### DHW detailed calculations

#### 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:
1. Water heater energy use to meet Total Hot Water Use (fixture load + appliances) (kBtu/day)
2. Total DHW system distribution loses for all loops and branches (kBtu/day)
3. 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