# The Affinity Laws- FAQ

At Holland, we work with applications involving sanitary centrifugal pumps every day. We’ve written before about centrifugal pumps and what advantages that they can offer. We occasionally receive questions like “How does variable speed affect my pump?” or

“Why does my motor spin at 1750 rpm and not 1800 rpm?” or “How does a 3600 rpm motor differ?”. In today’s post, we are going to try to answer some of these questions by taking a look at the Affinity Laws.

Since most centrifugal pumps are directly coupled to a standard induction motor, it follows that the pump speed is most often the motor speed. And because centrifugal pumps transfer the rotational energy from the rotor into the working fluid, it should not be a surprise that the rotational velocity and the diameter of a centrifugal pumps impeller is what determines the head, or pressure, the pump can develop.

So let us start with the motor. The speed, in RPM, of an AC induction motor depends on its number of poles and the line frequency of the power supply. This can be summ

arized by the formula:

**Speed (RPM) = 2 * f (Hz) * 60-sec / Poles**

Where f is frequency, in Hertz, and poles are the number of poles of the motor. Thus we see standard electric motor speeds for a 2-pole and 4-pole motor at 60 Hz to be 3,600 rpm and 1,800 rpm, respectively. So why does your 4-pole motor spin at 1,750 rpm instead of 1,800 rpm? This is due to the physics between the motor’s rotor and stator—the rotor is trying to “catch up” with the stator’s magnetic field but it will actuall

y never quite get there. This is called motor “slip” and different motors have different levels of slip.

Now what happens if we vary a motor speed on a centrifugal pump? Thanks to VFD’s, we can take the fixed 60 Hz frequency from a power supply and vary the frequency to the motor. And by varying the input frequency to the motor, we can vary the motor speed to your heart’s desire. It’s like magic! Changing the motor speed means there is a corresponding change in the pump head, flow, and power requirements of the pump. The Affinity Laws can help determine what sort of changes one can expect. Let’s take a look at them:

- The volumetric flow (Q) is proportional to the change in motor speed (N). Algebraically, this can be written: Q
_{new}= Q_{old}* (N_{new}/ N_{old}) - The pump head, or pressure, (H) is proportional to the square of the motor speed. Algebraically this is written: H
_{new}= H_{old}* (N_{new}/ N_{old})^{2} - The power requirement (P) is proportional to the cube of the motor speed. Algebraically: P
_{new}= P_{old}* (N_{new}/ N_{old})^{3}

Another set of Affinity Laws deals with changes to the diameter of the impeller. This set of laws can help to predict flow, head, and power for geometrically scaling the pump. They are written as follows:

- The volumetric flow (Q) is proportional to the cube of the impeller diameter (D). Algebraically, this can be written: Q
_{new}= Q_{old}* (D_{new}/ D_{old})^{3} - The pump head, or pressure, (H) is proportional to the square of the impeller diameter. Algebraically this is written: H
_{new}= H_{old}* (N_{new}/ N_{old})^{2} - The power requirement (P) is proportional to the fifth power of the impeller diameter. Algebraically: P
_{new}= P_{old}* (N_{new}/ N_{old})^{5}

As you can see, centrifugal pump performance is greatly affected by a simple change in motor speed and/or impeller size. Production managers and equipment operators like to use VFD’s to increase production. However it’s important to keep in mind that increasing production means a greater head pressure and a greater demand in power. Whether you’re looking for a change in production or you simply need to size a new pump, contact a Holland Sales Engineer today.