• Category Archives: Airflow

A Ton of Air

I enjoy playing with numbers to gain insight into things that we often take for granted. There are many ballpark numbers that just about every HVAC tech has memorized, some more accurate than others. One very common ballpark number is airflow of 400 CFM per ton. One problem with this ballpark number is that it does not account for the required specific heat ratio for a particular application. But that is not what I want to talk about today. That airflow rate, 400 CFM per ton, is within the operating parameters of most HVAC equipment, even if it is not the most effective for a particular application.

What I want to show is how much work is involved in moving 400 CFM of air. At the ASHRAE “A” indoor condition of 80°F 50% relative humidity, a pound of air takes up about 13.6 cubic feet. Dividing 400 CFM by 13.6 tells us how many pounds of air the blower is moving each minute: 400/13.6 = 29.4 pounds per minute. Multiplying that times 60 tells us how many pounds of air the blower is moving per hour: 29.4 x 60 = 1764.7 pounds of air per hour. Recalling that a ton of weight is 2000 pounds, an airflow of 400 CFM is nearly a literal ton of air per hour! To get exactly a ton we would need to move 453.3 CFM: 453.3 / 13.6 = 33.3 33.3 x 60 = 2000 pounds per hour. But of course that 400, or 453 is just the airflow per ton of cooling capacity, not the total airflow. So a 2 ton system moving 800 CFM would be moving 3529 pounds per hour. If that same system were moving 906 CFM, it would be moving 4000 pounds of air an hour. That is a lot of weight to push around.

Think of the total external static pressure as the hill up which the blower must move all that weight. It becomes obvious that if the hill is higher, the blower will have to work harder. Think of the external static pressure a blower must operate against as the hill up which it must move all that weight. Forward curved centrifugal blowers lose capacity against higher external static pressures. Just as water pumps move less water if you make them move the water higher, centrifugal blowers move less air against higher static pressure.

In the case of constant airflow ECM motors, the blower motor puts in the work to overcome the loss of blower wheel efficiency to move all that weight up the steeper hill. In the case of constant torque electronic motors, while the motor gives a steady output, the blower wheel still loses efficiency. There is a decrease in the amount of air the blower can move. In the case of PSC motors, not only does the blower wheel lose efficiency, but the motor also loses capacity. The airflow drop can be drastic. So give the poor blower a break. Use air filters with low pressure drop and keep them clean. After all, the blower IS doing a ton of work! Check out my book, Fundamentals of HVACR published by Pearson if you would like to investigate further.

Airflow by the Numbers

You may be familiar with the formula: BTUH = CFM x ΔT x 1.08. This same formula is often rearranged to use for determining airflow by measuring the heat input and temperature rise: CFM=BTUH/( ΔT x 1.08). To get the BTU per hour (BTUH) with electric strips you use the formula BTUH = volts x amps x 3.41 BTUH/watt. Together the formula looks like: CFM = (volt x amps x 3.41)/ ( ΔT x 1.08). The factor 3.41 comes from physics. It is the number of BTUs produced by one watt-hour of electricity. But where does the 1.08 factor come from? The “magic number” 1.08 is convenience factor. It is basically a bunch of math combined into one factor as a short cut.

You may recall that the specific heat formula is used for changing the temperature of something. The specific heat formula is
BTU = weight x ΔT x Specific Heat
This has one big problem, we don’t measure airflow by weight, but by volume. AHRI Standard air weighs 0.075 pounds per cubic foot. We can convert air volume to air weight by multiplying the air volume by 0.075 lbs/ft3. Another issue is that we tend to measure airflow by the minute and BTUs by the hour. You can fix that by multiplying times 60. Finally, we need the specific heat of air, which is 0.24. When you multiply the air volume by 0.075 to turn CFM into pounds per minute, multiply pounds per minute by 60 to get pounds per hour, and multiply by the specific heat of air 0.24, you end up with 1.08 (60 x .075 x 0.24 = 1.08). The number is not really a constant because the density of the air varies a lot with temperature, which changes the “magic number.” This formula is accurate for dry air at around 70°F, but it is NOT accurate when the air temperature gets very much colder or warmer than 70°F. For example, 1.08 really does not work with flue gas or airflow in freezers because the air density has changed, which changes the convenience factor. At 400°F the air only weighs 0.043 lbs/ft3, changing the convenience factor to 0.62 (60 x 0.043 x 0.24 = 0.62). At 0°F, air weighs 0.086 lbs/ft3, changing the convenience factor to 1.24 (60 x 0.086 x 0.24 = 1.24). Air density also changes with elevation and humidity, although the change due to humidity is small. Even the specific heat of air changes as the air temperature changes, but again, the changes are small. This is all to say that if you are dealing with air around room temperature, feel free to use the 1.08 convenience factor. However, if you are dealing with air at a much different temperature, you should look up the weight of air at the temperature you are working with. The table below lists the weight of a cubic foot of air at different temperatures and provides a reworked convenience factor so that you can perform correct air calculations at temperatures other than 70°F.

TemperatureWeight lb/ft3Convenience FactorTemperatureWeight lb/ft3Convenience Factor
0°F0.086251.24175°F0.062550.90
10°F0.084411.22200°F0.060180.87
20°F0.082651.19225°F0.057970.84
30°F0.080961.17250°F0.055910.81
40°F0.079351.14275°F0.053990.79
50°F0.077801.12300°F0.052190.76
60°F0.076311.10325°F0.050510.74
70°F0.074871.08350°F0.048940.72
80°F0.073491.06375°F0.047460.70
90°F0.072171.04400°F0.046080.68
100°F0.070891.02425°F0.044780.66
110°F0.069651.00450°F0.043570.64
120°F0.068460.99475°F0.042420.63
130°F0.067300.97500°F0.041340.61
140°F0.066190.95525°F0.040310.60
150°F0.065110.94550°F0.039330.59
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