### An excellent resource for water system designers.

by Ed Butts, PE, CPI

I discussed the fundamental concepts of pump curves and their proper use for determining total dynamic head and pump selection in two past columns (May 2005 and June 2005). Now I want to demonstrate how to calculate and develop a system head curve for use with pump curves.

This discussion will be old hat for many of you while it will be new to others. Hopefully, the information will serve as a refresher course for those who long ago learned about pump and system head curves but might not work with them on a regular basis and as a training course for those new to the business or unfamiliar with the application of pump or system head curves.

### System Head Curves: An Introduction

A system head curve is a common type of tool used in pump selection and system design and sizing. It combines elements of the performance (H-Q) curve of the specific pump under consideration with the combined static, operating, and frictional loss heads (the total dynamic head or TDH) of the system under design.

The intersection point of these two curves is generally considered as the actual operating point or the condition of service (COS) for the pump. System head curves can be a valuable tool for analyzing pumping systems with different pumps, multiple or variable head conditions, multiple pump speeds, or various impeller trims on the same sheet of paper. They are adaptable for low or high head conditions, multiple flow conditions, or with one or more pumping units.

Formerly, system head curves were developed by using a tedious process involving the plotting of various pump curve conditions against an alternating set of system capacity vs. head conditions. Advancements in computer technology now permit the same type of system head plotting in a much shorter time and with superior accuracy.

A system head curve is plotted in a similar fashion as a pump curve, but the primary difference involves the plotting of the system conditions. Both curves generally follow the same convention of plotting capacity on the “x” axis against head on the “y” axis. The specific nature of the two curves dictates the curve ascends, starting with the static head, with increasing head values along the “y” axis for the system head curve, and descends, starting with the pump’s shutoff head, along the same axis for the pump curve.

### System Head Curves: Centrifugal Pumping System

My earlier articles on pump curves detailed the fundamental concepts of pump curves, including use of the “x” or horizontal axis of the curve to display the pump capacity and using the “y” or vertical axis for the head. As an example, we examined an imaginary application of 250 GPM, calculated a total dynamic head requirement of 195 feet, and picked a pump with an efficiency of 77% to do our job (Figure 1).

Now we will use that same example and verify the acceptability of our selection by using the other factors of a pump curve, specifically the interrelationship of a pump curve with a system head curve, net positive suction head (NPSH), and horsepower.

Using a typical pumping condition and dividing the total head into static and dynamic components (Table 1)

Design flow: 250 GPM Type of pump: End-suction centrifugal pump with a 15-foot suction lift or 21 feet of total dynamic suction lift (TDSL) = (15-foot suction lift + 5.5 feet of friction losses + 0.5 foot VelocityHead)

To summarize, our typical pump selection has a static head requirement of 30 feet that, when added to the operational head and frictional losses of 165 feet, equals a total of 195 feet of total dynamic head (TDH).

Note as the suction lift increases during pumping conditions, this increase in lift will also translate to additional head. Whether this value is included in the static or dynamic column is not as important as the need to include it in the 195 feet of total dynamic head and 21 feet of total suction lift.

The static head is the component of the total dynamic head that is always present, regardless of the flow or even if the pump is on or off. The operating head is the pressure required by the system and the frictional losses are a variable totally dependent on the flow, pipe diameter, interior roughness, pipeline length, and number and type of valves and fittings.

In our example, we are examining the friction losses at a single flow rate of 250 GPM, but it must be remembered friction losses increase rapidly as the flow rate increases. Designers in some cases prefer to include factors such as operating pressure (30 psi in our example) as part of the fixed head since it is not a true variable and is always regarded as an element of the TDH.

However, for total accuracy, operating pressure often varies from system to system and is not the same as elevation, a constant and fixed static head component that should be included in the operating head category.

In order to develop a system head curve, points are plotted on a gridline throughout the operating range of the system. For the pump itself, points should be plotted beginning at the shutoff head of the pump and continuing at increasing capacity and decreasing head at intervals from 10%-30% of the flow rate increments, depending on the performance range of the pump to runout capacity. For the system head component of the curve, the initial point should be plotted beginning at the static head, the lowest conceivable operating condition, and plotted with increasing head conditions at the appropriate system capacity across the range of the curve.

### System Head Curves: Well Pump Example

In this next example, we will apply the fundamentals of selecting a pump for the same application as the first example. But this time the pump will be extracting water from a deep well with the following conditions.

We are using a submersible or alternate centrifugal pump (Figure 2), and it can be noted our imaginary water system now has a static water level (SWL), or fixed head condition, of 10 feet. As the well begins to pump, it develops a drawdown of 5 additional feet to create a pumping water level (PWL) of 15 feet. This value added to the friction loss from the pump and riser pipe creates a total well lift of 18 feet.

The balance of the system head conditions remains the same as in the previous example. This is created from the sum of all static head values, including any elevation increase or decrease, and is often considered as the minimum head plus all dynamic head conditions from the operating pressure and friction losses. In cases with an increase of elevation, the change would be shown as a positive value. For a decrease of elevation, the change would be recorded as a negative value.

A typical well system head curve is thus developed from Table 2.

