Sensible Heat and Flow

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.

Turned round, the equation sizes a heating circuit: the flow is the heat divided by 4.186 and by the temperature drop across the emitters. The drop is a design choice, and it decides the pipework — a heat pump designed on 5 K (9 °F) moves four times the water of a boiler on 20 K (36 °F) for the same heat, and the friction that water meets rises faster than the flow does.

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.

The constant belongs to the fluid, and it changes the plant

Water's specific heat capacity is unusually high, and most of the convenient rules of thumb in heating are built on it. Replace the water with something else and the arithmetic keeps working while the plant changes.

A glycol mix carries meaningfully less heat per kilogram than water and is also denser and more viscous, so a loop protected against freezing needs a HIGHER flow rate for the same duty, larger pipes or pumps to deliver it, and a corresponding penalty in pump energy. That penalty is a design consequence of the antifreeze rather than an installation fault, and it is routinely discovered after the pump has been selected on water figures.

Air is the opposite extreme. Its specific heat per kilogram is about a quarter of water's and its density is about a thousandth, so the same duty needs roughly three thousand times the volume. That single ratio is why ducts are enormous and pipes are small, and why moving heat with water and distributing it locally with air is the standard arrangement rather than a preference.

Recovery and first-hour delivery are not the same as capacity

A storage water heater answers two different questions. How much hot water is stored is a volume; how fast it can reheat is a POWER, and the equation on this page is the one that converts between them.

Neither alone describes what a household experiences. The useful figure combines the two — what can be drawn in a busy hour, which is the stored volume plus whatever the heater recovers during that hour — and a small tank with a large burner and a large tank with a small element can produce identical figures by different routes.

Which route is better depends on the draw pattern rather than on the number. A pattern of short, frequent draws suits fast recovery; a single large simultaneous demand suits storage. This is also why an instantaneous heater is sized entirely on flow rate and temperature rise and has no storage term at all: it is this equation with nothing else in it.

Where the equation stops: latent heat, and standing losses

Sensible heat changes a temperature. It does not cover a change of STATE, and the energy involved in changing state is not a correction — it is of the same order as heating the substance across its whole liquid range.

So any problem involving evaporation, condensation, freezing or thawing needs a separate term this equation does not contain. Dehumidification, cooling coil loads, swimming pool evaporation, ice melting on a driveway and condensation on a cold surface are all latent problems, and sizing them on temperature alone under-states them substantially.

The other omission is time. This equation gives the power needed while the fluid is flowing, and a system spends much of its life not flowing. Standing losses from a cylinder, distribution losses from uninsulated pipework, and the energy spent reheating a recirculation loop all accumulate as ENERGY without appearing in a power calculation — which is why a well-sized heater can still be expensive to run and why the fix is insulation and control rather than a bigger burner.