Methods for sizing storage water heaters vary. Those using recovery versus storage curves are based on extensive research. All methods provide adequate hot water if the designer allows for unusual conditions. To serve a hot-water load adequately, the needs of both the peak energy withdrawal rate and total integrated energy delivery for end uses must be met. Meeting these needs can be done either by providing a heating rate large enough to meet the peak energy withdrawal rate of the system (and modulating that heating input for smaller loads), or by providing a lower heating rate combined with storage (from which the peak rates can be satisfied). Lower costs are usually achieved by using at least some storage. A variety of different heating rate/storage volume combinations can be used to meet the needs of a given water-heating load profile (Hiller 1998).
Commercial and Institutional
Most commercial and institutional establishments use hot or warm water. The specific requirements vary in total volume, flow rate, duration of peak load period, and temperature. Water heaters and systems should be selected based on these requirements.
This section covers sizing recommendations for central storage water-heating systems. Hot-water usage data and sizing curves for dormitories, motels, nursing homes, office buildings, food service establishments, apartments, and schools are based on EEI-sponsored research (Werden and Spielvogel 1969a, 1969b). Caution must be taken in applying these data to small buildings. Also, within any given category there may be significant variation. For example, the motel category encompasses standard, luxury, resort, and convention motels.
When additional hot-water requirements exist, increase the recovery and/or storage capacity accordingly. For example, if there is food service in an office building, the recovery and storage capacities required for each additional hot-water use should be added when sizing a single central water-heating system.
Peak hourly and daily demands for various categories of commercial and institutional buildings are shown in Table 6. These demands for central-storage hot water represent the maximum flows metered in this 129-building study, excluding extremely high and very infrequent peaks. Table 6 also shows average hot-water consumption figures for these buildings. Averages for schools and food service establishments are based on actual days of operation; all others are based on total days. These averages can be used to estimate monthly consumption of hot water, but are not intended for sizing purposes because they do not show the time distribution of draws.
Research conducted for ASHRAE (Becker et al. 1991; Thrasher and DeWerth 1994) and others (Goldner 1994a, 1994b) included a compilation and review of service hot-water use information in commercial and multifamily structures along with new monitoring data. Some of this work found consumption comparable to those shown in Table 6; however, many of the studies showed higher consumption.
Additional Data.
Fast Food Restaurants. Hot water is used for food preparation, cleanup, and rest rooms. Dish washing is usually not a significant load. In most facilities, peak usage occurs during the cleanup period, typically soon after opening and immediately before closing. Hot-water consumption varies significantly among individual facilities. Fast food restaurants typically consume 250 to 500 gal per day (EPRI 1994).
Supermarkets. The trend in supermarket design is to incorporate food preparation and food service functions, substantially increasing the usage of hot water. Peak usage is usually associated with cleanup periods, often at night, with a total consumption of 300 to 1000 gal per day (EPRI 1994).
Apartments. Table 7 shows cumulative hot-water use over time for apartment buildings, taken from a series of field tests by Becker et al. (1991), Goldner (1994a, 1994b), Goldner and Price (1999), and Thrasher and DeWerth (1994). These data include use diversity information, and enable use of modern water-heating equipment sizing methods for this building type, making it easy to understand the variety of heating rate and storage volume combinations that can serve a given load profile (see Example 1). Unlike Table 6, Table 7 presents low/medium/high (LMH) guidelines rather than specific singular volumes, and gives better time resolution of peak hot-water use information. The same information is shown graphically in Figure 15. Note that these studies showed that occupants on average use more hot water when water-heating costs are included in the rent, than if the occupants pay directly for water-heating energy use.
The low-use peak hot-water consumption profile represents the lowest peak profile seen in the tests, and is generally associated with apartment buildings having mostly a mix of the following occupant demographics:
The medium-use peak hot-water consumption profile represents the overall average highest peak profile seen in the tests, and is generally associated with apartment buildings having mostly a mix of the following occupant demographics:
Families
Singles
On public assistance
Single-parent households
The high-use peak hot-water consumption profile represents the highest peak profile seen in the tests, and is generally associated with apartment buildings having mostly a mix of the following occupant demographics:
In applying these guidelines, the designer should note that a building may outlast its current use. This may be a reason to increase the design capacity for domestic hot water or allow space and connections for future enhancement of the service hot-water system. Building management practices, such as the explicit prohibition (in the lease) of apartment clothes washers or the existence of bath/kitchen hook-ups, should be factored into the design process. A diversity factor that lowers the probability of coincident consumption should also be used in larger buildings.
The information in Table 7 and Figure 15 generates a water-heating equipment sizing method for apartment buildings. The cumulative total hot-water consumption versus time (which includes all necessary load diversity information) can be used to select a range of heating rate and storage volume options, all of which will satisfy the load. The key is that plots of cumulative total hot-water consumption versus time as shown in Figure 15 also represent, by the slope of a line drawn from zero time through the cumulative volume used at any given time, the average hot-water flow rate up to that point in time. Up to any point in time, the minimum average heating rate needed to satisfy the load is one that can heat the average hot-water flow rate through that time from the local entering cold-water temperature to the water-heating system delivery temperature. (More accurately, the heating rate needed is determined by the local slope of the hot-water use versus time curve, not the average slope. This is because storage can supply the hot water supplied up to a selected time, and the heating rate only needs to provide the additional energy after storage is depleted. Eventually, however, storage needs to be reheated, which must also be considered. See the two methods shown in Example 1.) The storage volume needed for that heating rate is the total cumulative flow through that time (Hiller 1998). To evaluate the range of minimum required heating rates and their corresponding minimum required storage tank volumes, it is easiest to pick various volumes in Figure 15 or Table 7, then determine the heating rate and time period that correspond to them, as shown in Example 1. Final selection of water-heating system heating rate and storage size is then made by examining the first and operating costs of the various combinations.
Hotels. Hotel hot water uses tend to be grouped into three major categories: (1) guest room circuit, (2) laundry circuit, and (3) food service/commercial kitchen circuit. Guest room circuits tend to have the following hot water loads: (1) guest showers and baths, (2) guest room sink use, (3) guest room cleaning, and (4) common area cleaning. Bathing (showers and baths) is the largest single hotel hot-water use category, often exceeding all other hot-water uses combined. Research results from Hiller and Johnson (2015, 2016a, 2016b, 2016c, 2017a, 2017b) present findings on a study of a large conference hotel and a roadside travel hotel. The work provides guidance on sizing of the water heating system, including storage volumes and heating rates of water heaters, based on these two studies. ASHRAE members can obtain copies of RP-1544 reports at no cost via the ASHRAE Technology Portal (technologyportal.ashrae.org).
