§4 slice 4: hot_water_mixer_showers_monthly_l_per_day (line (42a)m)

Appendix J equations J1–J3. Per-day hot water draw for mixer showers
combines the per-day shower count (rising with N, depressed slightly
when a bath is also present) with each outlet's flow × 6 min × Table J5
behavioural factor, then multiplied by the cold-water-dependent hot
fraction (41 °C delivery vs 52 °C hot supply, Tcold from J1).

Multi-outlet handling: N_shower is split across outlets so a dwelling
with two identical mixers produces the same (42a)m total as a single
outlet — the count only matters when outlets have different flow rates.
Instantaneous electric showers belong in (64a)m and must be excluded
from the input.

Validated against the Elmhurst non-RR fixtures (both 1 vented mixer at
7 L/min, mains Tcold):
  - 000490 N=2.1468 → Jan V_d,hot = 52.6878
  - 000474 N=1.8896 → Jan V_d,hot = 48.9139

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

packages/domain/src/domain/sap/worksheet/tests/test_water_heating.py

@@ -19,6 +19,7 @@ from domain.sap.worksheet.water_heating import (
     TABLE_J1_TCOLD_FROM_MAINS_C,
     assumed_occupancy,
     hot_water_baths_monthly_l_per_day,
+    hot_water_mixer_showers_monthly_l_per_day,
     hot_water_other_uses_monthly_l_per_day,
 )
 
@@ -212,6 +213,118 @@ def test_hot_water_baths_low_water_use_reduces_warm_water_by_5pct() -> None:
         assert l == pytest.approx(n * 0.95, abs=1e-9), f"month {m+1}"
 
 
+def test_hot_water_mixer_showers_matches_elmhurst_worksheet_000490() -> None:
+    """SAP10.2 §4 line (42a)m via Appendix J equations J1–J3.
+
+    Bath present so:
+        N_shower         = 0.45 × N + 0.65                      (J1)
+        V_warm,i[m]      = flow × 6 × J5_fbeh[m]                (step 1d)
+        V_d,warm,i[m]    = V_warm,i × N_shower / N_outlets      (J2)
+        V_d,hot,i[m]     = V_d,warm,i × (41−Tcold[m])/(52−Tcold[m])  (J3)
+
+    000490: 1 vented mixer outlet at 7 L/min, mains Tcold,
+    N=2.1468, bath present → Jan V_d,hot ≈ 52.69 L/day.
+    """
+    # Arrange
+    expected = (
+        52.6878, 51.8960, 50.7422, 48.5346, 46.9054, 45.0886,
+        44.0560, 45.2010, 46.4562, 48.4069, 50.6619, 52.4859,
+    )
+
+    # Act
+    monthly = hot_water_mixer_showers_monthly_l_per_day(
+        n_occupants=_w000490.LINE_42_OCCUPANCY,
+        has_bath=True,
+        mixer_shower_flow_rates_l_per_min=(7.0,),
+        cold_water_temps_c=TABLE_J1_TCOLD_FROM_MAINS_C,
+    )
+
+    # Assert
+    for m, (actual, exp) in enumerate(zip(monthly, expected)):
+        assert actual == pytest.approx(exp, abs=1e-3), f"month {m+1}"
+
+
+def test_hot_water_mixer_showers_matches_elmhurst_worksheet_000474() -> None:
+    """Same (42a)m formula for 000474 (N=1.8896, 1 vented mixer at 7 L/min)."""
+    # Arrange
+    expected = (
+        48.9139, 48.1788, 47.1076, 45.0582, 43.5457, 41.8591,
+        40.9004, 41.9634, 43.1287, 44.9397, 47.0332, 48.7265,
+    )
+
+    # Act
+    monthly = hot_water_mixer_showers_monthly_l_per_day(
+        n_occupants=_w000474.LINE_42_OCCUPANCY,
+        has_bath=True,
+        mixer_shower_flow_rates_l_per_min=(7.0,),
+        cold_water_temps_c=TABLE_J1_TCOLD_FROM_MAINS_C,
+    )
+
+    # Assert
+    for m, (actual, exp) in enumerate(zip(monthly, expected)):
+        assert actual == pytest.approx(exp, abs=1e-3), f"month {m+1}"
+
+
+def test_hot_water_mixer_showers_zero_when_no_outlets() -> None:
+    """Appendix J J1 third branch: no shower outlets → N_shower=0 → (42a)m
+    is all zeros regardless of N."""
+    # Arrange / Act
+    monthly = hot_water_mixer_showers_monthly_l_per_day(
+        n_occupants=3.0,
+        has_bath=True,
+        mixer_shower_flow_rates_l_per_min=(),
+        cold_water_temps_c=TABLE_J1_TCOLD_FROM_MAINS_C,
+    )
+
+    # Assert
+    assert all(v == pytest.approx(0.0, abs=1e-9) for v in monthly)
+
+
+def test_hot_water_mixer_showers_no_bath_present_uses_higher_n_shower_branch() -> None:
+    """J1 second branch: with no bath the per-day shower count rises from
+    0.45N+0.65 to 0.58N+0.83 (higher slope and intercept). For N=2 the
+    ratio is (0.58×2+0.83)/(0.45×2+0.65) = 1.99/1.55 = 1.284."""
+    # Arrange / Act
+    with_bath = hot_water_mixer_showers_monthly_l_per_day(
+        n_occupants=2.0, has_bath=True,
+        mixer_shower_flow_rates_l_per_min=(8.0,),
+        cold_water_temps_c=TABLE_J1_TCOLD_FROM_MAINS_C,
+    )
+    no_bath = hot_water_mixer_showers_monthly_l_per_day(
+        n_occupants=2.0, has_bath=False,
+        mixer_shower_flow_rates_l_per_min=(8.0,),
+        cold_water_temps_c=TABLE_J1_TCOLD_FROM_MAINS_C,
+    )
+
+    # Assert — V_d,hot scales linearly with N_shower; ratio is identical
+    # for every month and equals (1.99/1.55).
+    expected_ratio = (0.58 * 2.0 + 0.83) / (0.45 * 2.0 + 0.65)
+    for m, (b, nb) in enumerate(zip(with_bath, no_bath)):
+        assert nb == pytest.approx(b * expected_ratio, abs=1e-6), f"month {m+1}"
+
+
+def test_hot_water_mixer_showers_two_outlets_distributes_shower_count_evenly() -> None:
+    """V_d,warm,i = V_warm,i × N_shower / N_outlets — adding a second
+    identical outlet halves the per-outlet daily warm water, but two
+    outlets summed equals one outlet's contribution. Net (42a)m is
+    unchanged for identical flow rates."""
+    # Arrange / Act
+    single = hot_water_mixer_showers_monthly_l_per_day(
+        n_occupants=2.0, has_bath=True,
+        mixer_shower_flow_rates_l_per_min=(8.0,),
+        cold_water_temps_c=TABLE_J1_TCOLD_FROM_MAINS_C,
+    )
+    twin = hot_water_mixer_showers_monthly_l_per_day(
+        n_occupants=2.0, has_bath=True,
+        mixer_shower_flow_rates_l_per_min=(8.0, 8.0),
+        cold_water_temps_c=TABLE_J1_TCOLD_FROM_MAINS_C,
+    )
+
+    # Assert
+    for m, (s, t) in enumerate(zip(single, twin)):
+        assert t == pytest.approx(s, abs=1e-9), f"month {m+1}"
+
+
 def test_assumed_occupancy_floor_at_n_eq_1_for_small_dwellings() -> None:
     """Appendix J piecewise definition: TFA ≤ 13.9 m² → N=1 exactly. A
     tiny studio flat at the boundary is the most common trigger."""

