Some HVAC techs hesitate when it comes to performing duct repairs because they worry about creating additional airflow problems. But what if there were a quick and simple way to anticipate what would happen to static pressures if you increased or decreased airflow?

Air balancers have used formulas called fan laws for decades to accurately and quickly make these predictions.

Let’s look at how you can use one of these laws to predict and prevent static pressure problems before they occur.

### WHAT IS A FAN LAW, ANYWAY?

Fan laws are mathematical formulas for predicting system changes when airflow adjustments are made. There are three laws that cover various system properties, ranging from fan speed (rpm) to motor amperage.

In this article, we’ll look at Fan Law 2, which predicts new static pressure after making airflow changes.

You can apply it in the field to determine changes in total external static pressure (TESP), filter pressure drop, coil pressure drop, and duct system pressures. It’s an easy double-check that gives you the assurance to move forward with repairs or alter your plans before writing a scope of work.

### THE FAN LAW 2 FORMULA

A truth that Fan Law 2 reveals is that static pressure changes at the square of airflow; in other words, pressure increases a little more than twice the airflow rate. For example, let’s say you increased fan airflow by 10 percent. This would equal an approximate static pressure increase of 21 percent.

At first glance, Fan Law 2 looks intimidating. This statement comes from someone who is not a fan of math. In fact, it was my least favorite subject growing up. However, once I understood the components of Fan Law 2 and how the formula worked, I felt a lot more confident about using it in the field.

Fan Law 2 uses the following formula to calculate the relationship between airflow and static pressure:

(cfm2 ÷ cfm1)2 x SP1 = SP2

As you review it, you’ll notice that you divide once and multiply twice when you work the formula.

Intimidating, right? Let’s break down the formula into bite-sized chunks, starting with the abbreviations, subscript numbers, and how to work the fan law.

• cfm = cubic feet per minute, or airflow
• SP = static pressure

Each abbreviation in Fan Law 2 has a subscript number at the bottom right. They represent the value you are currently measuring or trying to determine.

An abbreviation with (1) next to it indicates the measured or known value in the formula. It is typically the live measurement you obtain in the field. In some fan law variations, it is referred to as the “old” value.

An abbreviation with (2) next to it indicates the design or target value. It is the measurement in the formula that you’re solving or trying to determine. In some fan law variations, it is referred to as the “new” value.

The parentheses in the formula indicate that you need to do this part of the formula first — remember PEMDAS? In our example, cfm2 is the target airflow value and cfm1 is the known airflow.

When you see the superscript (2) outside of the parentheses, on the upper right-hand side, you need to square your answer or ratio from inside the parentheses. To square a number, you simply multiply it by its own value. For example, if you square the number 4, it equals 16.

4 x 4 = 16

### USING IT IN THE FIELD

Let’s say you’re renovating a 3-ton system and you want to use a 20 x 25 x 5 media filter. The air-handling equipment has a maximum-rated TESP of .50 inches of water column (in. w.c.) and needs 1,200 cfm (400 cfm per ton x 3 = 1,200) of required airflow.

You look at the manufacturer specifications for the air filter and see it is rated for 1,040 cfm at a .08 in. w.c. pressure drop. That’s a great pressure drop for an air filter! They shouldn’t have a pressure drop higher than 20 percent of the air-handling equipment’s maximum-rated TESP. So, a pressure drop higher than .10 in. w.c. (20 percent x .50 = .10) could use up too much fan capacity and result in low fan airflow. The only problem is the filter is rated for 2.5 tons of airflow, not 3.

With the information provided, you can use Fan Law 2 to determine what filter pressure drop will rise to if it’s used on a 3-ton system.

The information would fit into the Fan Law 2 formula as follows:

(cfm2 ÷ cfm1)2 x SP1 = SP2

• cfm2 = 1,200 cfm (the target airflow)
• cfm1 = 1,040 cfm (the known airflow)
• SP1 = .08 in. w.c. (the known static pressure)
• SP2 = ?? in. w.c. (the target static pressure you’re solving for)

Let’s take the Fan Law 2 formula and place all the numbers from above into it. The formula now looks like this:

(1,200 ÷ 1,040)2 x .08 = SP2

First, divide cfm2 (1,200) by cfm1 (1,040) to determine the ratio of airflow increase: 1,200 divided by 1,040 equals 1.15, or a 115 percent airflow increase.

1.152 x .08 = SP2

Next, square the airflow ratio increase by multiplying 1.15 times itself (1.15 x 1.15), which equals 1.32.

1.32 x .08 = SP2

Finally, multiply the manufacturer-rated filter pressure drop, or SP1 (.08) times the squared airflow ratio increase to determine SP2, or the target static pressure you’re solving for.

.11 in. w.c. = SP2

If you’ll remember, we were trying to keep filter pressure drop less than .10 in. w.c. to avoid using up too much fan capacity and potentially having low fan airflow. The estimated filter pressure drop is barely over .10 in. w.c.

Would you feel comfortable using this filter? While the numbers are close, it allows no room for the filter to load up with dirt over time. A wise choice would be to avoid using a single filter of this size and perhaps add another one or use a different filter media to reduce pressure drop.

### NEXT STEPS

Your challenge is to take this formula and use it on the next system that you consider improving. Use it to predict static pressure changes and see where you will end up before you make any changes to the equipment or fan airflow.

Remember, there are also additional fan laws you can use to determine changes in fan rpm, pulley size, motor amp draw, brake horsepower, and adjusting branch airflow. They follow many of the same principles discussed in this article. To receive a one-page sheet of the most common fan law variations, send me an email request for your pdf copy.

If you’re an HVAC contractor or technician interested in learning more about fan laws, contact me at davidr@ncihvac.com or call 800-633-7058. NCI’s website, www.nationalcomfortinstitute.com, is full of free technical articles and downloads to help you improve your professionalism and strengthen your company.

Publication date: 3/18/2019