If the two pumps under consideration were both centrifugal pumps, verification that the suction lift would not be excessive is often conducted next. In both examples, the maximum suction lift is estimated at 21 feet. An examination of the NPSHR in Figure 1 indicates this unit requires approximately 10 feet of NPSH at the design point of 250 GPM. As this value essentially matches the maximum lift of this pump at sea level (32 feet of NPSHA at sea level – 10 feet NPSHR = 22-foot maximum lift), the designer may wish to consider an alternate pump or redesign the suction side of the installation to lower frictional losses.

The proper use of a system head curve is nothing more than an engineering tool allowing a designer to plot the calculated values of total head, which vary according to flow, using the same axes as the capacity and head.

In our example, since we know the minimum value of head the pump must work against is the static head, we would plot this first point on the “y” vertical head axis at 30 feet (as shown in Figure 3). By calculating the total friction losses (for both suction and discharge sides) at various flow rates and then adding that value to the static head, we can create a curved or diagonal line that steadily rises from the left, or beginning side, of the curve until it intersects our design flow rate or the pump’s operational point—in this case, 250 GPM at 192-195 feet of head.

This provides confirmation to our initial design calculations and can save a significant amount of grief and embarrassment when applied correctly. As seen in Figure 3, the increase of head from the beginning value of 30 feet of static head to the ending value of 260 feet at approximately 320 GPM is comprised greatly of frictional losses.

As the flow rate increases, so do the friction losses—even if the static head remains constant throughout the operating range. This is a fundamental canon of hydraulics and what helps make the system head curve work as a design element.

In this type of example, it is also vital to keep track of the 30 psi of operating pressure and include this head value with every increasing H-Q value. As previously indicated, it is not as important to place this value into the static or dynamic head columns as it is to ensure this value is included at all points along the curve. I personally find it more conducive to include factors such as the operating pressure used to operate sprinklers in the dynamic column as this type of value is truly not a static or fixed component of the total head. However, it really doesn’t matter so long as this value is included at each H-Q point. Generally, plotting of points at each 10%-30% increment of flow increase will provide a system head curve with reasonable accuracy.

### Words of Caution

Now for a few words of caution. In our examples, the value of operating pressure has been fixed at 30 psi, or 70 feet of head, throughout the entire operational range. In the real world, although not necessarily common, the value of required pressure can conceivably increase or decrease at any point along the curve. These changes, up or down, must be included on the system head curve to maintain accuracy when they occur.

In other words, if for some reason the required operating pressure at 100 GPM was only 20 psi (or 46 feet), then the corresponding point on the system head curve line would be 10 psi or 23 feet less at 169 feet, instead of 192 feet as shown.

Another situation to be aware of, and one which is more common, is where a component of the static head can change significantly, as in a well pumping application where the pumping lift changes in relation to the flow rate. As shown in our well example, in which the static pumping lift is fixed at 10 feet but increases to 15 feet as the well is being pumped, this increase must also be reflected in the system head computations.

In the world of water wells, a variation of well lift with a change of flow rate is a typical occurrence and must be considered when plotting a system head curve. If the suction lift in the well was actually 12 feet at 125 GPM and 15 feet at the design flow of 250 GPM (not an unreasonable assumption), then the value of the plot at 125 GPM would be 3 feet less (189 feet) than the value shown in the example.

The most important aspect of using a system head curve is to calculate and plot accurate points along the curve at various flow rates, while always considering any changes in operating conditions such as pressure, pumping lifts, or frictional losses and then connecting the plots with a line.

The system head curve, when applied and used correctly, is an excellent resource for the water system designer to confirm the operating point of a pump and one I feel should be used more often in water system design.

Finally, Figure 1 and Figure 2 reflect pumps capable of delivering the needed capacity and head at the stated design condition of 250 GPM at 190-195 feet TDH. However, the slope of the pump curves are drastically different and a factor that should always be considered in design. As can be seen, the pump curve in Figure 1 reflects a pump with a flat slope with shutoff head only 5-10 feet higher than the operating condition, while the pump in Figure 2 indicates a selection with a steeper slope where shutoff head is approximately 270 feet, almost 75 feet higher than the operating condition.

Both selections have individual merits and considerations for use, although prudent caution should be employed for both. The flat curve pump is not as resistant to variations in head and more prone to a severe drop in performance for factors such as future pump wear, additional well drawdown, and possible system head increases as the pump with the steeper curve. However, the pump displayed in the Figure 1 curve is also often more energy efficient throughout its operating range and not as susceptible to over-pressuring the system if the system’s head should change. In addition, selection of a pump with an H-Q curve indicated in Figure 2 would generally provide a better response and wider speed ranges when operating with a variable frequency drive.

In all cases, it is the responsibility of the system designer to develop a system head curve with accurate conditions and plot the pump curves under consideration along the system head curve to fully evaluate possible selections and make an informed selection choice.

Until next month, work safe and smart.

Ed Butts, PE, CPI, is the chief engineer at 4B Engineering & Consulting, Salem, Oregon. He has more than 40 years of experience in the water well business, specializing in engineering and business management. He can be reached at epbpe@juno.com.