## 5.2 B4.2. Cold Water Inlet Temperature

The water heater inlet temperature is assumed to vary on a daily basis with the following relationship defined by the data included in the climate zone weather files. For each day of the year, Tinlet will be calculated as follows:

T inlet = T ground × 0.65 + T avg 31 × 0.35 | Equation 9

where

Tavg31 = outdoor dry-bulb temperature averaged over all hours of the previous 31 days (note for January days, weather data from December will be used)

Tground = Ground temperature (°F ) for current day of year, calculated using Equation 10.

For each day (θ = 1 TO 365) T ground (θ ) = TyrAve − 0.5 × (TyrMax − TyrMin ) × COS(2 × π × ((θ − 1) / PB) − PO − PHI ) × GM | Equation 10

where

TyrAve = average annual temperature, °F

TyrMin TyrMax | = = | the lowest average monthly temperature, °F the highest average monthly temperature, °F
PB | = | 365
PO | = | 0.6
DIF | = | 0.025 ft 2/hr
BETA | = | SQR(π/(DIF*PB*24))*10
XB | = | EXP(-BETA)
CB | = | COS( BETA)
SB | = | SIN( BETA)
GM | = | SQR((XB*XB - 2.*XB*CB + 1)/(2.*BETA*BETA))
PHI | = | ATN((1.-XB*(CB+SB)) / (1.-XB*(CB-SB)))

B5. Hourly Distribution Loss for Central Water Heating Systems

This section is applicable to the DHW system type 3 and 4, as defined in B1. Purpose and Scope. The distribution losses accounted for in the distribution loss multiplier (DLM), Equation 5, reflect distribution heat loss within each individual dwelling unit. Additional distribution losses occur outside dwelling units and they include losses from recirculation loop pipes and branch piping feeding individual dwelling units. The hourly values of these losses, HRDL, shall be calculated according to Equation 11. Compliance software shall provide input for specifying recirculation system designs and controls according to the following algorithms.

HRDL k = NLoop k × HRLL k + HRBL k | Equation 11

where

HRDLk= Hourly central system distribution loss for kth system (Btu).

HRLLk= Hourly recirculation loop pipe heat loss (Btu). This component is only applicable to system type 4. See Equation 12.

HRBLk= Hourly recirculation branch pipe heat loss (Btu), see Equation 20.

NLoopk= Number of recirculation loops in water heating system k. This component is only applicable to system type 4. See section 4.3.

A recirculation loop usually includes multiple pipe sections, not necessarily having the same diameter, that are exposed to different ambient conditions. The compliance software shall provide input entries for up to six pipe sections with three sections for supply piping and three sections for return piping for users to describe the configurations of the recirculation loop. For each of the six pipe sections, input entries shall include pipe diameter (inch), pipe length (ft), and ambient conditions. Ambient condition input shall include three options: outside air, underground, conditioned or semi-conditioned air. Modeling rules for dealing with recirculation loop designs are provided in Section 4.3.

Outside air includes crawl spaces, unconditioned garages, unconditioned equipment rooms, as well as actual outside air. Solar radiation gains are not included in the calculation because the impact of radiation gains is relatively minimal compared to other effects. Additionally, the differences in solar gains for the various conditions (e.g., extra insulation vs. minimum insulation) are relatively even less significant.

The ground condition includes any portion of the distribution piping that is underground, including that in or under a slab. Insulation in contact with the ground must meet all the requirements of Section 150.0(j), Part 6, of Title 24.

The losses to conditioned or semi-conditioned air include losses from any distribution system piping that is in an attic space, within walls (interior, exterior or between conditioned and unconditioned spaces), within chases on the interior of the building, or within horizontal spaces between or above conditioned spaces. It does not include the pipes within the residence. The distribution piping stops at the point where it first meets the boundaries of the dwelling unit.