## 5.4 B5.2. Hourly Recirculation Branch Pipe Heat Loss Calculation

The proposed design and standard design shall use the same branch pipe heat loss assumptions. Branch pipe heat loss is made up of two components. First, pipe heat losses occur when hot water is in use (HBUL). Second, there could be losses associated with hot water waste (HBWL) when hot water was used to displace cold water in branch pipes and hot water is left in pipe to cool down after hot water draws and must be dumped down the drain.

The Total Hourly Branch Losses (HRBLk) shall include both components and be calculated as:

HRBL k = Nbranch k × ( HBUL + HBWL) | Equation 20

where

HBUL = Hourly pipe loss for one branch when water is in use (Btu/hr), see Equation 21. HBWL = Hourly pipe loss for one branch due to hot water waste (Btu/hr), see Equation 24. Nbranchk = Number of branches in water heating system k, see Equation 29.

The hourly branch pipe loss while water is flowing is calculated in the same way as recirculation pipe heat loss with non-zero water flow (PLWF) using the following equations:

HBUL = æ GPH k ö × ρ × C × (T − T ) ç NBranch ÷ p b,in b,out è k ø | Equation 21

where

Tb,in = Average branch input temperature (oF). It is assumed to be equal to the output temperature of the first recirculation loop section, T1,out

Tb,out = Average branch output temperature (oF), see Equation 22.

− UA b T = T + (T − T ) × e ρ ×C p ×Flow b b,out amb,b b,in amb,b | Equation 22

where

Tamb,b = Branch pipe ambient temperature (°F) Branch pipes are assumed to be located in the conditioned or semi-conditioned air.

UAb = Branch pipe heat loss rate (Btu/hr-°F), see Equation 23

Flowb = Branch hot water flow rate during use (gal/hr). It is assumed to be 2 gpm or 120 gal/hr.

The branch pipe heat loss rate is

UA b = Len b ×U insul,b | Equation 23

where

Lenb = Branch pipe length (ft). See Equation 31.

Uinsul,b = Loss rate for insulated pipe (Btu/hr-ft-oF), evaluated using Equation 17 with branch- specific values, as follows --

Diab = Branch pipe diameter (inch), see Equation 30

Thickb = Branch pipe insulation minimum thickness (inch) as defined in the Title 24 Section 120.3, TABLE 120.3-A for service hot water system.

Condb = Branch insulation conductivity, assumed = 0.26 Btu in/hr-ft2- oF

hb = Branch combined convective/radiant surface coefficient (Btu/hr-ft2- oF) assumed = 1.5.

The hourly pipe loss for one branch due to hot water waste is calculated as follows.

HBWL = æ Dia + 0.125 ö 2 N waste × SCH waste,m × f vol × 7.48 × π × ç b ÷ × Len b × ρ × C p × (T b,in − T inlet ) è 24 ø | Equation 24

where

Nwaste = Number of times in a day for which water is dumped before use. This depends on the number of dwelling units served by a branch. Statistically, the number of times of hot water waste is wasted is inversely proportional to the number of units a branch serves, see Equation 25.

SCHwaste,m = Hourly schedule of water waste, see Table B-3.

fvol = The volume of hot water waste is more than just the volume of branch pipes, due to branch pipe heating, imperfect mixing, and user behaviors. This multiplier is applied to include these effects and is assumed to be 1.4.

Tin,b = Average branch input temperature (oF). It is assumed to equal to the output temperature of the first recirculation loop section, TOUT,1.

Tinlet = The cold water inlet temperature (ºF) according to Section 3.3 Cold Water Inlet

N waste = 19.84 × e−0.544×Nunit b | Equation 25 Method WH-BRWF

where

Nunitb= Number of dwelling units served by the branch, calculated using Equation 26 (note that Nunitb is not necessarily integral).

Nunit = Nfloor b 2 | Equation 26 Method WH-BRNU

#### Table B-3. Branch Water Waste Schedule

Hour | SCH wastem
1 | 0.01
2 | 0.02
3 | 0.05
4 | 0.22
5 | 0.25
6 | 0.22
7 | 0.06
8 | 0.01
9 | 0.01
10 | 0.01
11 | 0.01
12 | 0.01
13 | 0.01
14 | 0.01
15 | 0.01
16 | 0.01
17 | 0.01
18 | 0.01
19 | 0.01
20 | 0.01
21 | 0.01
22 | 0.01
23 | 0.01
24 | 0.01