How to Correct for Air Density

Four hundred CFM per ton has been the gold standard for cooling airflow since Willis Carrier proclaimed it so nearly a century ago. While the basic principal is still true, let’s take a look at airflow from a different angle and see how air density can have a significant effect on how our systems perform.

Most efficiency and performance calculations are based on "standard air." Standard air is at sea level, 50% relative humidity, 70F, and weighs .075 pounds per cubic foot. While this standard air density is good enough for 90% of us here in the United States that live below 2,000 foot elevation, those living at higher elevations must add an additional step to their engineering and measurement practices to remain accurate.

A mile above sea level, for example, cooling systems typically need 500 CFM per ton to operate properly. This is necessary because a cubic foot of air passing through a coil at that elevation has only 75% of the goop in it than a cubic foot of air has at sea level.

Goop? Granted, that's not a very technical term. Let me explain.

One good example of the reality of this unseen goop is basic heat transfer from a typical gas fired heat exchanger. Air, or, more correctly, the goop in it, passes through a heat exchanger and absorbs the heat. If air wasn’t heavy, it couldn’t absorb the heat and carry it from the heater through the duct and into the rooms in the building.

A typical home has more than 1,000 pounds of air in it. If a typical home is 2,000 sq.ft. with an average ceiling height of 8 feet, the home holds 16,000 cu.ft. of air. Here’s the math; 16,000 cu.ft. of air times .075 pounds equals 1,200 pounds of air. That’s a lot of goop. Fortunately, this substance is see-through and not very sticky, so we’ve become quite used to living it, moving through it and breathing it.

If you read the manufacturer’s data for gas-fired furnaces, each will offer correction factors to apply to BTU output ratings that compensate for air density. I have included a table at the end of the article that can be used to correct for air density in our design and air measurements at high altitude and under extreme temperatures.

How to Correct for Air Density

There are two primary forces that change the density of air that we can plot on the following air density table to make correcting for density quite easy. Along the top of the table is altitude, and along he left side of the table is the temperature of the air.

When testing air at temperatures or altitudes other than at “standard air,” the density of the air changes. As altitude or temperature increases, the weight of the air decreases.

To determine the actual amount of air (or, again, the goop in the air) being delivered through your system under non-standard conditions, multiply the volume of air measured by the corresponding factor shown in the air density correction table.

For example: If 1,200 CFM of air was measured at 40F Fahrenheit at an elevation of 7,000 feet above sea level using a non-compensating anemometer by performing a duct traverse, what is the actual amount of air in the duct?

Here's the formula:
1,200 CFM x 0.82 (THE FACTOR FROM THE CHART) = 984 CFM of standard air.

Or in simpler terms, there’s only 82% of the weight of air under these conditions as there is at 70 degrees at sea level.

To determine the amount of air needed under non-standard conditions, divide the amount of standard air needed by the corresponding factor as illustrated here:

Say the manufacturer’s data requires 1,600 CFM of standard air for a furnace to operate properly under standard air conditions. But, the system is moving airflow that is 100F at an elevation of 5,000 feet above sea level. Using a non-compensating balancing hood, how much of this "extreme air" will be required for the system to operate properly? Here's the calculation:

1,600 CFM of standard air divided by 0.78 (THE FACTOR FROM THE CHART) = 2,051 CFM of extreme air

That's what would be needed for the heating system to operate as designed at sea level.

CFM Per Ton

Take a look at the bottom row of the chart to determine how much air is needed for each ton of cooling at various elevations, assuming an average air temperature of 70F. At 3,000 feet elevation, required cooling airflow is 450 CFM per ton.

Unless absolute accuracy is required, compensation for air density is not applied below 2,000 feet elevation, or for residential heating or cooling temperatures. However, by understanding the corrections, you may choose to apply them to your engineering or testing numbers as needed.

Many projects are designed specifying standard air even though the system is installed under extreme conditions. If not specified on the drawings, contact the designer to verify under which conditions the system was designed. If needed, adjust the calculations for temperature or elevation as the table directs.