Example 1.
Evaluate the range of water-heating system heating-rate and storage volume combinations that can serve a 58-unit apartment building occupied by a mix of families, singles, and middle-income couples in which most adults work. The peak expected number of building occupants is 198, based on the assortment of apartment sizes in the building. Assume a water-heating system delivery temperature of 120°F, design entering cold-water temperature of 40°F, and heating device thermal efficiency of 80%.
Simplified Method.
Solution: The stated occupant demographics represent a medium load. Multiplying the volume per person versus time from the medium values in Table 7 by the number of occupants gives the cumulative amount needed at any point in time and the average flow rate (and hence heating rate) required through that time.
At 5 min, the peak design cumulative volume is (0.7 gal) × (198 people) = 138.6 gal. The average flow rate over 5 min is 138.6 gal/5 min = 27.72 gal/min. The required heating rate is thus, from Equation (1) and dividing by the input efficiency,
Assuming 70% of the storage tank volume can be extracted at a useful temperature (the other 30% being degraded by mixing in the tank), the required tank volume for this heating rate is
Note that, because the heating rate divided by storage capacity (7056 Btu/h · gal) exceeds 4000 Btu/h · gal, this system is considered an instantaneous water heater.
At 60 min, (4.8 gal/person)(198 people) = 950.4 gal. Average flow rate = 950.4 gal/60 min = 15.8 gal/min.
Doing these calculations at other volumes and times yields the combinations of heating rate and storage volume that can serve the load (Table 8).
More Accurate Method.
The preceding simplified method calculates the needed heating rate by computing the average water flow rate from the beginning of all draws for the day. In reality, because some storage is present, the water-heating device only needs to provide a heating rate computed from the local slope of the hot-water use curve, not the average slope. In other words for example, the flow over the first 5 min could have been provided entirely from storage without any heat input at all. The water heater only needs to heat in real time the amount of hot water needed over succeeding time periods. Consequently, the simplified heating rate computational method works, but results in some degree of heating rate oversizing.
Solution: Using the more accurate heating rate sizing method is similar to using the simplified method, except the local slope of the hot-water use curve versus time must be found at each time interval to determine the necessary heating rate.
At 5 min, the peak design cumulative volume (Table 8) is 139 gal. At 15 min, the peak design cumulative volume (Table 8) is 337 gal. The incremental flow rate (representing the local slope of the hot water use line) is hence (337 gal − 139 gal)/10 min = 19.8 gal/min. The needed heating rate is thus more accurately computed as
Note that heating rate divided by storage capacity (5040 Btu/h · gal) exceeds 4000 Btu/h · gal, so the more accurately sized system is still considered an instantaneous water heater.
From Table 8, the peak design cumulative volume at 120 min is 1584 gal, and is 2178 gal at 180 min. The incremental flow rate slope is thus (2178 gal − 1584 gal)/(180 min − 120 min) = 9.9 gal/min. The heating rate needed when using 1584 gal of storage is more accurately computed as
From Table 8, the peak design cumulative volume at 180 min is 2178 gal, and at 1440 min is 9702 gal. Consequently, the incremental flow rate slope is (9702 gal − 2178 gal)/(1440 min − 180 min) = 5.97 gal/min. The heating rate needed when using 2178 gal of storage is thus more accurately computed as
It is important to recognize, however, when using this more accurate heating rate sizing method, that storage must eventually be reheated. The minimum heating rate used should therefore not be less than that computed using the 24 h average flow rate.
Doing these calculations at other volumes and times yields the more accurate combinations of heating rate and storage volume that can serve the load, as shown in Table 9.
There are several techniques to size water-heating systems using the more limited draw profile information in older data. Figures 16 to 23 show relationships between recovery and storage capacity for various building categories. Any combination of storage and recovery rate that falls on the proper curve satisfies building requirements. Using the minimum recovery rate and maximum storage capacity on the curves yields the smallest hot-water capacity able to satisfy the building requirement. The higher the recovery rate, the greater the 24 h heating capacity and the smaller the storage capacity required. Note that the data in Figures 16 to 23 predate modern low-flow fixtures and appliances.
These curves can be used to select recovery and storage requirements to accommodate water heaters that have fixed storage or recovery rates. Where hot-water demands are not coincident with peak electric, steam, or gas demands, greater heater inputs can be selected if they do not create additional energy system demands, and the corresponding storage tank size can be selected from the curves.
Ratings of gas-fired water-heating equipment are based on sea-level operation and apply up to 2000 ft. For operation above 2000 ft, and in the absence of specific recommendations from the local authority, equipment ratings should be reduced by 4% for each 1000 ft above sea level before selecting appropriately sized equipment.
Recovery rates in Figures 16 to 23 represent the actual hot water required without considering system heat losses. Heat losses from storage tanks and recirculating hot-water piping should be calculated and added to the recovery rates shown. Storage tanks and hot-water piping must be insulated.
The storage capacities shown are net usable requirements. Assuming that 60 to 80% of the hot water in a storage tank is usable, the actual storage tank size should be increased by 25 to 66% to compensate for unusable hot water.
Figure 24 shows hourly flow profiles for a sample building in each category, so that readers may better understand the nature of energy withdrawal rate profiles that may need to be met in such applications. These buildings were selected from actual metered tests, but are not necessarily typical of all buildings in that category. Figure 24 should not be used for sizing water heaters, because a design load profile for a real building may vary substantially from these limited test cases.
Example 2.
Determine the required water heater size for a 300-student women’s dormitory for the following criteria:
a. Storage with minimum recovery rate
b. Storage with recovery rate of 2.5 gph per student
c. With the additional requirement for a cafeteria to serve a maximum of 300 meals per hour for minimum recovery rate, combined with item a; and for a recovery rate of 1.0 gph per maximum meals per hour, combined with item b
Solution:
a. The minimum recovery rate from Figure 16 for women’s dormitories is 1.1 gph per student, or 330 gph total. At this rate, storage required is 12 gal per student or 3600 gal total. On a 70% net usable basis, the necessary tank size is 3600/0.7 = 5150 gal.
b. The same curve shows 5 gal storage per student at 2.5 gph recovery, or 300 × 5 = 1500 gal storage with recovery of 300 × 2.5 = 750 gph. The tank size is 1500/0.7 = 2150 gal.
c. Requirements for a cafeteria can be determined from Figure 20 and added to those for the dormitory. For the case of minimum recovery rate, the cafeteria (Type A) requires 300 × 0.45 = 135 gph recovery rate and 300 × 7/0.7 = 3000 gal of additional storage. The entire building then requires 330 + 135 = 465 gph recovery and 5150 + 3000 = 8150 gal of storage.
