Sanitary Pump 101- Affinity Laws & Centrifugal Pump Control

In today’s installment of Sanitary Pump 101, we’re going to take a look at sanitary centrifugal pumps, specifically how they operate and what dictates performance and then how we can control them. In other words, the affinity laws. The affinity laws are a set of formulas that explain the relationship between shaft or impeller speed, discharge head, impeller diameter, and flow rate. With the affinity laws, we can predict how changes to one variable will impact the overall performance of the pump. Those are the Cliff Notes. Now let’s take a closer look!

The Affinity Laws

Let’s start by taking a look high level, whiteboard look, at the affinity laws. Unlike with a positive displacement pump, which gives us a fixed displacement per revolution regardless of pump discharge head, centrifugal pump performance is dictated by the affinity laws. For centrifugal pumps, the affinity laws state that:

  1. Flow is proportional to shaft speed or impeller diameter

Q1/Q2= (N1/N2) or (D1/D2)

  • Pressure is Proportional to the Square of Shaft Speed or Impeller Diameter

H1/H2 = (N1/N2)2 or (D1/D2)2

  • Power is proportional to the cube of shaft speed or impeller diameter

P1/P2= (N1/N2)3 or (D1/D2)3

So what do all of these formulas really mean? What they tell us is that for a given speed and impeller size, we’ll get predicted flow rate, discharge head, and power consumption. And because of this relationship, we can predict how the pump will perform with different impeller sizes, discharge heads, and speeds and we’ll also know what the power consumption is at each duty point. Basically, we can create curves that allows us to predict performance and size a pump.

Centrifugal Pump Control

Once we have the pump curves (which most manufacturers make widely available), we can see that we have three levers we can pull to change pump capacity or flow- speed, impeller size, and discharge head.

If we reduce the speed of the pump, we’ll reduce the flow and discharge head of the pump. This can be accomplished using a variable frequency drive.

If we put an orifice or restriction valve into the line, we will increase the discharge head, which will decrease capacity. If we decrease the discharge head, we’ll not only increase the capacity, but also power consumption. In the real world, this can manifest itself with the pump “kicking out” or tripping a VFD.

And finally, if we increase the impeller size, we’ll increase discharge head, pump capacity, and power consumption.

Hopefully your head doesn’t hurt. What is important to remember is that centrifugal pump performance is governed by the affinity laws which state that pump capacity, discharge head, speed, and impeller diameter are all related. And by altering one variable, we change the others. This means that if we need to get more flow from a centrifugal, we should look at increasing the impeller size or shaft speed, but be mindful that we’re also going to increase our power consumption. And if the pump is running off the curve and kicking our motor out, all we need to do is throttle it back.

And finally, if you have any questions about your centrifugal pumps performance or control, please contact a Triplex Sales Engineer today.

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