I was thinking about airflow recently and had a brain storm about calculating BTU's in an airstream. I wanted to see if it was sound thinking. Here it is.
Enthalpy tells us how many BTU's/lb that air of a particular temperature and water content contains. Knowing this, if I know the CFM's and the density of the air at a specified temperature, I ought to be able to figure out how many BTU's I am pumping around. If I then decide to change the temperature, I should be able to find out how many BTU's I will have to take out of the air or put in to change the mass of air to the new temperature. So, I made these calculations to test the speculation.
Dry Bulb Temperature = 55*F
CFM = 400
Density of air at 55*F = 0.07711 lbs/ft3
Enthalpy of dry air at 55*F = 13.2 BTUs/lb
400 CFM x 0.07711 lbs/ft3 = 30.844 lbs/minute of air moved
30.844 lbs/minute x 60 minutes/hour = 1850.64 lbs/hour of air moved
1850.64 lbs/hour x 13.2 BTUs/lb = 24428.45 BTUs/hour moved
New Dry Bulb Temperature = 70*F
CFM = 400
Density of air at 70*F = 0.07492 lbs/ft3
Enthalpy of dry air at 70*F = 16.8 BTUs/lb
400 CFM x 0.07492 lbs/ft3 = 29.968 lbs/minute of air moved
29.968 lbs/minute x 60 minutes/hour = 1798.08 lbs/hour of air moved
1798.08 lbs/hour x 16.8 BTUs/lb = 30207.74 BTUs/hour moved
Delta T = 70*F - 55*F = 15*F
Total air volume = 400 CFM * 60 minutes/hour = 24000 Cubic Feet
So if I pump 24000 cubic feet of air through my air conditioner and lower the temperature of the entire volume of air from 70*F to 55*F, the unit will have to remove 30207.74 BTU's - 24428.45 BTUs or 5779.29 BTU's from the air in the hour that it takes the unit to pump the air through it at 400 CFM. This of course is speaking of perfectly dry air.
Now I have the formula BTU/hr = 1.08 * CFM * delta T which presumably tells how many BTUs/hour it will take to change the temperature of a certain quantity of air flow a certain delta T. When I do the math with this . . .
CFM = 400
delta T = 15*F
BTU/hr = 1.08 * 400 * 15 = 6480 BTU/hr
Why the difference? 5779.29 BTU/hr versus 6480 BTU/hr? Is the 6480 actually taking into account some latent heat making it a "rough" estimate for the real world?