Centrifugal Pump Design Calculations

[Merilyn Mardis]

Totalhead and flow are the main criteria that are used to compare one pump with another or to select a centrifugal pump for an application. Total head is related to the discharge pressure of the pump. Why can't we just use discharge pressure? Pressure is a familiar concept, we are familiar with it in our daily lives. For example, fire extinguishers are pressurized at 60 psig (413 kPa), we put 35 psig (241 kPa) air pressure in our bicycle and car tires.For good reasons, pump manufacturers do not use discharge pressure as a criteria for pump selection. One of the reasons is that they do not know how you will use the pump. They do not know what flow rate you require and the flow rate of a centrifugal pump is not fixed. The discharge pressure depends on the pressure available on the suction side of the pump. If the source of water for the pump is below or above the pump suction, for the same flow rate you will get a different discharge pressure. Therefore to eliminate this problem, it is preferable to use the difference in pressure between the inlet and outlet of the pump.

The manufacturers have taken this a step further, the amount of pressure that a pump can produce will depend on the density of the fluid, for a salt water solution which is denser than pure water, the pressure will be higher for the same flow rate. Once again, the manufacturer doesn't know what type of fluid is in your system, so that a criteria that does not depend on density is very useful. There is such a criteria and it is called TOTAL HEAD, and it is defined as the difference in head between the inlet and outlet of the pump.

You can measure the discharge head by attaching a tube to the discharge side of the pump and measuring the height of the liquid in the tube with respect to the suction of the pump. The tube will have to be quite high for a typical domestic pump. If the discharge pressure is 40 psi the tube would have to be 92 feet high. This is not a practical method but it helps explain how head relates to total head and how head relates to pressure. You do the same to measure the suction head. The difference between the two is the total head of the pump.

Total head is the height that the liquid is raised to at the discharge side of the pump less the height that it is raised to at the suction side (see Figure 25). Why less the height at the suction side? Because we want the energy contribution of the pump only and not the energy that is supplied to it.

What is the unit of head? First let's deal with the unit of energy. Energy can be expressed in foot-pounds which is the amount of force required to lift an object up multiplied by the vertical distance. A good example is weight lifting. If you lift 100 pounds (445 Newtons) up 6 feet (1.83 m), the energy required is 6 x 100= 600 ft-lbf (814 N-m).

Head is defined as energy divided by the weight of the object displaced. For the weight lifter, the energy divided by the weight displaced is 6 x 100 / 100= 6 feet (1.83 m), so the amount of energy per pound of dumbbell that the weight lifter needs to provide is 6 feet. This is not terribly useful to know for a weight lifter but we will see how very useful it is for displacing fluids.

You may be interested to know that 324 foot-pounds of energy is equivalent to 1 calorie. This means that our weight lifter spends 600/324 = 1.8 calories each time he lifts that weight up 6 feet, not much is it.

If we use energy to describe how much work the pump needs to do to displace a volume of liquid we need to know the weight. If we use head, we only need to know the vertical distance of movement. This is very useful for fluids because pumping is a continuous process, usually when you pump you leave the pump turned on, you don't start and stop the pump for every pound of fluid displaced. We are mainly interested in establishing a continuous flow rate.

The other very useful aspect of using head is that the elevation difference or static head can be used as one part of the value of total head, the other part being friction head as shown in these next figure. One shows the friction head on the discharge side and the other the friction head on the suction side.

How much static head is required to pump water up from the ground floor to the second floor, or 15 feet up? Remember that you must also take into consideration the level of the water in the suction tank. If the water level is 10 feet below the pump suction connection then the static head will be 10 + 15 = 25 feet. Therefore the total head will have to be at least 25 feet plus the friction head loss of the fluid moving through the pipes.

Friction head is the amount of energy loss due to friction of the fluid moving through pipes and fittings. It takes a force to move the fluid against friction, in the same way that a force is required to lift a weight. The force is exerted in the same direction as the moving liquid and energy is expended. In the same way that head was calculated to lift a certain weight, the friction head is calculated with the force required to overcome friction times the displacement (pipe length) divided by the weight of fluid displaced. These calculations have been done for us and you can find the values for friction head loss in Table 1 for different pipe sizes and flow rates.