With 1 gph recovery at the maximum hourly meal output, the recovery required is 300 gph, with 300 × 2.0/0.7 = 860 gal of additional storage. Combining this with item b, the entire building requires 750 + 300 = 1050 gph recovery and 2150 + 860 = 3010 gal of storage.
Note: Recovery capacities shown are for heating water only. Additional capacity must be added to offset system heat losses.
Example 3.
Determine the water-heater size and monthly hot-water consumption for an office building to be occupied by 300 people under the following conditions:
a. Storage with minimum recovery rate
b. Storage with 1.0 gal per person storage
c. Additional minimum recovery rate requirement for a luncheonette open 5 days a week, serving a maximum of 100 meals per hour and an average of 200 meals per day
d. Monthly hot-water consumption
Solution:
a. With minimum recovery rate of 0.1 gph per person from Figure 19, 30 gph recovery is required; storage is 1.6 gal per person, or 300 × 1.6 = 480 gal. If 70% of the hot water is usable, the tank size is 480/0.7 = 690 gal.
b. The curve also shows 1.0 gal storage per person at 0.175 gph per person recovery, or 300 × 0.175 = 52.5 gph. The tank size is 300/0.7 = 430 gal.
c. Hot-water requirements for a luncheonette (Type B) are in Figure 20. With a minimum recovery capacity of 0.25 gph per maximum meals per hour, 100 meals per hour requires 25 gph recovery, and the storage is 2.0 gal per maximum meals per hour, or 100 × 2.0/0.7 = 290 gal storage. The combined requirements with item a are then 55 gph recovery and 980 gal storage.
Combined with item b, the requirement is 77.5 gph recovery and 720 gal storage.
d. Average day values are found in Table 6. The office building consumes an average of 1.0 gal per person per day × 30 days per month × 300 people = 9000 gal per month and the luncheonette will consume 0.7 gal per meal × 200 meals per day × 22 days per month = 3100 gal per month, for a total of 12,100 gal per month.
Note: Recovery capacities shown are for heating water only. Additional capacity must be added to offset the system heat losses.
Example 4.
Determine the water heater size for a 200-unit apartment house under the following conditions:
a. Storage with minimum recovery rate
b. Storage with 4 gph per apartment recovery rate
c. Storage for each of two 100-unit wings
Minimum recovery rate
Recovery rate of 4 gph per apartment
Solution:
a. The minimum recovery rate, from Figure 21, for apartment buildings with 200 apartments is 2.1 gph per apartment, or a total of 420 gph. The storage required is 24 gal per apartment, or 4800 gal. If 70% of this hot water is usable, the necessary tank size is 4800/0.7 = 6900 gal.
b. The same curve shows 5 gal storage per apartment at a recovery rate of 4 gph per apartment, or 200 × 4 = 800 gph. The tank size is 200 × 5/0.7 = 1400 gal.
c. Solution for a 200-unit apartment house having two wings, each with its own hot-water system.
With minimum recovery rate of 2.5 gph per apartment (see Figure 21), a 250 gph recovery is required, and the necessary storage is 28 gal per apartment, or 100 × 28 = 2800 gal. The required tank size is 2800/0.7 = 4000 gal for each wing.
The curve shows that, for a recovery rate of 4 gph per apartment, storage is 14 gal per apartment, or 100 × 14 = 1400 gal, with recovery of 100 × 4 = 400 gph. The necessary tank size is 1400/0.7 = 2000 gal in
a. Storage with minimum recovery rate
b. each wing.
Note: Recovery capacities shown are for heating water only. Additional capacity must be added to offset the system heat loss.
Example 5.
Determine the water-heater size and monthly hot-water consumption for a 2000-student high school under the following conditions:
a. Storage with minimum recovery rate
b. Storage with 4000 gal maximum storage capacity
c. Monthly hot-water consumption
Solution:
a. With the minimum recovery rate of 0.15 gph per student (from Figure 23) for high schools, 300 gph recovery is required. The storage required is 3.0 gal per student, or 2000 × 3.0 = 6000 gal. If 70% of the hot water is usable, the tank size is 6000/0.7 = 8600 gal.
b. Net storage capacity is 0.7 × 4000 = 2800 gal, or 1.4 gal per student. From the curve, a recovery capacity of 0.37 gph per student or 2000 × 0.37 = 740 gph is required.
c. From Table 6, monthly hot-water consumption is 2000 students × 1.8 gal per student per day × 22 days = 79,000 gal.
Note: Recovery capacities shown are for heating water only. Additional capacity must be added to offset the system heat loss.
Table 10 can be used to determine the size of water-heating equipment from the number of fixtures. However, caution is advised when using this table, because its data are very old, taken well before the introduction of modern low-flow fixtures and appliances. To obtain the probable maximum demand, multiply the total quantity for the fixtures by the demand factor in line 19. Note that, as the number of fixtures becomes very small (e.g., for a water heater to serve a single small apartment), the demand (diversity) factors listed in Table 10 are no longer valid. In all cases, total demand is never less than the demand for the largest single fixture. The heater or coil should have a water-heating capacity equal to this probable maximum demand. The storage tank should have a capacity equal to the probable maximum demand multiplied by the storage capacity factor in line 20.
Example 6.
Determine heater and storage tank size for an apartment building from a number of fixtures.
Solution:
Showers. In many housing installations such as motels, hotels, and dormitories, peak hot-water load is usually from shower use. Table 10 indicates the probable hourly hot-water demand and recommended demand and storage capacity factors for various types of buildings. Hotels could have a 3 to 4 h peak shower load. Motels require similar volumes of hot water, but peak demand may last for only a 2 h period. In some types of housing, such as barracks, fraternity houses, and dormitories, all occupants may take showers within a very short period. In this case, it is best to find the peak load by determining the number of shower heads and rate of flow per head; then estimate the length of time the shower will be on. It is estimated that the average shower time per individual is 7.5 min (Meier 1985).
