaporation from free water surfaces. Papers, AmericanSociety of Civil Engineers, p. 1297, October. Himus, G.W., and J.W. Hinchley. 1924. The effect of a current of air on the rate of evaporation of water below the boiling point. Chemistryand Irulustry 43: 840. Jones, R., C.C. Smith, and G. Lrf. 1993. Measurement and analysis of evaporation from an inactive outdoor swimmingpool. Proceedings of the 1993 Conference of the AmericanSolar Energy Society, p. 399. Lrf, G.O.G. 1991. Evaporation from swimming pools. Letter in Heating, Piping, and Air Conditioning, October, p. 39. Lurie, M., and N. Michailoff. 1936. Evaporation from free water surfaces. Ind. atut Eng. Chem.28(3): 345. ASHRAE Transactions: Symposia

Meyer. 1942. Evaporation from lakes and reservoirs. Minnesota Resources Commission, June. Millar, F.G. 1937. Evaporation from free water surfaces. Canadian Meteorological Memoirs 1: 43. NSPI. 1987/88. 1987 and 1988 swimming pool and spa industry market reports. National Spa and Pool Institute. Reeker, J. 1971. Water evaporation in indoor swimming pools. Gesutulheits-Ingenieur, March, pp. 72-80 (Germany). Rohwer, D. 1931. Evaporation from free water surfaces. Tech. Bulletin No. 271, U.S. Dept. of Agriculture. Root, D. 1983. Howto determine the heat load of swimruing pools. Solar Age, November,p. 20. Shah, M.M.1990. Calculated evaporation from swimming pools. Heating, Piping, a~l Air Conditioning, December, p. 103. APPENDIX Exampleof Evaporation Reduction and Cost Savings by Use of Pool Cover PoolStatistics 23,000 ft Pool surface area 21,000 ft Surrounding deck area Water temperature 800F Air temperature 80°F Relative humidity in natatorium 50 % Hours closed per year 4,500 Annual average atmospheric temperature 45°F Powerto exhaust and fresh air fan 10 kW 3 Heat source, natural gas 1,000 Btu/ft Average air movementover water surface 5 fpm Roomair dew point (from psychrometric chart) 61.5°F From vapor pressure tables, at 80°F Pw = 1.033 in. Hg at 61.5°F Pa = 0.550 in. Hg (Convenient source of vapor pressure data is tables in ASHRAEFutMamentals. ) Calculations Water-Heating Saving Using evaporation equation, W= (72 + .36v)(Pw pa)/Y, Evaporation heat = (72 + .36 × 5)(1.033 - 0.550) 235.7 Btu/h.ft Water heating saved by covering pool = 35.7 × 3000 × 4500 = 483 mmBtu per year Air-Heating Saving Evaporation rate = 36.2/1048 × 3000 = 103.6 lb/h Humidity ratio at 82°C, 50%RH= 0.0117 lb/lb Humidity ratio winter average = 0.0020 lb/lb Minimumventilation rate = 103.6/[60 × .075 × (0.0117 - .0020)] = 2,373 cfm 873

Minimumair heating saved = 60 x 2373 x 0.018 x (82 - 45) x 4500 = 427 mmBtu/yr MinimumTotal Heat Saving 483 mm+ 427 mm= 910 mmBtu saved/yr At 70%combustion efficiency, natural gas saving = 910 ram/100,000 × 0.70 = 13,000 ccf/yr Value of gas saved at $0.50/ccf = 0.5 × 13,000 = $6,500/yr Electricity Saving Fan energy reduction = 10 kW × 4500 h = 45,000 kWh/yr Value of electric saving at $0.05/kWh= $2,250/yr

DISCUSSION S.A. Sherif, Assodate Professor, Department of Mechanical Engineering, University of Florida, Gainesville: The accuracy of the water level measurementsin the pool seems to be quite high (+0.02 in.). Can the authors speak moreto this issue and describe the instruments they used to carry out the level measurements? C.C. Smith: Measurementsof water level are taken by a micrometerwith a scale readable to .001 inch. The micrometer is securely mountedto the side of the pool and is inside a stilling well to suppress waves. The sharp tip of the micrometerpoint is sprayed with silicon oil to reduce water adhesion. Thepoint is lowereduntil it visually contacts the water surface. The measurementis repeated until consistent readings are found to ±0.01 inch.

Total Annual Energy Saving Total saving = $6500 + $2250 = $8750/yr Alternate Saving Based on Ventilation Rate in ASHRAE Standard 69-1989, p. 5 Recommendedventilation rate = 0.5(3000 + 6000) 4500 cfm Air heating saving based on ASHRAE rate: 60 x 4500 x 0.018 x (82 - 45) x 4500 = 809 Btu/yr Total heat saving = 809 mm + 483 mm = 1292 mm Btu/yr Value of total heat saving = 1292 nun X .50/70,000 = $9,229/yr Total gas and electricity saving = $9229 + $2250 = $11,479/yr Economic Evaluation At typical installed cost of fully automatic swimming pool covers providing 95 %suppression of evaporation when pool is not in use, $36,000 total installed cost/0.95 × $8750= 4.33 years simple payback Based on ASHRAEStandard 69-1989, $36,000/0.95 × $11,479 = 3.30 years simple payback NOTE: Savings resulting from reduction in water treatment costs (primarily reduced chlo6ne requirements) and from reduced moisture damageto structure and equipment not included.

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