Calculating BTUs from hot air
Can someone help me figure out the calculations for how to get the amount of BTUs you get out of hot air at a specified flow rate? I know that it depends on a lot of different factors like moisture content of the air, but I guess I'm looking for a simplified equation that ball parks things.
For example, lets say I have a solar hot air panel. I know the fan flows 100 CFM and I know that it puts out air that is 20F above ambient. How many BTUs per hour is it going to spit out? 
I found this link here that seems to explain what you are looking for. https://www.ruppams.com/Sitedocs/RUP...alculation.pdf
It appears that given the above considerations, about 2160 BTU/hr. 
That is perfect. Thanks.

Use a psychometric chart and factor in humidity. There is a significant difference in the energy carried by dry air vs humid air, that 1.08 number is a vast oversimplification of the system you're trying to model.

I use 0.018 BTU/ft^3/deg F, the same as bmxeroh. It's almost certainly more accurate than typical temperature and airflow measurements. A one degree error on inlet and outlet temperatures could cause 10% error on temperature rise, plus another 10% air flow error, results in an easily believable 20% error. Accurate BTU measurements in HVAC systems can be a real challenge.
The largest assumption is that you are not adding or removing moisture. Then you would need a psychrometric chart. 
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efficiency?
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The energy out of the system is equal to the solar energy impinging on it. The efficiency of the system is the ratio of the energy that's actually in the form you can use (input  losses)/input. I argue that a cold collector absorbs more solar energy. Colder air creates less radiated/conducted loss in the piping outside the heated space. I think you might want more air and less temperature rise. BUT At some point the cost of moving the air is more than the solar energy recovered. Somewhere, there ought to be a peak in the net recovered energy curve. Would be interesting to measure the deltat at different air flow rates, plug that into the BTU formula and plot the result. You'll end up with a family of curves with solar input and outside temperatures as parameters. Then add some practical limits. Like, you may want to set a minimum output temperature for comfort reasons. Or a maximum air flow for noise reasons. Depending on the shape of the curves, it might be interesting to use a microcontroller to hunt for the peak in real time. There's some advantage to measuring the thing you actually want to know. You could even use a thermostat to divert any excess energy into a storage tank for use when less solar is available. 
CarbonKevin raises a valid point, so I pulled out an ASHRAE #1 pschrometric chart and did a pair of example calculations.
1) 40 deg F in, 60 deg F out, 0 RH, 100 CFM in. From the chart, 12.6 ft^3 per lb in, 9.6 BTU/lb in, and 14.6 BTU/lb out. The calculation: (14.6  9.6) X 100 CFM / 12.6 ft^3/lb X 60 min/hr = 2380 BTUH. 2) 85 deg F in, 105 deg F out, 100% RH in, 100 CFM in. From the chart, 14.3 ft^3/lb in, 49.4 BTU/lb in, and 54.1 BTU/lb out. The calculation: (54.1  49.4) X 100 CFM / 14.3 ft^3/lb X 60 min/hr = 1970 BTUH. The simplified approximation is 0.018 BTU/ft^3/deg F X 20 deg F X 100 CFM X 60 min/hr = 2160 BTUH. That's 10% low at the lower temperature, and 10% high at the higher temperature, and very close at normal room temperature. The error from the simplified approximation is less than the typical error from measuring temperature and CFM. 
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