Flow rate from a shower head varies depending on type, size, and water pressure. At 40 psi water pressure, available shower heads have nominal flow rates of blended hot and cold water from about 2.5 to 6 gpm. In multiple-shower installations, flow control valves on shower heads are recommended because they reduce flow rate and maintain it regardless of fluctuations in water pressure. Flow can usually be reduced to 50% of the manufacturer’s maximum flow rating without adversely affecting the spray pattern of the shower head. Flow control valves are commonly available with capacities from 1.5 to 4.0 gpm.
If the manufacturer’s flow rate for a shower head is not available and no flow control valve is used, the following average flow rates may serve as a guide for sizing the water heater:
Note that the maximum flow rate allowed by U.S. federal energy efficiency standards is 2.5 gpm, as of 1992. However, higher-flowrate models are still sold.
Food Service. These establishments are required to provide a sufficient supply of hot water to meet the peak hot-water demand requirements set forth by the overseeing regulatory body, usually the county health department. Cities and counties adopt or modify state or federal hot-water sizing guidelines for food service establishments to meet the needs of their locality. The procedure for sizing water heaters for restaurants typically includes the following steps:
List all hot-water end-use fixtures by type and by count.
Characterize each fixture for maximum hot-water use per hour and per minute.
Calculate the peak hot-water demand for water heaters with and without storage.
Obtain the water heater temperature rise required for winter.
Calculate the minimum water heater input rate.
Select the water heater type, input rate, and storage capacity (in a few jurisdictions).
It is important to note that the hot-water requirements for various fixtures presented in Table 11 are based on various resources (see the table notes), which are currently used by food service facilities and health departments to size hot-water heaters. Some equipment flow data in these guidelines predates current low-flow fixtures used in kitchens. Specifically, the flow rate requirements for prerinse spray valves have dropped from 5 gpm to a federally mandated maximum flow rate of 1.6 gpm, and, similarly, flow rate requirements for aerators on public hand sinks have dropped from 2.2 gpm to 0.5 gpm.
Note that the sizing guidelines required by local mandate for commercial food service applications specify only the required heating rates; they do not address the storage volume requirements of storage water heaters. Because of this, it is not really possible to size storage water heaters with the information specified. Although for some types of storage water heaters it may be possible to provide the storage water heater heating rate specified, there is no way to know how large the tank needs to be with that information alone. More information is needed regarding the time spacing of draws throughout the day before adequate storage volume can be specified. It is possible to design or select storage water heating systems that will perform adequately but do not have as high a heating rate as may be specified in local mandates, as long as adequate amounts of storage are provided. In this regard, the outdated practice of specifying needed storage water heater heating requirements without regard to storage volume used is an impediment to use of newer higher efficiency technologies, such as gas- or electric heat pump water heaters and solar water heating systems. Such systems would normally be provided with lower heating rates and more storage when meeting loads, to minimize first costs.
The intent of the heating rate sizing guidelines for storage heaters is an attempt to ensure that hot water is available during operating hours to meet the food preparation and sanitation needs of the facility for food safety reasons. Thus, the food service sizing guideline is the minimum bar that some localities may accept for specified heating rates. However, this differs from the combination of heating rate and storage volume that may actually work for a given installation. The sizing guidelines are limited in that they only focus on calculating the energy input rate to the water heater without providing guidance on minimum hot-water storage requirements (except for North Carolina), and hot-water delivery performance considerations (e.g., performance limitations of tankless heaters with door-type dishwashers). The food safety sizing guidelines for water heaters also do not consider after-hours cleanup, when the peak hourly hot-water use occurs in some facilities; this may cause emptying of the tank on a nightly basis. Rapidly using hot water and filling the tank with cold water can cause thermal fatiguing of the tank, greatly reducing the operating life in gas storage heaters (Fisher-Nickel 2010). There is no current method for calculating the minimum storage requirement for a food service facility or sizing storage heaters based on the ratio of storage capacity and energy input rate. This is a difficult task, because hot-water use on an average daily, peak hourly, or per-minute basis greatly varies between food service facilities, especially in larger facilities, even of equal size and type. Variations in staff operating practices (e.g., after-hours store cleaning), equipment maintenance, and other operations between two identical facilities can cause large differences in hot-water consumption. This sizing guideline and associated examples are intended to clarify the prevailing food safety sizing guidelines, which in many cases are not comprehensive and are difficult to follow.
After the maximum flow rate has been calculated using Table 11, the required heater(s) may be sized using manufacturers’ specification sheets that cross-reference temperature rise and flow rate, or using Equation (11):
where
| qi | = | heater input, Btu/h |
| Qh | = | flow rate, gph |
| cp | = | specific heat of water = 1.00 Btu/lb · °F |
| ρ | = | density of water = 8.33 lb/gal |
| Δt | = | temperature rise, °F |
| η | = | heater efficiency |
Sizing water heater input rate in food service may require following local food safety department water-heater sizing guidelines, which typically provide end-use fixture flow rates, temperature rise, and heater efficiency values to calculate minimum flow rate or recovery rate. An alternative to using these input rate sizing guidelines requires the commercial kitchen to hire a professional engineer to submit for approval an alternative water-heater sizing calculation. This latter method is typically too costly and time consuming in the build-out or renovation of most commercial kitchens.
Dishwashers in food service facilities typically dictate the water heater outlet temperature required. Dishwashers generally require delivery of 140°F water for rinse operation, but inlet temperature can range from a minimum of 120°F for a low-temperature dishwasher to 180°F for a high-temperature dishwasher without a booster heater. For a typical hot-water system distribution line, heat losses require the water heater thermostat to be set at an elevated temperature (typically between 145 to 150°F) to deliver 140°F water to the dishwasher or booster heater.
In restaurants, bacteria are killed by rinsing washed dishes with 180 to 195°F water for several seconds. In addition, an ample supply of general-purpose hot water, usually at 140 to 150°F, is required for the wash cycle of dishwashers. Although a water temperature of 140°F is reasonable for dish washing in private dwellings, in public places, the NSF (e.g., Standard 3) or local health departments require 180 to 195°F water in the rinsing cycle. However, the NSF allows a lower temperature of 120 to 140°F when low temperature or fill and dump machines are used with the use of a chemical sanitizing rinse. The two-temperature hot-water requirements of food service establishments present special problems. The lower-temperature water is distributed for general use, but the 180°F water should be confined to the equipment requiring it and should be obtained by boosting the temperature. It is dangerous to distribute 180°F water for general use. ANSI/NSF Standard 3-2001 covers the design of dishwashers and water heaters used by restaurants.
