Calculating the System Curve

In order to analyze many pumping systems, a thorough understanding of "System Curve" is required. Understanding variable speed systems, parallel pump systems, and series pump systems all rely on understanding the system curve. Also, predicting the energy usage of a pump with different diameter impellers relies on an understanding of system curve. (See the Summer 2001 Newsletter on this site for a discussion of the energy savings potential of trimming pump impellers). Keys to understanding the system curve are:

1. Each piping system has a unique performance curve called its system curve.
2. The system curve defines the relationship between flow quantity through the system and the total resistance that the system offers to flow. Units most often used in the English system are GPM for flow and "feet" for total resistance where GPM is short for gallons per minute and "feet" is short for feet of head.
3. The system curve is completely independent of any pump curve. One could install any pump in a given piping system, and the system curve would not change.
4. The system curve is parabolic shaped. It can be completely defined and plotted if two operating points are known.
5. When a pump is installed and operated in a system, the point of operation (expressed in flow and head) will be at a single point where the pump curve and the system curve intersect. This is logical, because the system must operate on its curve, and the pump must operate on its curve, so the point of operation of an installed pump must be common to both curves.
6. When we "balance" a pump’s capacity by throttling a valve, we actually shift the system curve by adding or subtracting resistance to flow. The balanced point of operation is where the pump curve and "new" system curve intersect.

To draw a system curve, it is first necessary to calculate the resistance to flow through the system (the "head") at one operating point. This is normally done at the design flow point. For example, if the design flow is 200 GPM, the head is calculated at 200 GPM. The method for doing so is beyond the scope of this paper. (For a discussion of this topic go to the Technical Library tab of the Fluid Handling WEB site, and see the article entitled, "Calculating the Pump Head"). An understanding of that article is necessary to understand development of the system curve.

As discussed in the aforementioned article, the resistance to flow for a closed system consists only of friction head (also called pressure drop). Velocity head, static head, and pressure head do not affect the resistance to flow in a closed system.

It is generally accepted that the resistance to flow varies with the square of the quantity of flow. Assume that a flow rate of 100 GPM results in a friction head of 75 ft. in a given system.

• Doubling the flow in the same system to 200 GPM would result in a friction head of: (200 GPM/100 GPM)² X 75 ft. = 300 ft.
• Reducing the flow to 80 GPM in the same system would result in a friction head of:

This squared relationship allows us to plot a complete system curve very quickly once we have calculated the design flow and design head. By completing Table 1, we can quickly determine six points, which should be a sufficient number to construct a reasonably smooth curve. To use this table, one must first have calculated the design flow (DF) and the design head (DH).

Let’s look at an example:

Example 1: Assume a design flow (DF) of 200 GPM at a design head (DH) of 30.0 ft. Calculate the system curve points. The points are calculated as follows:

Remember that in closed systems, the friction head is the total head as well, so the values in the right hand column represent the heads for the system curve.

For open systems, the formula for the system head is:

Velocity head appears in italics to remind us that velocity head is generally ignored, as it is insignificant in hydronic applications (see the article called, "Calculating the Pump Head" on this WEB site for a more complete explanation).

Neither static head nor pressure head vary with flow. This is logical, because the height of the system (static head) remains fixed regardless of the flow rate; the pressures in the "beginning" and "final" vessels are independent of flow rate as well. So each point consists of friction head which varies with flow, and static and pressure heads, which do not.

Consider the following example:

A process system consists of an open tank, a pressurized tank, and piping between the two. A pump delivers water from the open tank to the pressurized tank. The friction head for the piping has been calculated at 30 ft. at 200 GPM. The water level in the pressurized tank is located 5’ above the level in the open tank. The pressurized tank operates at 4 PSIG. Calculate the points for the system curve.

Note that the friction head is exactly the same as in the previous example, so there is no need to recalculate that. The other heads are:

• Static Head = 5’
• Pressure Head = (4 PSIG –0 PSIG) X 2.31 ft./PSIG = 9.2 ft.

Remember that the static head and pressure head are fixed. We can construct the following table (Table 3).

The curves from Table 2 (for a closed system) and Table 3 (for an open system) have been plotted below in Figure 1. Note that each curve demonstrates characteristics of its particular system type.

1. The closed system curve is parabola-shaped and passes through the origin (0 GPM at 0 ft) and through the design point (200 GPM at 30 ft.). All closed system curves pass through the origin in the design point.
2. The open system curve is parabola-shaped and meets the Y axis at a head equal to the sum of the static head plus the fixed head. It also passes through the design point. All open system curves exhibit these traits.

The system curve tells us little in and of itself. However, when combined with pump curves, it is an essential element in predicting the point of operation. Therefore, it is important to understand how to construct system curves for both closed and open systems. This article outlines a procedure for doing so, and serves as the basis for understanding several other articles contained within this WEB site.

                          12130 W. Carmen Ave. / Milwaukee, WI 53225-2135 / Phone: 414-358-2646 / Fax: 414-358-8388