**Water Heater Unit Energy **(case - central)

**Energy for domestic hot water** (kbtu/day) is calculated as:

Total water heater energy use = to the

sum of:

- Water heater energy use to meet Total Hot Water Use (fixture load + appliances) (kBtu/day)

- Total DHW system distribution loses for all loops and branches (kBtu/day)

- Daily water heater standby heat losses (kBtu/day).

This daily energy estimate is multiplied by the number of days in each month and the resulting 12 monthly estimates are summed to obtain the final annual energy use.

(1)

** Water heat energy use to meet fixture** load is calculated as:

((

**Total Hot Water Use***8.293752*1.000743*(

**Water Heater Temperature Rise**))/thermal_efficiency)*(1-((wh_ua_central*(

**Water Heater Temperature Rise**))/rated input converted to Btuh))/1000

Where: **thermal_efficiency** is the user input value for
integrated water heater or boiler - btu/hr (Only
>75kBtu water heaters)

wh_ua_central is the user input value for integrated water heater or
storage tank standby Loss (UA), btu/hr (Only >75kBtu water heaters)

Total Hot Water Use (water_use_mf) is calculated as the product of:

The sum of dishwasher, clothes washer, fixture usage

The number of units

The occupancy rate (1-vacancy)

Where; dishwasher and clothes washer usage are user-entered gallons/week

**Water Heater Temperature Rise** is calculated as:

set_point_temp - inlet water temperature for the location, degrees F.

(2)

**DHW system distribution loses** are calculated as total_mf_distribution_heat_loses/thermal_efficiency/1000

Where: thermal_efficiency is the user input value for integrated water heater or boiler - Thermal Efficiency,btu/hr (Only >75kBtu water heaters)

total_mf_distribution_heat_losses is the sum of

( pipe_loop_heat_loss_total):loop 1 to n

Total Daily pipe branch pipe heat loss, for all branches, Btu/day. This is calculated as per EQ RE-20 in CEC CASE Report (see also attachment below)

#### CEC CASE, Equation RE-20

Total Hourly Branch Losses
= Nbranchk×(HBUL + HBWL), where:

HBUL =
Hourly pipe loss for one branch when water is in use (Btu/hr).

HBWL =
Hourly pipe loss for one branch due to water waste (Btu/hr)

Nbranchk = Number of branches in water heating system k.

(3)

**Standby losses** are calculated as (24*wh_ua_central*(set_point_temp-ambient_temp))/1000)

Where: wh_ua_central is the user input value for integrated water heater or storage tank - Standby Loss (UA),btu/hr (Only >75kBtu water heaters)

**Water Heater Unit Energy **(case - unit)

**Energy for domestic hot water** is calculated as:

The sum, for all water heater types, of the products of:

Typical energy use for the water heater type

water heater multiplier for the water heater type

**Typical energy use for the water heater type**

(((**Total Water use***8.293752*1.000743*(**Water Heater Temperature Rise**))/recovery_efficiency)*(1-((wh_ua_unit*(set_point_temp_user-ambient_temp))/rated_input_btu))+(24*wh_ua_unit*(set_point_temp_user-ambient_temp)))/1000

**Water heater standby loss** (wh_ua) is calculated using WHAM energy factor convert method, btu/hr (<75kBtu):

((1/energy_factor)-(1/recovery_efficiency))/(67.5*((24/41093.71)-(1/(recovery_efficiency*rated_input_btu))))

**Total Water use** (water_use_unit) is calculated

((-1.78+0.9744*occupants_total_mf+6.3933*occupants_0_5_mf+10.5178*occupants_6_13_mf+15.3052*(occupants_14_64_mf+occupants_65_plus_mf)-0.1277*set_point_temp+0.1437*tank_size*water_heater_multiplier/num_units-0.1794*inlet_temp+0.5115*average_temp+10.2191*adult_at_home_mf-dw_base_use-cw_base_use)*senior)*low_flow_fixture_adjust

**Water Heater Temperature Rise** is calculated as:

set_point_temp_user - inlet water temperature for the location, degrees F.

**Base dishwasher load** is calculated as

(0.692*occupants_total_mf+1.335*SQRT(occupants_total_mf))

**Base clothes washer load** is calculated as

(1.1688*occupants_total_mf+4.7737*SQRT(occupants_total_mf))