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If you know the flow rate and the change in temperature you can work out how much energy is required.  It takes 1kcal to raise 1L of water by 1C.

So let's say:

Flow rate:      100L/hr

Temp-delta:  10C

That means every hour you're having to heat 100L of water by 10C, which requires 1000 kilo-calories per hour, or 1.162 kWH per hour.  A 1.162kW heating element will provide you with 1.162kWH every hour.

Hi,

thanks for the response. So what you are saying then is that I need to know not only the temperature, but the flow rate of both the inlet and the outlet?

Indeed. That's how most electric showers regulate the water temperature - by varying the flow rate.

Being pedantic (sorry)  you need two temperatures and one flow rate. Measure the temperature of the inlet, temperature of the outlet and the flow rate from input to output.

Flow meters are available as commercial units with either analogue voltage out or pulses proportional to flow rate.

e.g Grundfoss VFS range

Thanks again for the responses. Unfortunately I'm not going to be able to add a flow meter at this stage! I'd almost given up but have just now noticed on the information sticker on the side of the indoor unit says "heating water flow" 1.5m3/hr. So, is the flow rate for a heat pump constant? Or is this value completely irrelevant to the COP calculation?

I think trying to measure the COP of a heat pump without a calibrated Heat Meter is likely to lead to inaccuracy.  A Heat Meter consists of a flow meter and two temperature sensors as described above, but its calibrated and unfortunately normally rather expensive.  Sure you could put something together yourself, but I would only look at the relative change in COP and not take too much notice of the absolute number.

As you have said you are not able to add a flow meter at this stage, so I suggest an alternative method of monitoring your heating energy consumption.  The method uses Heating Degree Days (HDD) to evaluate your heating energy use and is a method widely used for all heating systems.  Simply HDD's are a measure of how cold it is and it is reasonable to assume heating energy use will be proportional to HDD's.  Obviously you can generate the HDD's yourself with an outside temperature sensor.

The method is described in the link, but simply plotting Heating Daily Energy Use vs Heating Degree Days should yield a strong correlation and a regression or trend line should be a good fit to the data.  Assuming you are only using the heat pump for heating and have selected the correct base temperature then the gradient of the trend line is going to be a performance coefficient of your house and heat pump.

So once you have the slope of the trend line the following relationship can be used to obtain the heat pump COP.  Where U is the total heat loss of the house and U/COP is the gradient of the trend line.