Calculating System Curve
Advanced
Analysis of Pumping Systems Requires and Understanding of "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:
 Each piping system has a unique
performance curve called its system curve.
 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.
 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.
 The system curve is parabolic shaped. It
can be completely defined and plotted if two operating points are
known.
 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.
 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.
Calculate the Design Flow and Head as a
First Step to Draw the System Curve
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.
System Curve for Closed Systems
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:
(80 GPM/100 GPM)^{2} X 75
ft. = 48 ft.
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).
Table 1, Closed System Curve (Friction Head
Only)
System Flow Rate, GPM 
Friction Head Formula 
Friction Head, Ft. 
1.1 X DF 
1.21 X DH 

DF 
DH 
DH 
.75 X DF 
0.56 X DH 

.50 X DF 
0.25 X DH 

.25 X DF 
0.06 X DH 

0 Flow 
0.00 X 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:
Table 2, (Closed System)
System Flow Rate, GPM 
Friction Head Formula 
Friction Head, Ft. 
1.1 X DF = 220 
1.21 X DH 
36.3 
DF = 200 
DH = 30 
30.0 
.75 X DF = 150 
0.56 X DH 
16.9 
.50 X DF = 100 
0.25 X DH 
7.5 
.25 X DF = 50 
0.06 X DH 
1.8 
0 Flow 0 
0.00 X DH 
0.0 
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.
Calculating System Curve Points for Open
Systems
For open systems, the formula for the
system head is:
Total System Head = Friction Head + Static
Head + Pressure Head + Velocity Head
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).
Table 3 (Open System)
System Flow Rate, GPM 
Friction Head, Ft. 
Static Head, Ft. 
Pressure Head, Ft. 
Total Head, Ft. 
220 
36.3 
5.0 
9.2 
50.5 
200 
30.0 
5.0 
9.2 
44.2 
150 
16.9 
5.0 
9.2 
31.1 
100 
7.5 
5.0 
9.2 
21.7 
50 
1.8 
5.0 
9.2 
16.0 
0 
0.0 
5.0 
9.2 
14.2 
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.
 The closed system curve is
parabolashaped 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.
 The open system curve is
parabolashaped 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.
Figure 1, Typical System Curves for Open
and Closed Systems
Summary
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. 