packages/domain/src/domain/sap/worksheet/water_heating.py

@@ -61,6 +61,9 @@ _BATH_VOLUME_L: Final[float] = 73.0
 # Appendix J equation J8 / J3 mixing temperatures.
 _HOT_DELIVERY_TEMPERATURE_C: Final[float] = 52.0
 _WARM_BATH_TEMPERATURE_C: Final[float] = 42.0
+_WARM_SHOWER_TEMPERATURE_C: Final[float] = 41.0
+# Appendix J step 1d: assumed shower duration in minutes per event.
+_SHOWER_DURATION_MIN: Final[float] = 6.0
 
 
 def assumed_occupancy(total_floor_area_m2: float) -> float:
@@ -77,6 +80,51 @@ def assumed_occupancy(total_floor_area_m2: float) -> float:
     return 1.0 + 1.76 * (1.0 - exp(-0.000349 * x * x)) + 0.0013 * x
 
 
+def hot_water_mixer_showers_monthly_l_per_day(
+    *,
+    n_occupants: float,
+    has_bath: bool,
+    mixer_shower_flow_rates_l_per_min: tuple[float, ...],
+    cold_water_temps_c: tuple[float, ...],
+) -> tuple[float, ...]:
+    """SAP 10.2 §4 line (42a)m via Appendix J equations J1, J2, J3.
+
+    Mixer showers draw from the main hot water system (cylinder or combi)
+    and mix with cold to a 41 °C delivery. The per-day shower count is
+
+        N_shower = 0.45 × N + 0.65    (bath present)
+                 = 0.58 × N + 0.83    (no bath)
+                 = 0                  (no shower outlets)
+
+    Each outlet's warm-water draw for a month is the flow rate × 6 min ×
+    Table J5 fbeh. The hot fraction is (41 − Tcold[m])/(52 − Tcold[m]).
+    Per-outlet daily warm water is scaled by N_shower / N_outlets, then
+    summed across outlets to give (42a)m.
+
+    Instantaneous electric showers belong to worksheet (64a)m, not (42a)m
+    — those should be excluded from `mixer_shower_flow_rates_l_per_min`.
+    """
+    n_outlets = len(mixer_shower_flow_rates_l_per_min)
+    if n_outlets == 0:
+        return tuple(0.0 for _ in range(12))
+    if has_bath:
+        n_shower = 0.45 * n_occupants + 0.65
+    else:
+        n_shower = 0.58 * n_occupants + 0.83
+    monthly: list[float] = []
+    for fbeh, tcold in zip(TABLE_J5_BEHAVIOURAL_FACTOR, cold_water_temps_c):
+        f_hot = (_WARM_SHOWER_TEMPERATURE_C - tcold) / (
+            _HOT_DELIVERY_TEMPERATURE_C - tcold
+        )
+        v_hot_total = 0.0
+        for flow in mixer_shower_flow_rates_l_per_min:
+            v_warm_per_outlet = flow * _SHOWER_DURATION_MIN * fbeh
+            v_d_warm = v_warm_per_outlet * n_shower / n_outlets
+            v_hot_total += v_d_warm * f_hot
+        monthly.append(v_hot_total)
+    return tuple(monthly)
+
+
 def hot_water_baths_monthly_l_per_day(
     *,
     n_occupants: float,