The data provided in Table 12 shows the range of water heater flow rate and hourly hot-water demand requirements for various types of low- and high-temperature sanitizing dishwashers based on 100% operating capacity of the machines. Loading a dishwasher at 100% capacity is impractical in most commercial kitchens. Some local health departments assume a 70% operating rinse capacity for sizing dishwashers’ hot-water demand, except for rackless-type conveyor machines where the fresh-water rinse is continually operating when the machine is in operation. Some dishwashers use only a cold-water supply for rinse and (with some models) for the tank fill, allowing them to operate without any connection to the hot-water line. These undercounter and door-type machines typically use integrated booster heaters and exhaust-air heat recovery to preheat the cold water for the next rinse cycle.
Examples 7, 8, and 9 demonstrate the use of Equation (11) in conjunction with Tables 11 and 12.
Example 7.
Determine the maximum hot-water flow rate demand for tankless water heaters and the maximum hourly average hot-water flow rate demand for storage water heaters for a commercial kitchen with a one-compartment food preparation sink, one standard three-compartment sanitation sink, two hand sinks, two lavatories, one mop sink, one prerinse sink with a 1.15 gpm spray valve, and one high-temperature door-type dishwasher (1.0 gal/rack, 11 s rinse time, 57 racks/h) with a built-in 40°F temperature rise booster heater.
Solution: The end-use fixtures and hot-water demand requirements for sizing the heating rate of storage or tankless water heaters are shown in the following table:
The minimum flow rate for sizing the heating rate of a tankless water heater is 14.6 gpm. Likewise, the minimum flow rate for sizing the heating rate of a storage water heater is 186 gph.
Example 8.
Determine the energy input requirements (heating rate) for both a tankless and a storage water heater for the commercial kitchen described in Example 7. Examine both gas and electric resistance energy source options. Assume an operating efficiency of 70% for the noncondensing gas option, 85% condensing for the condensing gas option, 90% for the electric storage option, and 99% for the electric tankless option. Assume the design entering cold-water temperature (winter) is 50°F and the water heater outlet temperature is 150°F. This is a little higher than the 140°F required by the dishwasher booster heater, to account for piping heat losses.
Solution: The temperature rise required is 150 – 50 = 100°F. For a tankless water heater, the required heating rate using Equation (11) is computed as
Thus, for the 70% gas tankless option, the required energy input rate is 729,708/0.70 = 1,042,440 Btu/h. It is common practice to install one or more 199,000 Btu/h units in parallel in commercial facilities to meet minimum flow rate requirements. Using this approach, six standard-efficiency tankless units, each rated at 199,000 Btu/h, are required to meet this load. For the 85% gas condensing tankless option, the required heating rate is 729,708/0.85 = 858,480 Btu/h, requiring five 199,000 Btu/h condensing tankless heaters. For the 99% electric tankless option, the required energy input rate is 729,708/0.99 = 737,079 Btu/h. Four 184,000 Btu/h or six 123,000 Btu/h electric resistance tankless heaters are required to meet the hot-water demand.
Because tankless water heaters have no storage volume, these heating rates are adequate for use in specifying appropriate water heaters.
Sizing tankless heaters using manufacturers’ specification sheets data on maximum flow rate at a given temperature rise is a common approach, because the data are readily provided. Flow rate data varies slightly among manufacturers of similar products at the same input rate based on the efficiency of the unit. A 199,000 Btu/h standard-efficiency heater typically provides a maximum of 3.3 gpm of water at a 100°F temperature rise, whereas a condensing heater provides 3.8 gpm. To meet the flow requirements of 14.6 gpm for this facility, five standard-efficiency 199,000 Btu/h units installed in parallel for a combined input rate of 995,000 Btu/h are required to meet the load by providing a maximum combined flow rate of 16.5 gpm. To meet the flow requirements with condensing high-efficiency tankless heaters, four 199,000 Btu/h units for a combined input rate of 796,000 Btu/h are required, for a maximum combined flow rate of 15.2 gpm. It is important to note that using the manufacturer’s stated maximum flow rate at a given temperature rise to calculate the number of tankless units based on the maximum flow rate calculation of 14.6 gpm is a less conservative approach, because it relies on the rated thermal efficiency of the heater instead of the typical operating efficiency.
For the storage water heaters, the required heating rate is computed as
Thus, for the 70% gas storage water heater, the required heating rate is 154,938/0.70 = 221,340 Btu/h. For the 85% gas condensing storage water heater, the required heating rate is 154,938/0.85 = 182,280 Btu/h. For the 90% electric resistance storage water heater, the required heating rate is 154,938/0.90 = 172,153 Btu/h.
Note that this information in insufficient to properly specify a storage water heater, because a method for calculating the minimum storage volume is needed. Moreover, once storage is incorporated, note that the loads can be met by using smaller heating rates than those computed here, using larger storage tanks. In this respect, the heating rates mandated by a typical health department become a barrier to using higher-efficiency equipment, such as heat pump water heaters or solar water heating, whose heating capacities are more expensive than standard efficiency equipment, and whose cost-effective system designs therefore favor smaller heating rates and larger storage volumes. Although this is true, the majority of water heaters in commercial kitchens are specified using the food safety guidelines to calculate the minimum input rate of conventional gas or electric water heaters. In doing so, one or more storage heaters may be selected to meet this total requirement. Typically, one 250,000 Btu/h gas storage heater (or two 120,000 Btu/h units) rated at 80% thermal efficiency is chosen. An energy-efficient approach is to select a high-efficiency condensing water heater rated at 95% thermal efficiency, which is assumed to be operating at 85% operating efficiency in this kitchen with continuous recirculation. A 199,000 Btu/h condensing gas storage heater will meet the requirements for this facility and is a better value, because it reduces operating costs and is competitive on first costs. One 184,000 Btu/h or two 92,000 Btu/h electric resistance storage heaters could be selected from manufacturers’ specification sheets to meet the hot-water demand.
Example 9.
For the commercial kitchen described in Example 7, what is the condensing storage water heater input rating if the facility chooses to install a dishwasher that only requires a cold-water hookup? Assume that the facility can benefit by reducing the required outlet temperature by 20°F from 150°F. Also assume that, by removing the need for continuous recirculation, this measure improves the operating efficiency from a nominal 85% to 90%.
