# Numbers and calculations

It is always important to do simple calculations. This as FAR better than going by gut feeling and guesswork.

#### Some useful figures and conversions

1 kW (kilowatt) is a unit of Power or a rate of energy. (A 1 bar fire consumes 1 kW)

There are 3,411 Btu’s in 1 kWatt. i.e. 10kWatts = 31,400 Btu/hr.

There are 860 kcal/hr in 1 kW

A normal immersion heater uses 3kW when heating

1 kWh. (kilowatt hour) is a quantity of energy

( A 1 kW heater would use 24kWhr per day )

I kWatt Hr. = 1 unit of electricity = 1 bar fire used for one hour.

1 kJoule x 3,600 = 1 kWhr.

Note heat pumps are rated by their heat output, not their electrical power input.

The formula that links heat, time and temperure is –
kW (heat)   =    water flow (litres/sec)  x  4.2  x   Temerature rise (dt in celcius )
(4.2 is the specific heat of water)

If 10Kwatts were extracted from water having a flow rate of 0.8Lit/sec then the temperature would drop by 3°C (3K).

Water tanks and storage cylinders.
You can use the formula above to work out how quickly a cylinder would heat up given a known heat input.  A flow rate of 0.0277 lit/sec would fill a 100 litres cylinder in 1 hour.   Using the formula –  a 3kW heater would rise a 100 litre cylinder by about 26 degrees in 1 hour.

A heat pump with a heat output of 10kW and a COP of 4 can be represented by the following equations:-

COP = heat output / electricity consumption

10kW / 2.5kW = COP of 4

the heat extracted from the ground = heat delivered – electricity consumption = 10kW – 2.5kW = 7.5kW

0°C = 32°F (freezing point of water)

10°C = 50°F

20°C = 68°F (room temperature)

100°C = 212°F (boiling point of water)

or, if you have a calculator, °F-32,/9,x5=°C, °Cx9,/5,+32=°F

1 lit/sec = 3.6m³/Hr. = 13.19 Galls(UK)/min.

This chart gives an indication of flow rates for a 10kw (heat output) heat pump taking heat from a river or spring source.

(the extracted heat has been assumed to be 7.5kW) In our example, for a river source system, the flow rate would need to be at least 0.6 litres/ second to minimise the risk freezing in the evaporator.   For a spring source, the flow rate would ideally be the same, but if the supply was limited, or pumping used a lot of energy, then half that rate may suffice.

Note, these are example values. Manufacturer’s data should be available for specific equipment.

Water purity for normal copper-brazed stainless heat-exchangers as used in almost all heat pumps.

The following list will give some idea of the requirements. Check with the heat pump manufacturer to get specific data relating individual heat pumps.

Sulphate < 100 mg/l  Free chlorine < 0.5 mg/l   Chloride < 300 mg/l   Nitrate < 100 mg/l   pH value 6.5 – 9   Electr. conductivity 50 – 1000 µS/cm    Oxygen < 2 mg/l