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Calculation of Btus generated during Heating

Ted Cummings | Posted in General Questions on

I am writing an article for the GBA and wish to depict a graph of the Kwh used by my Ground Source Heat Pump vs. the outdoor temperature.  On that graph I would also like to show the actual BTUs released into the air of the house, during Heating, corresponding to  those same Kwh.  
The sensors in the GSHP, which operates with 3 variable speed motors,
(compressor, blower and  loop pump), give me data, including the following: 

While operating at 60% capacity the GSHP should theoretically generate 18,000 Btu. (maximum capacity of 30,000Btu)  
Sensors show that at that 60% capacity:
Compressor: 913 watts,
Blower:          54.5 watts,  600 CFM,  102.3ºF Leaving Air Temp, 70º Room Air
Loop Pump: 18 watts,       2.8 GPM,  52.9 Entering Water Temp,  46.6 Leaving Water Temp. 
The Operating Manual indicates that at that 60% capacity and Entering Water Temperature of 52.9º the COP should be  5.43 (5.2 for EWT of 50º, 6.0 for EWT of 60º)

In order to obtain the Btus transferred into the house air I tried two methods: 
1.  Power used converted to Btus: (I assumed all of the mechanical energy eventually is converted to heat within the house)
((913w x 5.43)+54.5w+18w) watts/hr x 3.412Btu/watt = 17,163 Btu/hr [17,354 Btu/Kwh] (This figure depends upon one believing the manufacturers COP specifications)
2.  Change in Air Temperature
600 CF/min x 60 min/hr x .0182 Btu/CF/ºF x (102.3º – 70ºF) = 21,163 Btu/hr [21,398 Btu/Kwh](This figure depends upon believing the sensors readings of CFM and Air Temp.  I have no reason to disbelieve the Air Temp readings but I believe the CFM is a bit more iffy).  I tend to believe this method.  

The theoretical 18,000 Btu falls almost exactly half way between the two.  

What would be the most accurate way to figure out just how many Btus are added to the house….one of the above formulas or some other way ?

Ted Cummings
[email protected]
 

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Replies

  1. Akos | | #1

    Since the system COP depends on a lot of factors, I would not trust it for the calculation.

    To get an accurate btu, you need to measure a flow rate.

    If you have a decent length of straight duct, you can use a pitot tube flow meter, which tend to be reasonable accurate.

    The other option is to measure the water flow rate to the coil and measure the water deltaT across the coil. This tends to be more accurate, you can get a decent in-line flow meter for much less than a good air flow meter (Omega or Dewyer). You than just have to add on the blower power to figure out the BTU delivered to the house.

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