Solution: The total hot-water demand calculated in Example 7 drops from 186 gph to 129 gph when the hot-water demand of the dishwasher on the centralized water heater is eliminated. For the storage water heaters, the required heating rate is computed as
For the 90% gas condensing storage water heater, the required heating rate is 85,966/0.90 = 95,517 Btu/h. One 100,000 Btu/h gas condensing storage heater can be selected to meet the hot water demand using the food safety input rate sizing guidelines. Also, dishwashers that have only a cold water feed typically depend on heat recovery systems to preheat the incoming cold water from the exhaust or drainwater waste streams to a temperature of 110°F. They rely on larger secondary heating systems commonly referred to as booster heaters to heat the water to the 180°F sanitizing rinse temperature on a high-temperature machine. This requires the addition of a 70°F rise booster heater instead of a conventional 40°F booster heater that would be used in conjunction with entering 140°F water from the primary water heater.
Schools. Service water heating in schools is needed for janitorial work, lavatories, cafeterias, shower rooms, and sometimes swimming pools. Hot water used in cafeterias is about 70% of that usually required in a commercial restaurant serving adults and can be estimated by the method used for restaurants. Where NSF sizing is required, follow Standard 5. Shower and food service loads are not ordinarily concurrent. Each should be determined separately, and the larger load should determine the size of the water heater(s) and the tank. Provision must be made to supply 180°F sanitizing rinse. The booster must be sized according to the temperature of the supply water. If feasible, the same water can be used for both needs. If the distance between the two points of need is great, a separate water heater should be used. A separate heater system for swimming pools can be sized as outlined in the section on Swimming Pools/Health Clubs.
Domestic Coin-Operated Laundries. Small domestic machines in coin laundries or apartment house laundry rooms have a wide range of draw rates and cycle times. Domestic machines provide a wash water temperature (normal) as low as 120°F. Some manufacturers recommend a temperature of 160°F; however, the average appears to be 140°F. Hot-water sizing calculations must ensure a supply to both the instantaneous draw requirements of a number of machines filling at one time and the average hourly requirements.
The number of machines drawing at any one time varies widely; the percentage is usually higher in smaller installations. One or two customers starting several machines at about the same time has a much sharper effect in a laundry with 15 or 20 machines than in one with 40 machines. Simultaneous draw may be estimated as follows:
Possible peak draw can be calculated from
where
| F | = | peak draw, gpm |
| N | = | number of washers installed |
| P | = | number of washers drawing hot water divided by N |
| Vf | = | quantity of hot water supplied to machine during hot-wash fill, gal |
| T | = | wash fill period, min |
Recovery rate can be calculated from
where
| R | = | total hot water (machines adjusted to hottest water setting), gph |
| θ | = | actual machine cycle time, min |
Note: (θ + 10) is the cycle time plus 10 min for loading and unloading.
Commercial Laundries. Commercial laundries generally use a storage water heater. The water may be softened to reduce soap use and improve quality. The trend is toward installing high-capacity washer-extractor wash wheels, resulting in high peak demand.
Sizing Data. Laundries can normally be divided into five categories. The required hot water is determined by the weight of the material processed. Average hot-water requirements at 180°F are
Total weight of the material times these values give the average hourly hot-water requirements. The designer must consider peak requirements; for example, a 600 lb machine may have a 20 gpm average requirement, but the peak requirement could be 350 gpm.
In a multiple-machine operation, it is not reasonable to fill all machines at the momentary peak rate. Diversity factors can be estimated by using 1.0 of the largest machine plus the following balance:
For example, four machines have a diversity factor of 1.0 + 0.45 = 1.45.
Types of Systems. Service water-heating systems for laundries are pressurized or vented. The pressurized system uses city water pressure, and the full peak flow rates are received by the softeners, reclaimer, condensate cooler, water heater, and lines to the wash wheels. Flow surges and stops at each operation in the cycle. A pressurized system depends on an adequate water service.
The vented system uses pumps from a vented (open) hot-water heater or tank to supply hot water. The tank’s water level fluctuates from about 6 in. above the heating element to a point 12 in. from the top of the tank; this fluctuation defines the working volume. The level drops for each machine fill, and makeup water runs continuously at the average flow rate and water service pressure during the complete washing cycle. The tank is sized to have full working volume at the beginning of each cycle. Lines and softeners may be sized for the average flow rate from the water service to the tank, not the peak machine fill rate as with a closed, pressurized system.
Waste heat exchangers have continuous flow across the heating surface at a low flow rate, with continuous heat reclamation from the wastewater and flash steam. Automatic flow-regulating valves on the inlet water manifold control this low flow rate. Rapid fill of machines increases production (i.e., more batches can be processed).
Heat Recovery. Commercial laundries are ideally suited for heat recovery because 135°F wastewater is discharged to the sewer. Fresh water can be conservatively preheated to within 15°F of the wastewater temperature for the next operation in the wash cycle. Regions with an annual average temperature of 55°F can increase to 120°F the initial temperature of fresh water going into the hot-water heater. For each 1000 gph or 8330 lb per hour of water preheated 65°F (55 to 120°F), heat reclamation and associated energy savings is 540,000 Btu/h.
Flash steam from a condensate receiving tank is often wasted to the atmosphere. Heat in this flash steam can be reclaimed with a suitable heat exchanger, to preheat makeup water to the heater by 10 to 20°F above the existing makeup temperature.
Swimming Pools/Health Clubs. The desirable temperature for swimming pools is 80°F. Most manufacturers of water heaters and boilers offer specialized models for pool heating; these include a pool temperature controller and a water bypass to prevent condensation. The water-heating system is usually installed before the return of treated water to the pool. A circulation rate to generate a change of water every 8 h for residential pools and 6 h for commercial pools is acceptable. An indirect heater, in which piping is embedded in the walls or floor of the pool, has the advantage of reduced corrosion, scaling, and condensation because pool water does not flow through the pipes, but its disadvantage is the high initial installation cost.
The installation should have a pool temperature control and a water pressure or flow safety switch. The temperature control should be installed at the inlet to the heater; the pressure or flow switch can be installed at either the inlet or outlet, depending on the manufacturer’s instructions. It affords protection against inadequate water flow.
