Applying the Temperature Rise Airflow Formula

Many techs are familiar with the temperature rise formula for checking airflow. It is derived from the specific heat formula:

BTU = weight x ΔT x Specific Heat
(Note ΔT is simply shorthand for the change)

After rearranging the formula to solve for weight, changing the weight of air to a volume, and reconciling BTUs per hour with Cubic feet per minute you end up with

CFM = Btuh/(1.08 x ΔT)  

For heat pumps we get the Btuh by measuring both the voltage and current and multiplying them by 3.41. The formula becomes

CFM = (volts x amps x 3.41)/(1.08 x ΔT)

For furnaces we measure the firing rate in Btuh and multiply it by the furnace combustion efficiency. The formula becomes

CFM = (Btuh input x %Efficiency)/(1.08 x ΔT)    
 (Note %Efficiency is stated as a decimal in this formula.)

Did you ever wonder where the 1.08 comes from? The "magic number" 1.08 is a convenience constant. It is basically a bunch of math combined into one factor as a short cut. When you multiply the airflow by 60 to get airflow per hour, multiply by the density of air 0.075 pounds per cubic foot to convert volume to weight, and multiply by the specific heat of air 0.24, you end up with 1.08. The factor is often rounded to 1.1 because it makes the math easier.

The number is not really constant because the volume of the air varies with altitude, temperature, and humidity. A change in any of these variables changes the density of air, which in turn changes the "magic number." The factor 1.08 in this formula is only accurate for dry air at 70°F at sea level. For example, 1.08 really does not work with flue gas or airflow in freezers because the air volume has changed, which changes the convenience factor. Similarly, 1.08 does not work in Denver because the altitude changes the air pressure, changing the density. Even the relative humidity changes the factor. The ubiquitous 1.08 is for dry air at 0% relative humidity – a condition that is never seen in Georgia. Changing the relative humidity to 50% changes the air volume, which changes the factor.

Lets look at some examples. 0°F air at sea level has a density of 0.086 pounds per cubic foot, while 300°F air at sea level has a density of 0.052 pounds per cubic foot. Instead of the commonly quoted 1.08, these densities produce factors of 1.24 for 0°F air and 0.746 for 300°F air. If the air is 70°F but at 5000 feet elevation, the factor becomes 0.9 because the air density has changed due to the increased elevation. Even changing from 0% relative humidity to 50% relative humidity changes the density to 0.0741 instead of 0.0745 (the 0.075 for 70°F air is rounded). This changes our convenience factor to 1.07.

If you would like to play with different scenarios, there is an online air density calculator that takes all three factors into account at http://www.denysschen.com/catalogue/density.aspx
Just multiply the density times 14.4 to get your new magic number. What is 14.4? Oh, you get that by multiplying 0.24 times 60.

For more details on checking airflow using the temperature rise I recommend a great article by Norm Christopherson on the nuts and bolts of measuring airflow using temperature rise. You can find it on docstoc by clicking HERE.

Delta T vs TD

Once again my good friend Brian Baker is keeping me honest. After my last posting  about Delta T where I said that Delta T was the same thing as Temperature Difference, Brian sent me a copy of a Sporlan Cold War Article by Garth Denison. It is essentially a refrigeration glossary of useful terms, including Delta T and TD – short for Temperature Difference. In this listing, Mr. Denison makes a distinction between Delta T and TD (temperature difference). He defines Delta T as a temperature difference between two points in the same media and TD as temperature difference between two different media. So Delta T is a temperature change in something, while TD (temperature difference) is the difference in temperature between two different things. Although the distinction is subtle, it makes some sense. Remember that the Δ symbol really stands for change. The change is represented by the change in shape of the triangle from top to bottom. In the case of a water cooled condenser, the Delta T would be the change in temperature of the water from 80°F entering the condenser to 90°F leaving the condenser. The TD, or temperature difference, would be the difference between the 90°F water leaving the condenser and the 100°F refrigerant inside the condenser.  

Desired Air Conditioning Temperature Drop

I was recently asked for a formula to determine the temperature drop between the return air and supply air of an air conditioning system. While it is logical to check the temperature drop, determining exactly what it should be is not as simple as plugging in readily available numbers into a formula. Two operating conditions can have a pronounced effect on the results: the relative humidity of the return air and the amount of airflow. Most air conditioning systems condition the air two ways. They cool the air, referred to as sensible cooling; and they take water out of the air, referred to latent cooling. Only sensible cooling creates a temperature drop. Removing water from the air takes system capacity. The more water the system removes from the air, the less capacity is left for reducing the air temperature. Standard airflow is 400 CFM per ton for most systems, but that does not mean your system is actually operating at 400 CFM per ton. If you move less air across the coil, the air will be cooled a little more. To determine the temperature drop you must know the outdoor ambient temperature, the return air dry bulb, the return air wet bulb, the CFM of airflow, and the system’s sensible cooling capacity at that condition.

Take for example, a system that is removing no water out of the air operating at 100% sensible cooling with a standard 400 CFM per ton of airflow and producing 12,000 Btuh per hour. The temperature difference is calculated as TD = 12000/(400 x 1.08) = 28°F TD. If the airflow is reduced, the TD becomes 12000/(350 x 1.08) = 32°F. Increasing the airflow would make the TD 12000/(450 x 1.08) = 25°F. In humid climates, the latent capacity can easily be as much as one third of the total capacity, reducing the sensible cooling capacity to 8,000 Btuh. These same airflows would then give TDs of: 8000/(400 x 1.08)=19°F, 8000/(350 x 1.08)=21°F,8000/(450 x 1.08)=16°. In reality, these TDs would be a little off because the overall system capacity would be a bit less with the decreased airflow and a bit more with increased airflow. The system capacity will also change depending upon the outdoor ambient. The 12.000 Btuh per ton is a nominal figure based on the AHRI rating condition of 95°F outdoor ambient, 80°F indoor dry bulb and 67°F wet bulb.

You can try to account for duct gain by reducing the expected TD by some amount: say 3°F - 5°F. However, it is really difficult to use TD at the registers because the duct gain from one system to another can vary a lot. Ducts in the attic will pick up more heat than ducts in a crawl space. Duct leakage also has a big effect. If 10% of the air entering the coil comes from a 150°F attic, that obviously will affect the delivered air temperature. The rule of thumb people have used for many years is a TD of 15°F to 20°F across the coil, not at the registers. Looking at the above calculations, you can see where this comes from. However, it is also easy to see how little you actually know if you don’t really know all the operating conditions, the system airflow, and the system capacity at those conditions. If all you do is measure the return and supply air temperatures at the registers, you don’t really know much.