This is another calculation on heating water, this time relating hot water flow rates and boiler power. It too ends with a handy rule which can be applied without reference to a manufacturer’s manual.
Suppose we want a hot water flow rate of, say, 9 litres per minute, from a combi boiler or instantaneous water heater – how much power do we need?
We’ll assume for the moment a temperature rise of 50 celsius, so cold water entering the boiler at 10C leaves at 60C.
1 litre weighs 1 kilogram, so we’re heating 9 kilograms per minute, or 9/60 = 0.15 kilogram per second.
The energy needed to do this is:
mass of water x temperature rise x specific heat capacity of water
which in this case is 0.15 x 50 x 4.2 = 31.5 kilojoule per second. A kilojoule per second is the same thing as a kilowatt, so we need a 31.5 kilowatt heat source. As some heat from burning gas is lost, it would be wise to allow another 5% when calculating the boiler net heat input needed. This is the
same as multiplying by 1.05, and 31.5 x 1.05 = 33kW.
(Note: if a boiler manufacturer specifies the boiler heat output, maybe as “DHW output”, that is the heat directly available to heat the water and no efficiency correction is needed.)
The usefulness of these calculations is in establishing the limit set by nature – no amount of clever engineering can improve on this.
Let’s now look at a few boiler specifications:
Ideal Logic Combi 30: specified flow rate 12.4 litre/min for 35C rise, requires 12.4/60 x 35 x 4.2 = 30.4kW. The specification states “DHW output (kW) Max” = 30.3kW. That’s slightly different from our figure due to their use of a more precise 4.18 for the specific heat capacity.
Worcester Bosch 28i junior (combi): 10 litre/min for 40C rise (notice how the temperature rise specification differs between manufacturers – another reason for being savvy with the calculation). This needs a heat source of 10/60 x 40 x 4.2 = 28kW, which tallies with the manufacturer’s rated heat output for hot water – the number appears in the name of the product.
Vaillant ecoTEC plus 837: DHW flow rate at 35°C rise: 15.2 litre/minute. So the heat required is 15.2/60 x 35 x 4.2 = 37.24kW. The manufacturer states 37kW and the 37 forms part of the product name.
Handy rule: multiply the hot water flow rate in litres/minute by the temperature rise in celsius. Divide by 100 and multiply by 7 to get the boiler DHW output in kW.
Example: 12 litre/min at 40C rise: 12 x 40 = 480.
480/100 = 4.8.
4.8 x 7 = 33.6kW boiler DHW output.