Sizing should be based on four considerations:
Conduction through the pool walls
Convection from the pool surface
Radiation from the pool surface
Evaporation from the pool surface
Except in aboveground pools and in rare cases where cold groundwater flows past the pool walls, conduction losses are small and can be ignored. Because convection losses depend on temperature differentials and wind speed, these losses can be greatly reduced by installing windbreaks such as hedges, solid fences, or buildings.
Radiation losses occur when the pool surface is subjected to temperature differentials; these frequently occur at night, when the sky temperature may be as much as 80°F below ambient air temperature. This usually occurs on clear, cool nights. During the daytime, however, an unshaded pool receives a large amount of radiant energy, often as much as 100,000 Btu/h. These losses and gains may offset each other. An easy method of controlling nighttime radiation losses is to use a floating pool cover; this also substantially reduces evaporative losses.
Evaporative losses constitute the greatest heat loss from the pool (50 to 60% in most cases). If it is possible to cut evaporative losses drastically, the pool’s heating requirement may be cut by as much as 50%. A floating pool cover can accomplish this.
A pool heater with an input great enough to provide a heat-up time of 24 h would be the ideal solution. However, it may not be the most economical system for pools that are in continuous use during an extended swimming season. In this instance, a less expensive unit providing an extended heat-up period of as much as 48 h can be used. Pool water may be heated by several methods. Fuel-fired water heaters and boilers, electric boilers, tankless electric circulation water heaters, air-source heat pumps, and solar heaters have all been used successfully. Air-source heat pumps and solar heating systems are often used to extend a swimming season rather than to allow intermittent use with rapid pickup.
The following equations provide some assistance in determining the area and volume of pools.
Elliptical
| Area | = | 3.14AB |
| A | = | Short radius |
| B | = | Long radius |
| Volume | = | 7.5 gal/ft3 ×Area × Average Depth |
Kidney Shaped
| Area | = | 0.45L(A+B) (approximately) |
| L | = | Length |
| A | = | Width at one end |
| B | = | Width at other end |
| Volume | = | 7.5 gal/ft3 ×Area × Average Depth |
Oval (for circular, set L = 0)
| Area | = | 3.14R2 + LW |
| L | = | Length of straight sides |
| W | = | Width or 2R |
| R | = | Radius of ends |
| Volume | = | 7.5 gal/ft3 ×Area × Average Depth |
Rectangular
| Area | = | LW |
| L | = | Length |
| W | = | Width |
| Volume | = | 7.5 gal/ft3 ×Area × Average Depth |
The following is an effective method for heating outdoor pools. Additional equations can be found in Chapter 6.
Obtain pool water capacity, in gallons.
Determine the desired heat pickup time in hours.
Determine the desired pool temperature. If not known, use 80°F.
Determine the average temperature of the coldest month of use.
The required heater output qt can now be determined by the following equations:
where
| q1 | = | pool heat-up rate, Btu/h |
| ρ | = | density of water = 8.33 lb/gal |
| cp | = | specific heat of water = 1.00 Btu/lb · °F |
| V | = | pool volume, gal |
| tf | = | desired temperature (usually 80°F) |
| ti | = | initial temperature of pool, °F |
| θ | = | pool heat-up time, h |
where
| q2 | = | heat loss from pool surface, Btu/h |
| U | = | surface heat transfer coefficient = 10.5 Btu/h · ft2 · °F |
| A | = | pool surface area, ft2 |
| tp | = | pool temperature, °F |
| ta | = | ambient temperature, °F |
Notes: These heat loss equations assume a wind velocity of 3 to 5 mph. For pools sheltered by nearby fences, dense shrubbery, or buildings, an average wind velocity of less than 3.5 mph can be assumed. In this case, use 75% of the values calculated by Equation (15). For a velocity of 5 mph, multiply by 1.25; for 10 mph, multiply by 2.0.
Because Equation (15) applies to the coldest monthly temperatures, results calculated may not be economical. Therefore, a value of one-half the surface loss plus the heat-up value yields a more viable heater output figure. Heater input then equals output divided by fuel source efficiency.
Whirlpools and Spas. Hot-water requirements for whirlpool baths and spas depend on temperature, fill rate, and total volume. Water may be stored separately at the desired temperature or, more commonly, regulated at the point of entry by blending. If rapid filling is desired, provide storage at least equal to the volume needed; fill rate can then be varied at will. An alternative is to establish a maximum fill rate and provide an instantaneous water heater that can handle the flow.
Industrial Plants. Hot water (potable) is used in industrial plants for cafeterias, showers, lavatories, gravity sprinkler tanks, and industrial processes. Employee cleanup load is usually heaviest and not concurrent with other uses. Other loads should be checked before sizing, however, to be certain that this is true.
Employee cleanup load includes (1) wash troughs or standard lavatories, (2) multiple wash sinks, and/or (3) showers. Hot-water requirements for employees using standard wash fixtures can be estimated at 1 gal of hot water for each clerical and light-industrial employee per work shift and 2 gal for each heavy-industrial worker.
For sizing purposes, the number of workers using multiple wash fountains is disregarded. Hot-water demand is based on full flow for the entire cleanup period. This usage over a 10 min period is indicated in Table 13. The shower load depends on the flow rate of the shower heads and their length of use. Table 13 may be used to estimate flow based on a 15 min period.
Water heaters used to prevent freezing in gravity sprinkler or water storage tanks should be part of a separate system. The load depends on tank heat loss, tank capacity, and winter design temperature.
Process hot-water load must be determined separately. Volume and temperature vary with the specific process. If the process load occurs at the same time as the shower or cafeteria load, the system must be sized to reflect this total demand. In some cases, it may be preferable to use separate systems, depending on the various load sizes and distance between them.
Ready-Mix Concrete. In cold weather, ready-mix concrete plants need hot water to mix the concrete so that it will not be ruined by freezing before it sets. Operators prefer to keep the mix at about 70°F by adding hot water to the cold aggregate. Usually, water at about 150°F is considered proper for cold weather. If the water temperature is too high, some of the concrete will flash set.
Generally, 30 gal of hot water per cubic yard of concrete mix is used for sizing. To obtain the total hot-water load, this number is multiplied by the number of trucks loaded each hour and the capacity of the trucks. The hot water is dumped into the mix as quickly as possible at each loading, so ample hot-water storage or large heat exchangers must be used. Table 14 shows a method of sizing water heaters for concrete plants.
