BTU (British Thermal Unit) Calculations

1 BTU=1 DEGREE FARENHEIT INCREASE IN ONE POUND OF WATER.

8.34 POUNDS IN ONE GALLON

BTU EXAMPLE:
Incoming water 50F outgoing water 120F 120 - 50 = DELTA T 70F
BTU's for 1 gallon of water is 70 (delta T) * 8.34 (pounds per gallon) = 583.8 BTU's
Flow Rate 2 Gallons per Minute
2 Gallons * 60 minutes = 120 Gallons per hour
120 Gallons * 583.8 BTU's per Gallon = 70,056 BTU's per Hour

For More Formulas, Equivalents, Etc. Click HERE

The following expression (equations) is used to calculate domestic hot water (DHW) energy saved by using solar energy. In technical terms the "solar fraction".

51 WellWaterSupply (L)S DHWFlow (L)=WellWaterHold
49 FurnaceDHWOut (L)S DHWFlow (L)=DHWOutHold

29 DHWOutHold (L)-WellWaterHold (L)=FurnWellDeltaT

50 SolarDHWOut (L)S DHWFlow (L)=SolarDHWHold
51 WellWaterSupply (L)S DHWFlow (L)=WellWaterHold

30 SolarDHWHold (L)-WellWaterHold (L)=TankWellDeltaT

31 TankWellDeltaT (L)/FurnWellDeltaT (L)=DHWEnergySaved

The following expression (equations) is used to calculate the solar BTUs contributed to the domestic hot water supply.

50 SolarDHWOut (L)S DHWFlow (L)=SolarDHWHold
51 WellWaterSupply (L)S DHWFlow (L)=WellWaterHold
55 SolarDHWHold (L)-WellWaterHold (L)=SolarWellDeltaT

56 LBSGallon=8.33000 (Constant)

57 SolarWellDeltaT (L)*GallonsDHW (L)=DHWDeltaTGal
58 DHWDeltaTGal (L)*LBSGallon (L)=SolarDHWBTUs

Calculating BTU's added to the storage tank by the solar collector.
These are BTU's calculated by actual temperature rise in the storage tank, not collector BTU's (which do not account for heat loss in the system or lack of efficiency in the heat exchanger)

Overview: Two things need to be calculated

1)Temperature rise in the tank while the collector pump is running.

TankMax - TankMin = Tank Delta T
Tank Delta T * 2,732 (BTU's to raise 328 gallon storage tank 1 degree farenheit) = Collector BTU's
Collector BTU's * Collector Pump (1 for On and 0 for Off) = Collector BTU's Pump On

2)The domestic hot water used while the collector pump is running.
More specifically, the BTU's added to the domestic hot water by the storage tank, called solar fraction. The solar fraction is calculated by measuring the delta T between the well water temperature and the output temperature of the domestic hot water heat exchanger (before the domestic hot water goes to the furnace).This is accomplished by using a flow detector to capture temperatures only when domestic hot water is being used and a flow meter to measure the gallons used. Temperatures used at other times are not valid.

Solar Heated DHW - Well = Solar Heated DHW Delta T
Solar Heated DHW Delta T * Gallons Used = Solar Heated Delta T in Gallons
Solar Heated DHW Delta T in Gallons * 8.33(pounds in 1 gallon of water) = BTU's Solar Heated DHW
BTU's Solar Heated DHW * Flow State(1 for Yes 0 for No) = DHW BTU's Used
DHW BTU's Used * Collector Pump (1 for On and 0 for Off) = DHW BTU's with Collector Pump On

Because domestic hot water use is reducing the BTU's in the storage tank while the collector pump is running, this number needs to be ADDED to the Collector BTU's Pump On.

DHW BTU's Used with Collector Pump On+Collector BTU's Pump On = Total BTU's added by Collector

Constants used in some expressions (equations).

53 FuelOilPrice=2.50000 (Constant)
54 OilFurnace (M)*FuelOilPrice (L)=HeatingOilCost

The following are used to show 0 degrees on feed and return temperatures in the system diagram live data when the radiant pump is not running.

32 RadiantPump (L)*RadiantFeed (L)=RadPumpFeed
33 RadiantPump (L)*RadiantReturn (L)=RadPumpReturn

The following are used to show 0 degrees on feed and return temperatures in the system diagram live data when the collector pump is not running.

34 60TubeCollFeed (L)*CollectorPump (L)=CollFeedPump
35 60TubeCollRtrn (L)*CollectorPump (L)=CollRtrnPump

The easy stuff. Delta T values.

28 60TubeCollRtrn (L)-60TubeCollFeed (L)=CollectorDeltaT
39 RadiantFeed (L)-RadiantReturn (L)=RadiantDeltaT

Test for showing storage tank max and min temperatures.

48 328GalTank (L)+328GalTankTest=328GalTankMax
59 328GalTank (L)+328GalTankTest=328GalTankMin

Constants used in expressions.

47 328GalTankTest=0.0000 (Constant)
60 RadPumpScale=5.00000 (Constant)

Used to increase the scale of the radiant pump "on" state on the graph.

61 RadiantPump (L)*RadPumpScale (L)=RadiantPumpOn

WEL Settings

Below is a screen shot of the WEL Live Data Table. The left column shows device ID's. Where there is no device ID, there is an operator ( + - * / { }S) tied to the virtual device (the name you give for the result of the equation), which identifies the devices involved. The L after the device number means Live data, as opposed to Day or Month accumulations. You can also create a constant that would be applied to a result. For example device 53 defines a constant of 2.50, which is the price of 1 gallon of fuel oil. Device 56 is 8.33, which converts gallons to pounds for BTU calculations. Constants and expressions can be combined, with a limit of up to 128 devices.

WEL Calibration Table

"WellPumpOn" scale is 100 so that it will show up on the graph with values from 0-2,400.
"OilFurnace" scale is 1.5 because the furnace uses 1.5gal/hr of fuel oil.
"OilFurnaceOn" is jumpered from OilFurnace so I can also have a value large enough to show up on a graph with values from 0-160. The same is true for devices 4-7.
kWH scale is 2 because of the way pulses are counted.
Devices 10 and 11 are scaled to 1 as an "on" state.
GHLPHeater (greenhouse LP heater) is scaled negative (-) because the "off" state of the thermostat shows voltage. I used negative -10 so the value would show up on a graph with values from 0-160.
"OilFurnaceOff" is a virtual device I created so that when I turn the furnace off "The Present Hot Water Supply" would show 100% solar.
Temperature sensors are scaled to 1.8 and offset to 32 to convert the native sensor output of Celsius to Fahrenheit.
"GallonsDHW" is scaled to 30 because the flow meter counts once per gallon to the pulse input that accumulates 1/60 an hour. Confusing right? That's why I'm putting this on my website.
"DHWEnergySaved" scale is 100 to convert a decimal to a whole number percentage.
"Sun" sensor puts out volts, which I calibrated, with trial and error, to .6 for values of 0-100 percent.
"DHWOutHold" samples "DHWOut" temperatures as long as "DHWFlow" has a value of 1 (flow detected). Once the "DHWFlow" goes to 0 (no flow), the last temperature value is held. This prevents values from dropping to ambient, which would throw off BTU calculations. You want to calculate BTU's using temperatures only when hot water is actually being used.
Our flow detector will work to flow rates as low as 1/16th of a gallon per minute. Low flow detection is necessary because of mixing hot and cold water at the faucet, which can make hot water flow rates very low. Because we could not find a flow detector to meet our specifications, we designed and built our own.