The Centrifugal Pump Affinity Laws, sometimes known as the laws of similarity, describe how changes in RPM affect the GPM, HEAD, and HP.
In the United States, electricity is at 60 cycles per second (hertz). Usually, pump performance curves are based on standard electric motor speeds in RPM. The speed and diameter of the pump impeller blades control the pressure generated by the pump; therefore, speed is crucial to the pump’s performance. Also, the speed and the height of the blades control the GPM, or the pump’s flow. If there is a change in the speed, there would also be a change in the flow, head, and horsepower the pump will require and the data on the performance curve will need to be adjusted, but how would this be adjusted? If you guessed the Affinity Laws, you’re correct!
"You’ll want to have a better understanding of pump performance as the conditions change, and the these laws will help you predict or estimate that performance."
Before we dive into the laws, let’s go over what the abbreviations from above mean:
RPM - revolutions per minute
GPM - gallons per minute (flow)
HEAD - pressure
HP - horsepower
These laws were introduced using the law of similitudes, providing 3 basic relationships:
Law 1: Flow vs. diameter and speed
Law 2: Total Head vs. diameter and speed
Law 3: Power vs. diameter and speed
Law 1 shows a simple linear relationship between the RPM and flow, meaning when RPM is reduced, the flow is also reduced. For example, if the RPM drops to 70% of the original RPM, the GPM also drops to 70% of the original. You can see the example in the graph below.
Law 2 shows the relationship between RPM and the pressure: as RPM drops, the pressure (feet of head) also drops by the square. An example of this is if the RPM dropped to 70% of the original RPM, the pressure, or feet of head, would also drop by (70% x 70%) = (0.7 x 0.7) = 0.7 squared = 0.49 = 49% of the original value. The relationship between the pressure and the RPM is shown in the graph below.
Law 3 shows the relationship between the RPM and the power: as the RPM is reduced, the power consumption (brake horsepower) is reduced by the cube. In this example, similar to the others, the power would drop 70% of the original (07 x 0.7 x 0.7) = (0.7)^3 = 0.343 = 34.3% of the original value. An example of the relationship between the power and RPM is shown in the graph below.
There is both good news and bad news when it comes to the laws above. The good news is that this theory helps us understand the principle dynamics of the flow, head, and power. If you know your system head and flow requirements, a variable speed pump controller will do the rest automatically for you. You set the requirements and through a 4 - 20 mA signal the controller will slow down or speed up the pump to match your demand reducing operating costs. This is especially helpful where demand flucutates . The pump controller will modulate to the new requirments automatically.
The Importance of Affinity Laws
Now that we’ve talked about what they are, it’s time to talk about why they’re important. Simply put, if you don’t understand and work with the laws they will work against you. Until recently, the affinity laws were mostly ignored, used only when someone was exporting a pump to another country with different electricity than the United States’ standard. But how can this be? We stated above that these laws are used to adjust the data on the performance curve, so if these laws were typically ignored in the past, how was the data being adjusted?
You’ll want to have a better understanding of pump performance as the conditions change, and this knowledge will help you predict or estimate that performance. These laws have been proven to be an excellent tool to predict a pump’s performance after changes have been made to one of the pump’s parameters. The laws are also important because they are your key to saving money in a hydronic system.
While we know this is a lot of information, we want you to be able to correctly check the performance of your pumps, and the Affinity Laws are the best way to do this, so get acquainted with the laws, make a cheat sheet of the formulas above, and in no time, you’ll be ready to begin calculating!