Hot Water Cylinder Size and Heat Pump Water Heater Savings

The storage and mixing equations are derived here from conservation of energy, with water density 1 kg/L and specific heat 4180 J/(kg·K). The latter and the 150 L worked heat-up example are from Nel, Booysen and van der Merwe (2016), § Energy consumption, Eq. (2), DOI:10.1016/j.esd.2016.03.006.

The design draw is the larger of the largest event and daily draw multiplied by the off-period fraction. A conservative hot-volume reserve equals $UA(T_s-T_r)t_{off}/[\rho c_p(T_s-T_c)]$. Add that reserve before dividing by usable fraction $u$. The energy-volume result is also subject to a temperature-retention constraint. Inverting uniform no-draw cooling, $T_r+(T_s-T_r)\exp[-UA\,t_{off}/(\rho c_pV)]\ge T_{use}$, gives
$V_R=\frac{UA\,t_{off}}{\rho c_p\ln[(T_s-T_r)/(T_{use}-T_r)]}$
when $T_r<T_{use}$. The reported minimum is the larger of the draw-energy volume and $V_R$. If room temperature is at or above the use temperature, heat loss is zero, or the off period is zero, this extra bound is zero. Equality means the no-draw tank just retains the use temperature at the end of the gap. This separate screen does not establish comfort for an arbitrary sequence of draws.

This is a preliminary storage screen, not a certified first-hour rating.

Daily standing heat is $UA(T_s-T_r)\times24$ h at full setpoint. Daily draw heat plus standing heat gives $Q_d$. For the resistance heat fraction $b$, electricity is $Q_d[(1-b)/COP+b]$. COP is linearly interpolated between two user rating points at the selected storage temperature; no extrapolation is permitted.

No-draw recovery solves $C\,dT/dt=P-UA(T-T_r)$ exactly, including the zero-loss limit. The same first-order balance gives uniform no-draw cooling. Heating must exceed standing loss at the setpoint. Daily timer occupancy is $(1-b)Q_d/P_{hp}+bQ_d/P_{el}$, assuming sequential operation.

Annual totals use 365 identical days. Annual net saving is resistance electricity cost minus heat-pump electricity cost and incremental maintenance; simple payback is extra installed cost divided by positive annual net saving.

The animation is ideal piston displacement during a mixed-water event, ending at the event volume or the usable-volume limit. The separate draw-off chart compares that limit with $T_{out}=T_c+(T_s-T_c)e^{-V_{withdrawn}/V}$ for a perfectly mixed tank, without tap blending, heating or standing loss.

• The default is a 200 L tank, 200 L/day of mixed water at 40 °C, a 60 °C setpoint and 15 °C inlet. Default UA, usable fraction, heater powers, COP points, backup fraction and costs are explicit scenario assumptions, not catalogue ratings or market prices.
• Both alternatives use the same tank volume, UA and useful-water demand. A replacement with different insulation requires a separate run. The screening volume uses the UA entered for the selected tank; update it when changing product size.
• Use average thermal power and cycle COP including fan/compressor input at the entered storage temperature. Backup has unity conversion efficiency. The entered backup heat fraction includes any required boost or other fallback; the tool does not generate a hygiene schedule.
• Standing loss assumes the whole tank stays at setpoint all day, so energy and off-period reserve are conservative estimates. Uniform no-draw cooling also sets a minimum-volume retention bound. It is a separate approximation from the animated hot-layer temperature.
• All stated daily demand is useful water at one delivery temperature. Add distribution and circulation heat loads outside this tool. One equivalent timer window is assumed; peaks and off-period demand are covered by their larger total, not added twice.
• Money is a numeric count in one local currency; tariff units are inverse kWh and the labels identify the currency basis. Tariffs, installation premium and maintenance are user assumptions as of 27 October 2026.
• Manufacturer data cited in checks apply only to that older WWK 300 model and its published test conditions; they do not define this calculator's generic default COP curve.
• Unit display: the viewer's US switch converts temperature readings to °F and supported power units. Its litre fields retain L. Enter explicit US quantities such as 50 gal or 2 gal/min; the input parser converts them to the calculation units. The volume comparison table shows litres and US gallons together.

Use for preliminary domestic hot-water storage and energy comparisons with liquid water, a warmer storage tank than its surroundings, and cold < use < storage temperature. Use COP points at the same storage temperature and mode; this model does not predict COP from a refrigerant cycle or certify a product. Ambient interpolation alone does not capture humidity, defrost, cycling, duct restrictions or room cooling. Thermal output is separately entered and must reflect ambient conditions.

Hygiene and scalding: this tool cannot predict Legionella survival or verify the temperature throughout a tank or pipe network. DVGW's public guidance names at least 55 °C throughout a circulation system and warns that periodic high-temperature boosts do not replace proper operation. Refer to DVGW W 551 (2004-04); DVGW lists W 551-1 (2026-05) as a draft on its public installation page, consulted 27 October 2026. Check against the standard in force and the local rules applicable to the building. The 60 °C storage screening warning is not a compliance verdict. Have a qualified designer establish storage, circulation, turnover and scald-protection requirements. Do not use the timer or lower setpoint solely on the basis of predicted savings.

There is no detailed hourly comfort simulation, first-hour certification, tank pressure design, relief-valve sizing or circuit sizing. Installation work, electrical connections and commissioning belong to a qualified person. For EcoCute, split units, horizontal geysers or other designs, use their actual performance data and usable volume rather than assuming the illustrated vertical stratification applies.