Sizing Tankless Water Heaters
Although tankless water heaters are sometimes also referred to as instantaneous water heaters, in this chapter the two types are distinct. Larger instantaneous water heaters for bigger commercial, institutional, and industrial applications may still have some water storage tank volume, even though their ratio of heating rate divided by storage volume is large. Smaller commercial and residential systems only contain a volume of water sufficient to fill the chambers or tubing where the heating is done; they do not incorporate storage tanks, and are truly tankless as the term is used here.
Tankless water heaters offer potential efficiency advantages over tank-type units for several reasons. Because they do not store heated water, they have low standby energy loss (typically, only a small amount of electricity to run controls). This energy savings potential can be significant for low-use applications. Another potential advantage is that the lack of a storage tank means they are much smaller than tank-type units and can more easily be located close to points of use (especially electric tankless units). Locating units close to points of use reduces energy losses in the hot-water distribution system, sometimes substantially. This ease of positioning may also make it easier to use more than one water heater, reducing hot-water distribution system heat losses still further by eliminating even more piping.
There are many good applications of both electric and fossil-fired tankless water heaters in residences, commercial, institutional, and industrial settings. Tankless water heaters are especially useful for providing more localized heating in point-of-use or near-point-of-use applications because they do not take up much space. In general, tankless water heaters are designed to completely heat cold water in one pass through the heater. There are exceptions, however, because some models with advanced controls can also heat prewarmed water by controllable amounts. See the discussion below about modulating heat input rates.
Tankless water heaters generally have some sort of flow detection method (e.g., a flow switch or method of differential temperature measurement that indicates flow is occurring). Water heating only begins once water flow is confirmed. Outlet temperature from tankless water heaters is determined by the flow rate, entering cold-water temperature, and applied heating rate. Simpler systems do not actively control outlet temperature, other than to turn off the heat input if exit temperature exceeds a set value. These systems are more likely to specify the use of water flow restrictors to restrict flow through the units to minimize undesirably cool water exiting the units.
Systems with more advanced controls continuously monitor the exit water temperature and modulate the heat input and/or water flow rate to maintain the specified outlet temperature. Advanced electric tankless water heaters modulate power to the heating elements, either in steps (multiple heating elements) or by varying the voltage and/or current supplied to the heating elements, or both. Advanced fossil-fired tankless water heaters, which are available in both natural-gas- and propane-fired versions, modulate the heating rate by either modulating heat input in steps (e.g. using multiple burners), or by modulating gas flow rate to the burner(s), or some combination of the two. These designs can be used as booster heaters or in recirculated heating systems (i.e., they can work well with prewarmed entering water temperatures) because they can better control exit temperature.
One of the most important tankless water heater sizing considerations is having adequate heat input rate to heat the desired flow rate of water by a temperature rise needed to make the water warm enough to use. Table 15 shows the necessary heat input rate (not considering heat input efficiency: divide table values by heat input efficiency in decimal form [e.g., 0.8 for some fossil-fired heaters]) to determine total energy input rate required for tankless water heaters versus flow rate and needed temperature rise. The heating rates shown are computed using Equation (1).
Note that 105°F is about the minimum acceptable temperature for human use at fixtures. Accounting for heat loss in piping and/or when atomizing droplets in a showerhead, 110°F is a more typical requirement. The needed temperature rise in a cold climate where the entering cold-water temperature may be 35°F would thus be 110°F − 35°F = 75°F; in a warm climate where the entering cold water temperature may be 85°F, the temperature rise would be 110°F − 85°F = 25°F. For comparison, the temperature rise specified in the U.S. federal water heater testing and rating procedure is 135°F − 58°F = 77°F. For reference, typical flow rate ranges are as follows:
Hand-washing sinks: 0.2 to 1.0 gpm
Showers: 0.8 to 2.5 gpm
Bathtub fill rates: 1.0 to 6.0 gpm
Dishwasher fill rates: 1.0 to 3.0 gpm
Clothes-washing machine fill rates: 1.0 to 6.0 gpm
Residential whole-house recurring peak rates: around 3.0 to 4.0 gpm
Residential whole-house severe-peak flow rates: 6.0 to 8.0 gpm
As can be seen from Table 15, whole-house tankless water heaters need to be able to provide heating rates on the order of 75,000 to 150,000 Btu/h in all but the warmest climates. Note, however, that in single-family residential applications, users have the opportunity to learn what works and what does not, and are likely to adjust their hot-water use habits somewhat to obtain adequately hot water from whatever water-heating system is used. They could do this for example, by avoiding hot-water use from multiple fixtures simultaneously, and reducing demanded flow rates.
An important issue in the sizing of tankless water heaters is thus what peak hot-water energy rate load to design for. It is generally acceptable to design the water-heating system to meet a peak hot-water load (in terms of energy rate needed, not just water flow rate needed) that is not exceeded by 97.5% of all draws. The difficulty in sizing whole-house tankless water heaters comes in predicting how draws will coincide to create the peak energy demand rate. This peak coincident energy demand rate must be estimated by the person sizing the system, because ASHRAE does not currently have a statistically valid amount of data on peak residential water/energy flow rates with which to make recommendations. However, research (Buchberger et.al. 2015) has for the first time provided hot-water draw information from a statistically large number of residential test sites, allowing estimation of probabilities of various types of draws occurring versus time of day, probabilities of how such draws may overlap in time within and between households, and normal ranges of flow rates and total volumes for the various types of draws. Sizing recommendations are easier with storage-type water heaters because their sizing is done more based on integrated total energy requirements, and is not highly dependent on knowledge of peak flow rates.
An issue related to proper sizing of tankless water heaters is the size of fuel piping and electrical service needed. Because gas-fired tankless water heaters must have significantly higher fuel burn rates than typical tank-types, larger gas piping may be required. The same is true for electric tankless water heaters, where a whole-house unit may require larger wiring and often additional (multiple) circuit breakers. Consequently, large tankless water heaters, both gas and electric, can in some cases require a service entrance upgrade. Notably, diversified electrical demand for large numbers of electric tankless water heaters is not much different (generally a little lower) than tank types, because of the lower number of tankless water heaters that are on at any point in time compared to tank types. However, as number of users on an electrical line decreases, demand diversity decreases, which can result in increased electrical demand compared to tank types as the number of users on the line decreases to fairly few. The number that “few” represents varies with size of the tankless units. Hiller (2017) found that diversified electrical demand of 28 kW tankless water heaters in residences was similar to that of 4.5 kW storage water heaters when number of households exceeded 2 to 15, depending on averaging time interval.