Methodology
Sensible Heat and Flow
The single equation behind water heater sizing, duct heating and every temperature-rise problem on the site.
Power is flow times rise
Raising the temperature of a flowing fluid requires power proportional to three things: how fast the fluid flows, how much energy it takes to warm a kilogram of it by one degree, and how many degrees you are raising it. That is the whole of it.
For water at ordinary temperatures the specific heat capacity is about 4.186 kilojoules per kilogram per kelvin, and a litre weighs a kilogram closely enough for engineering purposes. That collapses the equation to a convenient form: kilowatts equal litres per minute times the rise in kelvin times 4.186, divided by sixty.
- Q
- power required (kW)
- ṁ
- mass flow rate (kg/s)
- c
- specific heat capacity (kJ/kg·K)
- ΔT
- temperature rise (K)
Why the winter mains temperature governs
Because the rise is directly proportional to the power, and the incoming temperature sets the rise. Mains water at fifteen degrees in July and four degrees in February produces a forty percent difference in the power needed for the same shower at the same flow.
This is the single most common reason a tankless water heater disappoints. Sized in summer, it is undersized in winter — and the failure mode is not a breakdown but a reduced flow or a cooler shower, which reads as a fault rather than as an undersize.
Sensible only
This equation covers sensible heat — energy that changes temperature. It says nothing about latent heat, the energy involved in changing phase. That distinction is why an air conditioner's capacity is not simply its ability to lower a thermometer: much of its work is condensing moisture out of the air, and in a humid climate the latent share can approach the sensible one.
Calculators that use this method
- Tankless Water Heater Sizing CalculatorSize an instantaneous water heater from simultaneous flow and the temperature rise your incoming water actually needs.
- Water Heater Sizing CalculatorGet a rule-of-thumb recommended tank size (in gallons) based on household size.
- Water Heater Recovery Time CalculatorEstimate how long a storage water heater takes to reheat a full tank after it's been drawn down.
Basis
- Specific heat capacity of water, approximately 4.186 kJ/kg·K at ordinary temperatures.