TP-09: Hot Water Demand | HEM Reference

Overview

Hot water demand quantifies the volume and energy required to supply domestic hot water (DHW) at specified temperatures throughout the year. The calculation is event-based: each draw-off (shower, bath, basin tap, kitchen sink) is modelled as a discrete event with a target temperature, duration or volume, and flow rate.

The methodology determines the volume of hot water drawn from the heating system per timestep, the energy content of that demand, and the additional volume lost in distribution pipework between events. Cold water inlet temperature varies with the time of year and is provided by external climate data. Instantaneous electric showers are treated separately because they do not draw from the central hot water system, though their warm water output contributes to internal heat gains.

Where a waste water heat recovery system (WWHRS) is connected to a mixer shower, the pre-heated cold water feed reduces the volume of hot water required from the heating system.

Inputs

Parameter	Symbol	Unit	Description
Shower flow rate	$\dot{V}_{s h o w er}$	litres/min	Flow rate of warm water at the shower head
Bath size	$V_{ba t h, ma x}$	litres	Maximum capacity of the bath
Bath flow rate	$\dot{V}_{ba t h}$	litres/min	Flow rate of the bath tap
Other hot water flow rate	$\dot{V}_{o t h er}$	litres/min	Flow rate at basin or kitchen taps
Event target temperature	$T_{t a r g e t}$	°C	Desired temperature of warm water at the tapping point
Event duration	$t_{e v e n t}$	minutes	Duration of the draw-off event
Event volume (bath)	$V_{e v e n t}$	litres	Volume of warm water drawn (bath events only, alternative to duration)
Hot water system temperature	$T_{h w}$	°C	Temperature of hot water supplied by the heating system
Cold water temperature	$T_{co l d}$	°C	Mains cold water inlet temperature for the current timestep
Electric shower rated power	$P_{r a t e d}$	kW	Rated electrical power of an instantaneous electric shower
WWHRS efficiency	$η_{w w h r s}$	%	Heat recovery efficiency of a waste water heat recovery system, interpolated from flow rate
WWHRS utilisation factor	$f_{u t i l}$	—	Fraction of shower events where WWHRS is active
WWHRS drain temperature	$T_{d r ain}$	°C	Assumed temperature of waste water entering the WWHRS heat exchanger (fixed at 35 °C)
Pipework internal diameter	$d_{p i p e}$	mm	Internal diameter of distribution pipework
Pipework total length	$L_{p i p e}$	m	Total length of distribution pipework
Number of tapping points	$N_{t a p}$	—	Total number of hot water tapping points (mixer showers + baths + other uses)

Calculation

Hot Water Fraction

All event types (showers, baths, other uses) share a common mixing equation. When hot water at temperature $T_{h w}$ is mixed with cold water at temperature $T_{co l d}$ to achieve a target temperature $T_{t a r g e t}$ , the fraction of hot water required is:

$f_{h o t} = \frac{T _{t a r g e t} - T _{co l d}}{T _{h w} - T _{co l d}}$

This fraction, applied to the total warm water volume for the event, gives the volume of hot water drawn from the heating system.

Mixer Shower Events

A mixer shower event has a specified flow rate, target temperature, and duration. The total volume of warm water delivered at the shower head is:

$V_{w a r m} = \dot{V}_{s h o w er} \times t_{e v e n t}$

where $\dot{V}_{s h o w er}$ is the shower flow rate in litres/min and $t_{e v e n t}$ is the event duration in minutes.

The volume of hot water drawn from the heating system is:

$V_{h o t} = V_{w a r m} \times f_{h o t}$

WWHRS Interaction

Where a waste water heat recovery system is connected to a mixer shower, the cold water feed is pre-heated by the WWHRS heat exchanger before mixing. The WWHRS return temperature is calculated as:

$T_{w w h r s} = T_{co l d} + \frac{η _{w w h r s} \times f _{u t i l}}{100} \times (T_{d r ain} - T_{co l d})$

where $T_{d r ain} = 35$ °C is the assumed waste water temperature entering the heat exchanger, and $η_{w w h r s}$ is the efficiency interpolated from the product's flow rate vs. efficiency curve.

The effect of the WWHRS on hot water demand depends on the system arrangement:

System A (pre-heated water to both shower and hot water system): The pre-heated temperature $T_{w w h r s}$ replaces $T_{co l d}$ in the hot water fraction calculation, and the return temperature is also made available to the hot water storage system as a pre-heated feed.

