Most filter manufacturers only provide pressure drop ratings for each filter at one rated airflow. So what do you do when you want to install that filter in a system that requires a higher airflow than what’s listed by the manufacturer? Fan law two will enable you to predict the increased filter pressure drop in less than a minute. The best part is the math is simple. Divide once, and multiply twice.

Fan laws allow us to look into the future and see what is going to happen before we pick up a wrench. Wouldn’t it be terrific to find a mathematical formula that would allow us to predict the future in other areas of our lives? That would make running a business or raising our children much easier. Unfortunately, those areas of our lives are a bit more complex than foreseeing the change in pressure drop over a filter. So, for now we will have to settle for predicting changes in static pressures.

**When to Use Fan Law Two**

Here’s the scenario. You are selecting a new filter for a three ton system that requires 1200 CFM in cooling mode. The family has a child with asthma and they want a filter that cleans the air more than a typical disposable filter. You find a filter advertised with a “low” pressure drop of .13-in. w.c. But after further investigation you see that this rated pressure drop is only at 1000 CFM.

The current system has been tested and you’ve verified that it’s delivering the required 1200 CFM. You are concerned however, because the fan is rated for .70-in. w.c. and set for high speed and is currently operating at .60-in. w.c. So you only have an additional .10-in. w.c. of static pressure available. The current filter pressure drop is .12-in. w.c.

Will this fan be able to “afford” the increased pressure drop of the new filter? What will the pressure drop of the new filter be at 1200 CFM if it is rated at .13-in. w.c. at 1000 CFM?

**Fan Law Two**

Before we calculate the new filter pressure drop and solve the problem, let’s take a close look at fan law two and become familiar with it. If you are not familiar with fan laws, the algebraic appearance of them can be intimidating. Remember this; although fan law two may look difficult, all you have to do is to divide once and multiply twice.

Let’s pick this formula apart. First, the abbreviation SP stands for static pressure. In this case, it’s the static pressure drop of the filter. CFM stands for cubic feet per minute or the volume of airflow per minute passing through the filter.

Each abbreviation is designated with a subset number (below and to the right) of 1 or 2. If the abbreviation has a 1 behind it, this means you’ve already measured the value in the formula. In this case, the filter manufacturer measured airflow at 1000 CFM. SP1 is the pressure drop of the filter that the manufacturer measured of 13-in. w.c.

If it has a 2 behind it, this means you either know what the number will be (this is true with CFM2, you know you will have airflow at 1200 CFM) or that this is the number you are solving for (SP2 will be the answer to the formula).

The parenthesis in the formula indicates the part of the formula that you solve first. And finally the 2 at the end of the formula (up high to the right) means to square the results of the math inside the parenthesis. To square something means to multiply it by itself.

**Step-By-Step Calculations**

So we take the formula above and pour in the numbers to the problem we are trying to solve. Now the formula looks like this:

The first step: divide 1200 by 1000. We do this because the manufacturer published pressure drop at 1000 CFM but we want to find the filter pressure drop at 1200 CFM. This will give you the ratio of the increase in airflow of 1.20 or airflow increased 120%.

Next, square the airflow increase ratio of 1.20. Multiply 1.20 times 1.20 to find 1.44.

Finally, multiply the manufacturer’s rated filter pressure drop of .13-in. w.c. at 1000 CFM times the squared increase in airflow ratio of 1.44 to find the pressure drop of the filter at 1200 CFM.

By using fan law two, we know at 1200 CFM the filter pressure drop will increase from .13-in. w.c to .19-in. w.c., for a total increase in static pressure of .06-in. w.c.

So, the pressure drop of the filter at 1200 CFM will equal just under .19-in. w.c. of pressure. That’s a 44% increase over the filter pressure drop at 1000 CFM.

Notice that airflow increased 20%, but the filter pressure drop increased 44%. That’s what fan law two demonstrates. Pressure increases at the square of airflow. Keep in mind that the formula is only effective when airflow increases up to 30% or less. When airflow increases more than 30%, the formula calculated pressure drop change may become excessive.

Remember our system scenario? The fan is rated at .70-in. w.c. At 1200 CFM the fan was operating at .60-in. w.c. With an increase in filter pressure drop of .06-in. w.c., the fan still has the capacity to move the required system airflow of 1200 CFM. So, we’re good to go.

Should the calculation show the fan did not have the capacity to handle the new filter, other changes in the system including increasing duct system capacity will be needed to relieve excess static pressure and assure the system can operate properly.

This fan law can also be used to calculate the increase or decreased pressure drop of any system component including a coil or a duct system or to calculate a change in total external static pressure.

Take the principles taught in fan law two and apply them to the next system that you improve to predict pressure changes. By learning to use fan law two effectively, you can predict the outcome before making changes in the system that will affect fan and component pressures and change the system airflow. Fan laws can also calculate the changes in fan airflow, RPM, pulley size and motor amp draw.

**Rob “Doc” Falke** *serves the industry as president of National Comfort Institute an HVAC based training company and membership organization. If you're an HVAC contractor or technician interested in a free fan law calculation report, contact Doc at robf@ncihvac.com or call him at 800-633-7058. Go to NCI’s website at nationalcomfortinstitute.com for free information, articles and downloads.*