Saturday, October 12, 2013

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.

1 comment:

  1. Are the Btuh heating or cooling? Say we have a 108,000 BTU furnace with a 3 ton cooling capacity. Would we plug in 108,000 or 36,000 Btu's?

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