In my seminars I talk about the three magic formulas you need to know if you want to understand how centrifugal pumps function.

Here they are:1.

As the velocity of a liquid increases, the pressure, ninety degrees to the flow, will decrease, and as the velocity of a liquid decreases the pressure, ninety degrees to the flow will increase.

2. Pressure acting on an area creates a force.

3. Velocity times area must remain a constant if liquid is to flow.

Let’s will look at each of these formulas in detail:

Formula number one explains how airplanes fly. It all started when the Wright brothers discovered the correct wing shape for an aircraft.

Look at the following diagram. You will note that the air is flowing under the wing at some velocity. The air going over the top of the wing has a longer path to travel, so its velocity must increase if it is to join with the air coming underneath the wing.

The air underneath the wing is at atmospheric pressure, but since the velocity is greater on the top of the wing the pressure falls to some value below atmospheric pressure. This causes the atmospheric pressure to push on the bottom of the wing lifting it, the airplane, and all the people inside up into the air. It will continue to do so as long as the wing is moving forward and the configuration of the wing does not change. Gravity offsets this lifting force and the aircraft flies between these two forces.

This same principle explains how an automobile carburetor works, why the shower curtain comes into the bath tub when you take a shower, and how a sailboat can sail faster than the wind.

Formula number two

explains why the wing lifted into the air:

Pressure x Area = Force

Pressure is measure in pounds per square inch (kilograms per square centimeter)

Area is measured in square inches (square centimeters)

The units for force then become pounds (kilograms) because the square inches (square centimeters) cancel out.

lbs / in^{2} x in^{2} = pounds

It is important for us to know the forces being generated because force over distance, in a given time period, is a measure of work, energy expended, or heat, depending upon which units we use.

Formula number three

explains the action of a venturi. As the area inside a venturi decreases the velocity of the fluid increases. This causes the pressure to decrease (formula #1) allowing atmospheric pressure to push a fluid into the venturi. Look at the following diagram

We use the venturi principle to add chemicals to a lawn, remove air from a condenser, add chemical to a boiler etc. It is the same principle we use to get fuel to the carburetor of your automobile.

Now we will look at the cross section of a centrifugal pump and these three formulas will explain why mechanical seals have so much trouble with shaft deflection.

This picture describes a volute pump because the impeller is not in the center of the casing. You will note that there is less clearance between the impeller and the cut water than there is between the impeller and the rest of the casing. You will also note that this area is increasing as you move from the cutwater, around the casing, to the discharge nozzle. Circular pumps have an equal area around the impeller. They are used to pump larger quantities of liquid, without having to create a head. The volute design is the most popular design because it will produce a head.

When we removed the packing from a centrifugal pump we lost a big part of the shaft support system. It therefore becomes very important that we keep the forces equal around the impeller to prevent shaft displacement. If the force increases on one side of the impeller it will deflect the attached shaft and interfere with the performance of the mechanical seal and pump bearings .

Since the impeller is symmetrical in shape (the area is the same all around the impeller) It is important that we do not let the pressure vary around the impeller or the resultant forces will not be equal. (Formula #2).

To keep the pressure equal around the impeller, you have to keep the velocity of the liquid constant around the impeller. (Formula #1).

Take another look at the cross section of the volute pump and you will note that the area (volume) surrounding the impeller is increasing as you move, in the direction of shaft rotation, from the cut water to the discharge nozzle. Formula #3

states that the velocity of the liquid times the area must remain a constant, so that means that the velocity of the liquid is decreasing as the area is increasing.

If the velocity of the liquid decreases, the pressure increases (Formula #1

.) Pressure times area creates a force (Formula #2)

and this force displaces the impeller and shaft in a direction towards 60° from the cut water.

In other words there is a constant force displacing the shaft that will impact on the performance of the mechanical seal.

If you design the impeller perfectly, and manufacture it just as it was designed, It is possible for the rotating impeller to continually add just the right amount of liquid to this volute area and prevent the velocity of the liquid from changing. When that occurs we say that the pump is operating at its best efficiency point. (B.E.P.) and there is no shaft deflection.

Centrifugal pumps seldom run at their best efficiency point (BEP). Let’s look at what happens when we go off the BEP:

If there is not enough head in the system (you are operating on the right hand side of the curve) the velocity of the liquid will increase as it approaches the discharge nozzle, causing the pressure to decrease and a force will be generated that will displace the impeller at 60° towards 240° from the cutwater.

Likewise if there is too much head on the system (you are on the left side of the pump curve), some of the fluid will recirculate back through the cutwater causing the velocity of the liquid to increase, making the pressure fall and a force will be generated pushing the impeller towards 60° from the cutwater.

Look at the diagram again and note those deflections:

In other papers on this web site I talk about methods of stabilizing the shaft for these “off design” operations. But the fact remains that shaft deflection continues to be a major source of mechanical seal problems, and will continue to be until the pump manufacturer accepts the responsibility of building a sensible pump.