$V_{h o t, A} = V_{w a r m} \times \frac{T _{t a r g e t} - T _{w w h r s}}{T _{h w} - T _{w w h r s}}$

System B (pre-heated water to shower only): The pre-heated temperature replaces $T_{co l d}$ in the hot water fraction calculation for the shower, but the hot water system continues to receive unheated mains water.

$V_{h o t, B} = V_{w a r m} \times \frac{T _{t a r g e t} - T _{w w h r s}}{T _{h w} - T _{w w h r s}}$

System C (pre-heated water to hot water system only): The shower hot water fraction uses the unmodified $T_{co l d}$ , but the WWHRS return temperature is stored and provided to the hot water system as its cold feed temperature.

$V_{h o t, C} = V_{w a r m} \times \frac{T _{t a r g e t} - T _{co l d}}{T _{h w} - T _{co l d}}$

Instantaneous Electric Shower Events

An instantaneous electric shower heats cold water directly using an electric element. It does not draw from the central hot water system.

The electrical energy consumed during the event is:

$E_{e l ec} = P_{r a t e d} \times \frac{t _{e v e n t}}{60}$

where $P_{r a t e d}$ is the rated power in kW, $t_{e v e n t}$ is the duration in minutes, and the division by 60 converts minutes to hours, giving energy in kWh.

The volume of warm water produced is derived from the energy input and the volumetric energy content of water:

$V_{w a r m} = \frac{E _{e l ec}}{c _{v o l} \times ( T _{t a r g e t} - T _{co l d} )}$

where $c_{v o l}$ is the volumetric heat capacity of water in kWh/(litre·K).

For internal heat gains accounting, an equivalent volume of hot water is calculated as if the same warm water had been produced by mixing:

$V_{h o t, e q u i v} = V_{w a r m} \times f_{h o t}$

This equivalent volume does not represent a demand on the hot water system. It is used solely to determine the internal gains from hot water use at tapping points.

Bath Events

A bath event can be specified either by volume or by duration. If specified by volume:

$t_{ba t h} = \frac{V _{e v e n t}}{V ˙ _{ba t h}}$

If specified by duration:

$V_{e v e n t} = t_{ba t h} \times \dot{V}_{ba t h}$

The warm water volume is clamped to the bath capacity:

$V_{w a r m} = min (V_{e v e n t}, V_{ba t h, ma x})$

The hot water demand is then:

$V_{h o t} = V_{w a r m} \times f_{h o t}$

Other Hot Water Uses

Other hot water uses (basin taps, kitchen sinks) follow the same flow-rate-and-duration model as mixer showers:

$V_{w a r m} = \dot{V}_{o t h er} \times t_{e v e n t}$

$V_{h o t} = V_{w a r m} \times f_{h o t}$

Energy Demand per Event

The energy content of the hot water drawn from the heating system for each event is:

$Q_{e v e n t} = c_{v o l} \times V_{h o t} \times (T_{h w} - T_{co l d})$

where $c_{v o l}$ is the volumetric heat capacity of water. With $ρ = 1.0$ kg/litre and $c_{p} = 4, 184$ J/(kg·K):

$c_{v o l} = ρ \times c_{p} = 4, 184 J/(litre \cdotp K)$

Converting to kWh:

$Q_{e v e n t} = \frac{4 , 184 \times V _{h o t} \times ( T _{h w} - T _{co l d} )}{3 , 600 , 000} [kWh]$

Distribution Pipework Volume

After each draw-off event, hot water remains in the distribution pipework and cools to ambient temperature. This volume is treated as an additional demand on the hot water system for the next event.

The average pipework length per tapping point is:

$L_{a v g} = \frac{L _{p i p e}}{N _{t a p}}$

The volume of hot water retained in the pipework per event is determined from the pipe geometry (internal diameter and average length). For each timestep, the total pipework volume loss is:

$V_{p i p e} = N_{e v e n t s} \times V_{p i p e, s in g l e}$

where $N_{e v e n t s}$ is the number of hot water events in the timestep (excluding instantaneous electric showers) and $V_{p i p e, s in g l e}$ is the volume of water in the average pipework run, in litres.

This pipework volume is added to the volumetric demand on the hot water system.

