Pump ED 101 Why Pump Curves Slope Down – Balancing Energy Joe Evans, Ph.D http://www.pumped101.com Have you ever wondered why the typical centrifugal pump performance curve slopes downward as flow increases? If you have, you are definitely in the minority because most of us have not. We just accept it as one of that pump’s many characteristics. There is a reason though and, it has to do with that precarious balancing act that is performed by energy. The most fundamental and important laws of physics are those that describe how some quantity, within a system, is conserved. And, one of the most useful is the “conservation of energy”. This law states that the total amount of energy, contained in an isolated system, remains constant. It can change forms or exist as a combination of forms but, the total energy can neither be increased nor decreased. And, it is the conservation of energy that best describes that sloping performance curve. Let’s begin by taking a look at an example we have all seen before. The work of Daniel Bernoulli explains a lot about hydraulics but, his theorem that describes fluid flow is a mainstay. It states that “during steady flow, the energy at any point in a conduit is equal to the sum of velocity energy, pressure energy, and potential energy due to elevation”. It also says that the sum will remain constant if there are no losses. Figure 1 shows this theorem in action.

Here, we see a pipe with water flowing left to right at 100gpm. Midway down the pipe is a narrow section but, it soon returns to its original diameter. The pressure gauge on the left is at 12 o’clock while the one in the middle is at 10 o’clock. And,

the one on the right is just a tad before 12 o’clock. So, what is happening here? If we assume that potential energy is zero, the total energy of the water flowing through the pipe is the sum of velocity and pressure energy. If flow is to remain constant, the velocity in the narrow section must increase. And, of course, it does. But, if energy is to also to remain constant the pressure in that narrow area must decrease by some proportional amount. And, this explains the lower gauge reading in the narrow section. So far this looks exactly like the conservation of energy but, why doesn’t pressure return to its original value when the water reenters the larger diameter on the right? Remember that Bernoulli says that the sum will remain constant if there are no losses. In this case we did experience a small loss due to the energy expended (as heat) in overcoming the additional friction, encountered in the narrow section. So, even though the gauge to the right shows a slightly lower pressure, total energy (which now includes heat energy) is conserved. In my September 2006 column (Centrifugal Farce and Affinity) we discussed how an impeller adds energy, in the form of velocity, to the fluid it is pumping. Well, if the centrifugal pump adds or increases energy, it doesn’t sound like it is a candidate for a conservation of energy award! Well, it turns out that once we get past the impeller it will strictly follow this conservation law. And, the whole pump can also conserve energy if we just expand the system in which it operates. Yes, that impeller does add additional energy to the pumped liquid but, it did so by converting the mechanical energy of rotation into velocity energy. And where did the mechanical energy come from? An electric motor which converted electrical energy into mechanical energy. And, that electrical energy was provided by a generator that used some other form of energy. Energy conversion and thus conservation depends on how we isolate or expand the system. Figure 2 compares the levels of velocity and pressure energy as water travels through a centrifugal pump from suction to discharge. Now, the actual energy levels will differ for every single centrifugal pump design but, the relationships shown by the chart will give you a good idea of what is happening. The dark blue area is the energy of pressure and the light blue area is that of velocity. The upper surface of the light blue area represents the total energy (pressure + velocity). In this example, the suction is under positive pressure and a valve on the pump’s discharge sets flow at BEP.

In the pump’s suction, velocity is relatively low and the energy of flow is due, primarily, to pressure. But, both remain constant during the water’s travel through this area. As water enters the impeller’s eye we see a change in the relationship of pressure and velocity. Compared to the suction, the eye is somewhat constricted so if flow is to remain constant velocity must increase. There is a proportional decrease in pressure but, total energy remains the same. Both the suction and eye areas can be considered an “isolated” system where total energy is conserved. Things change drastically as the water enters and traverses the vanes of the impeller. Pressure remains relatively constant but velocity and total energy increase continuously as the water encounters an ever increasing radius. Both velocity and total energy reach their maximum at the vane periphery. Once water exits the vanes and enters the volute, no additional energy is added. But, by the time water exits the volute the two energy forms have done a complete flip flop. This occurs because the increasing volume of the volute reduces velocity and promotes a corresponding increase in pressure. As water flows into the discharge pressure and velocity maintain a similar proportion. The volute and discharge are also an isolated system and energy is conserved in the same way as it was in our Bernoulli example. Now, suppose we use the discharge valve to change flow rate. How will Figure 2 change if we increase or decrease flow? Let’s focus our attention on the volute since a pump’s performance curve measurements are usually made at its discharge. If flow is decreased, its velocity will also decrease because the volume of water, per unit of time, traveling through the volute is smaller. And, if energy is to be conserved, pressure will increase proportionally. The exact opposite occurs when we increase flow. Since a greater volume, per unit of time, must exit the volute its velocity increases. Energy is conserved by a corresponding reduction in pressure. And, this is exactly what we see when we look at a typical performance curve - -

pressure drops as flow increases. Now, the change in volumetric velocity is not the only reason the performance curve slopes downward. It also has to due with the angle water enters and exits the impeller vanes. Right now you are probably saying to yourself - - enough already, I am convinced that conservation of energy takes place but it still doesn’t explain why pressure decreases as velocity increases and vice versa. Suppose, for a moment, that we could view water in a pipe at the molecular level. If there is no flow you would see the water molecules moving, at high speed, in every imaginable direction. They bump into both each other and the walls of the pipe, and these collisions cause them to change direction and become involved in even more collisions. Think absolute, utter chaos! It is the forces that arise from these collisions that causes water to exert a measurable pressure in all directions. When the water begins to flow, collisions between the molecules still occur but they tend to be milder because they are all traveling in the same direction. As the velocity of flow increases, even more of the molecules’ motion is in the direction of flow and the intensity of collisions is reduced proportionally. And, it is these lower collision forces that causes pressure to decrease. Many events in the field of hydraulics could be better understood if we could experience them at the molecular level. Joe Evans is the western regional manager for Hydromatic Engineered Waste Water Systems, a division of Pentair Water, 740 East 9th Street Ashland, OH 44805. He can be reached at joe.evans@pentairwater.com, or via his website at www.pumped101.com. If there are topics that you would like to see discussed in future columns, drop him an email.