Table 1 gives the flow rate and the friction head loss for water being moved through a pipe at a typical velocity of 10 ft /s. I have chosen 10 ft/s as a target velocity because it is not too large which would create allot of friction and not too small which would slow things down. If the velocity is less, then the friction loss will be less and if the velocity is higher the loss will be greater than is shown in Table 1. For the suction side of the pump, it is desirable to be more conservative and size pipes for a lower velocity, for example between 4 and 7 feet/second. This is why you normally see a bigger pipe size on the suction side of the pump than on the discharge. A rule of thumb is to make the suction pipe the same size or one size larger than the suction connection.

The pump characteristic curve has a similar appearance to the previous curve shown that I also called a characteristic curve that showed the relationship between discharge pressure vs. flow (see Figure 21). As I mentioned this is not a practical way of describing the performance because you would have to know the suction pressure used to generate the curve. Figure 30 shows a typical total head vs. flow rate characteristic curve. This is the type of curve that all pump manufacturers publish for each model pump for a given operating speed.

Not all manufacturer's will provide you with the pump characteristic curve. However, the curve does exist and if you insist you can probably get it. Generally speaking the more you pay, the more technical information you get.

It is unlikely that a centrifugal pump, bought off the shelf, will satisfy exactly your flow requirement. The flow rate that you obtain depends on the physical characteristics of your system such as friction which depends on the length and size of the pipes and elevation difference which depends on the building and location. The pump manufacturer has no means of knowing what these constraints will be. This is why buying a centrifugal pump is more complicated than buying a positive displacement pump which will provide its rated flow no matter what system you install it in.

To size and select a centrifugal pump, first determine the flow rate. If you are a home owner, find out which of your uses for water is the biggest consumer. In many cases, this will be the bathtub which requires approximately 10 gpm (0.6 L/s). In an industrial setting, the flow rate will often depend on the production level of the plant. Selecting the right flow rate may be as simple as determining that it takes 100 gpm (6.3 L/s) to fill a tank in a reasonable amount of time or the flow rate may depend on some interaction between processes that needs to be carefully analyzed.

The friction head depends on the flow rate, the pipe size and the pipe length. This is calculated from the values in the tables presented here (see Table 1). For fluids different than water the viscosity will be an important factor and Table 1 is not applicable.

According to calculation or the use of tables which is not presented here the friction loss for a 1" tube is has a friction loss of 0.068 feet per feet of pipe. In this case, the distance is 30 feet. The friction loss in feet is then 30 x 0.068 = 2.4 feet. There is some friction loss in the fittings, let's assume that a conservative estimate is 30% of the pipe friction head loss, the fittings friction head loss is = 0.3 x 2.4 = 0.7 feet. If there is a check valve on the suction line the friction loss of the check valve will have to be added to the friction loss of the pipe. A typical value of friction loss for a check valve is 5 feet. A jet pump does not require a check valve therefore I will assume there is no check valve on the suction of this system. The total friction loss for the suction side is then 2.4 + 0.7 = 3.1 feet.

According to calculation or the use of tables which is not presented here the friction loss for a 3/4" tube is has a friction loss of 0.23 feet per feet of pipe. In this case, the distances are 10 feet of run on the main distributor and another 20 feet off of the main distributor up to the bath, for a total length of 30 feet. The friction loss in feet is then 30 x 0.23 = 6.9 feet. There is some friction loss in the fittings, let's assume that a conservative estimate is 30% of the pipe friction head loss, the fittings friction head loss is = 0.3 x 6.9 = 2.1 feet. The total friction loss for the discharge side is then 6.9 + 2.1 = 9 feet.

What is the pump rating? The manufacturer will rate the pump at its optimum total head and flow, this point is also known as the best efficiency point or B.E.P.. At that flow rate, the pump is at its most efficient and there will be minimal amount of vibration and noise. Of course, the pump can operate at other flow rates, higher or lower than the rating but the life of the pump will suffer if you operate too far away from its normal rating. Therefore, as a guideline aim for a maximum variation of plus or minus 15% on total head.

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