Timestep Aggregation

Within each timestep, the total hot water demand on the heating system is the sum of all individual event demands plus the pipework volume losses:

$V_{h w, t o t a l} = \sum_{i = 1}^{N_{e v e n t s}} V_{h o t, i} + N_{e v e n t s} \times V_{p i p e, s in g l e}$

The total volume at tapping points (used for internal gains calculations) includes both the hot water system demand and the equivalent volume from instantaneous electric showers:

$V_{t a pp in g} = V_{h w, t o t a l, e x c l . p i p e} + V_{h o t, e q u i v, I E S}$

where $V_{h w, t o t a l, e x c l . p i p e}$ is the sum of $V_{h o t, i}$ for non-electric events (before pipework losses are added), and $V_{h o t, e q u i v, I E S}$ is the sum of equivalent volumes from all instantaneous electric shower events.

The total energy demand for the timestep is:

$Q_{h w} = \sum_{i = 1}^{N_{e v e n t s}} Q_{e v e n t, i} [kWh]$

Note that this energy demand covers only events that draw from the central hot water system. Instantaneous electric shower energy is accounted for separately as an electrical demand.

Cold Water Temperature

The cold water inlet temperature varies throughout the year and is provided as an hourly time series, indexed by the simulation timestep and the start day of the series. The temperature for the current timestep is looked up from this series. This temperature feeds into both the hot water fraction calculation and the energy demand calculation for every event type.

Pipework Cool-Down Losses

After each event, the hot water left in the distribution pipework cools to the surrounding air temperature. This heat loss is calculated separately for internal and external pipework runs:

$Q_{p i p e, in t} = N_{e v e n t s} \times Q_{coo l d o w n, in t}$

$Q_{p i p e, e x t} = N_{e v e n t s} \times Q_{coo l d o w n, e x t}$

where $Q_{coo l d o w n, in t}$ and $Q_{coo l d o w n, e x t}$ are the cool-down losses per event for internal and external pipework respectively. The cool-down loss for a single pipework section depends on the pipework volume, the hot water temperature, and the ambient temperature (internal air temperature for internal pipework, external air temperature for external pipework). These losses are passed to the pipework model described in TP-10: Pipework and Ductwork Losses.

Internal pipework heat losses contribute to internal gains (the heat warms the dwelling). External pipework heat losses are lost to outside.

Outputs

Quantity	Symbol	Unit	Description
Hot water volume demand	$V_{h w, t o t a l}$	litres	Total volume of hot water drawn from the heating system per timestep, including pipework losses
Volume at tapping points	$V_{t a pp in g}$	litres	Volume of hot water delivered at tapping points, including electric shower equivalent
Hot water energy demand	$Q_{h w}$	kWh	Energy content of the hot water demand per timestep
Hot water duration	$t_{h w}$	minutes	Total duration of hot water draw-off events per timestep
Number of events	$N_{e v e n t s}$	—	Count of hot water events in the timestep (excluding electric showers)
Equivalent electric shower volume	$V_{h o t, e q u i v, I E S}$	litres	Equivalent hot water volume from instantaneous electric showers, for internal gains
Internal pipework heat loss	$Q_{p i p e, in t}$	kWh	Pipework cool-down loss to internal air per timestep
External pipework heat loss	$Q_{p i p e, e x t}$	kWh	Pipework cool-down loss to external air per timestep

Assumptions

Water density is constant at $ρ = 1.0$ kg/litre. Temperature-dependent density variation is not modelled.
Specific heat capacity of water is constant at $c_{p} = 4, 184$ J/(kg·K).
The WWHRS drain temperature is fixed at 35 °C for all shower events, regardless of the shower target temperature.
WWHRS efficiency is interpolated linearly from the product's flow rate vs. efficiency data points.
Events within a timestep are processed sequentially. Overlapping events (two draw-offs running simultaneously) are not modelled; each event is assumed to have exclusive access to the hot water system.
The pipework volume loss applies once per event. After each event, the full pipework run is assumed to refill with hot water that subsequently cools.
Pipework length is divided equally among all tapping points to determine the average run length. Dedicated pipework lengths per outlet are not modelled.
Instantaneous electric showers operate at constant rated power regardless of target temperature or flow rate.
Bath warm water volume is clamped to the declared bath capacity; overflow is not modelled.

Cross-references

TP-01: Overview and Climate Data — simulation time indexing and timestep structure
TP-03: External Conditions — external air temperature used for external pipework cool-down losses
TP-04: Space Heating Demand — internal gains from hot water use at tapping points and pipework losses
TP-10: Pipework and Ductwork Losses — detailed pipework cool-down loss calculation; pipework geometry and insulation
TP-11: Hot Water Storage — hot water system temperature; storage losses; interaction with WWHRS System A/C pre-heated feed