*Editor's Note: This is the first in a six-part series on centrifugal pump efficiency. For other articles in this series, click *Centrifugal Pump Efficiency series.

In this multi-part series, we will investigate several aspects of centrifugal **pump efficiency**. First, I will define efficiency and give some examples. Next, I will examine some of the design criteria that ultimately dictate the efficiency exhibited by a particular pump.

I will also try to make that somewhat nebulous quantity, known as specific speed, more meaningful. I will illustrate its effect on the shape of a pump’s performance curve and overall pump efficiency.

Next, I will explain the contributions of individual pump components to a pump’s overall efficiency and show why the combined efficiency of a pump and its driver is the product, not the average, of the two efficiencies.

How pump efficiency can be preserved by changing impeller speed rather than reducing it diameter will also be examined. Then I will compare the value of peak efficiency versus the breadth of efficiency over a range of flow. The discussion will end with the importance, or sometimes unimportance, of efficiency as it relates to a particular application or process.

## What Is Pump Efficiency?

When we speak of the efficiency of any machine, we are simply referring to how well it can convert one form of energy to another. If one unit of energy is supplied to a machine and its output, in the same units of measure, is one-half unit, its efficiency is 50 percent.

As simple as this may seem, it can still get a bit complex because the units used by our English system of measurement can be quite different for each form of energy. Fortunately, the use of constants brings equivalency to these otherwise diverse quantities.

A common example of such a machine is the heat engine, which uses energy in the form of heat to produce mechanical energy. This family includes many members, but the internal combustion engine is one with which we are all familiar. Although this machine is an integral part of our everyday lives, its effectiveness in converting energy is far less than we might expect.

The efficiency of the typical automobile engine is around 20 percent. To put it another way, 80 percent of the heat energy in a gallon of gasoline does no useful work. Although gas mileage has increased somewhat over the years, that increase has as much to do with increased mechanical efficiency as increased engine efficiency itself.

Diesel engines do a better job but still max out around 40 percent. This increase is due, primarily, to its higher compression ratio and the fact that the fuel, under high pressure, is injected directly into the cylinder.

In the pump industry, much of the work involves two extremely simple, yet efficient, machines—the centrifugal pump and the AC induction motor. The centrifugal pump converts mechanical energy into hydraulic energy (flow, velocity and pressure), and the AC motor converts electrical energy into mechanical energy.

Many medium and larger centrifugal pumps offer efficiencies of 75 to 93 percent and even the smaller ones usually fall into the 50 to 70 percent range. Large AC motors, on the other hand, approach an efficiency of 97 percent, and any motor—ten horsepower and above—can be designed to break the 90 percent barrier.

The overall efficiency of a centrifugal pump is simply the ratio of the water (output) power to the shaft (input) power and is illustrated by the equation below:

**E _{f} = P_{W} / P_{S}**

*Where:*

E_{f}= efficiency

P_{w}= the water power

P_{s}= the shaft power

In the U.S., Ps is the power provided to the pump shaft in brake horsepower (BHP) and Pw is:

**P _{w} = (Q x H) / 3960**

*Where:*

Q= Flow (gallons per minute—GPM)

H= Head (feet)

The constant (3,960) converts the product of flow and head (GPM-feet) into BHP. These equations predict that a pump that produces 100 GPM at 30 feet of head and requires 1 BHP will have an overall efficiency is 75.7 percent at that flow point. An extension of the second equation also allows the computation of the BHP required at any point on a pump’s performance curve if we know its hydraulic efficiency. I will show some examples of this later in this series.

## How Is Pump Efficiency Attained?

The overall efficiency of a centrifugal pump is the product of three individual efficiencies—mechanical, volumetric and hydraulic. Mechanical efficiency includes losses in the bearing frame, stuffing box and mechanical seals. Volumetric efficiency includes losses due to leakage through the wear rings, balancing holes and vane clearances in the case of semi-open impellers. Hydraulic efficiency includes liquid friction and other losses in the volute and impeller.

Although mechanical and volumetric losses are important components, hydraulic efficiency is the largest factor. The centrifugal pump has a lot in common with the induction motor when it comes to the design phase. The commonality is that both have only two major components that can be modified by the designer. In the case of the motor, it is the rotor and the stator. For the centrifugal pump, it is the impeller and the volute (or diffuser). Let’s start our investigation of centrifugal pump efficiency with the impeller.

The affinity laws tell us quite a bit about the inner workings of an impeller. We know that, for any given impeller, the head it produces varies as the square of a change in speed. Double the speed and the head increases by a factor of four. If you keep speed constant, the same rule holds true for small changes in its diameter.

The flow through an impeller follows a similar rule, but in this case, its change is directly proportional to the speed or diameter change—double the speed or diameter, and the flow doubles. Actually, a change in rotational speed or impeller diameter refers to its peripheral speed or the speed, in feet per second, of a point at its periphery. It is this speed that determines the maximum head and flow attainable by any impeller.

The head produced by an impeller is almost entirely dependent upon its peripheral velocity, but flow is influenced by several other factors. Obviously, the width and depth (cross sectional area) of the flow passages (vanes) and the diameter of the impeller eye are important considerations as they determine the ease with which some volume of water can pass through the impeller.

Other factors such as vane shape also influence an impeller’s performance. But where do you start if you want to design an impeller from scratch? Do you take a wild guess about dimensions and shapes, make some samples and then test them?

In the early days, that is exactly what pump designers did. Today, however, they can draw on years of experience and, at a minimum, find a suitable starting point for the design. That starting point is specific speed. Next month, we will investigate specific speed and how it can predict the performance of a particular impeller.

## Where Can You Learn More?

There are many great pump books available today, but one of the classics is now available as a free download at Google Books. Pumping Machinery was authored by Arthur M. Green, a professor of mechanical engineering at Rensselaer Polytechnic Institute and was published by John Wiley & Sons over 100 years ago. It begins with a comprehensive history of pumps and ends with a detailed review of centrifugal pumps and their advances over the previous twenty years. You will be impressed at the level of knowledge possessed by the author. The number of illustrations is amazing and accounts for a significant portion of its 725 pages. This one gets an A+ rating from me.

*Pumps & Systems*, February 2012