Applies To Product(s): WaterGEMS, WaterCAD, SewerCAD Version(s): CONNECT Edition, V8i Area: Modeling Original Author: Scott Kampa, Bentley Technical Support Group, Tom Walski, Senior Product Manager

# Overview

The amount of head the pump must add to overcome elevation differences is dependent on system characteristics and topology (and independent of the pump discharge rate), and is referred to as static head or static lift. Friction and minor losses, however, are highly dependent on the rate of discharge through the pump. When these losses are added to the static head for a series of discharge rates, the resulting plot is called a system head curve.

In a simple situation, where you have two sources (tanks or reservoirs) and a single pipe, the system head curve can easily be generated with hand calculations. In a more complicated situation, where there are multiple sources, multiple pumps, demands, looping pipes, branching networks, etc., doing a manual calculation for the system head curve can be difficult, and provide only a rough estimate of the system head curve. A program like WaterGEMS or WaterCAD makes solving these much easier.

A system head curve depends on tank water levels, the operation of other pump stations in the system, the physical characteristics of the pipes (roughness, minor losses, etc.), and system demands. Because of this, the system head curve will reflect the system conditions at the time of the run. As the demands and tanks levels change or as other pump statuses change, the system head curve will change too. For that reason, there is a band of multiple system head curves over the course of a model run time.

Note: the System Head Curve tool is not available in HAMMER, since HAMMER is intended for transient simulations. See: Where is the System Head Curve and Combination Pump Curve tools in HAMMER?

# What is the Definition of a System Head Curve?

Defining "System Head Curve" in such a way that it applies to all situations including complex networks can be challenging. Here is one possible definition:

"A system head curves is defined as a curve (function) relating the head that must be provided at the pump to the flow rate at that pump location. The points on the system head curve are a property of the system and are independent of the specific pump used."

Here is another one that describes what the products do:

"Actual head required at a pump is determined by the difference in head between the suction and discharge sides of the pump in the model with the pump represented by an outflow from the suction side and an inflow into the discharge side. The relationship between the head difference and the pump discharge is called the system head curve."

When generating the system head curve, WaterGEMS, WaterCAD, SewerCAD basically replaces the pump with two nodes: a suction node and a discharge node. There must be a source, either a tank or a reservoir, on either side of the pump. It is from the elevations in these sources that the head before and after the pump is determined.

Note: the System Head Curve tool is not available in HAMMER, since HAMMER is intended for transient simulations. See: Where is the System Head Curve and Combination Pump Curve tools in HAMMER?

The suction node acts like a demand while the discharge node acts like an inflow, or negative demand (both with the same flow value, just one as outflow and one as inflow). The system head curve runs a series of steady state calculations with a range of flow values. These flows are the demand and inflow values. For a given flow, the difference in head is determined on either side of the pump. As the flows change, the head will change as well. The range of flow should be reasonable for the conditions expected in the system. Once the system head curve is available, an appropriate pump can be found that will deliver the needed head at the desired flows.

A note on "Static Head" or "Static Lift" - the zero flow point on the system head curve is sometimes referred to as the "static" head but it does not necessarily mean that all flows are forced to be zero, with the head being the difference between the upstream and downstream boundary conditions. If for example you have demands downstream of a pump, when the pump flow is zero (zero flow point on the system head curve), those demands must still be satisfied by the downstream boundary (for example a tank), which will lower the HGL on the pump discharge side.

In the CONNECT Edition releases of the products, Analysis > Analysis Tools > More > System Head Curves, or by right-clicking on a pump in the model and choose System Head Curve. In the V8i releases, you can open the system head curve dialog by going to the Analysis pulldown menu and choose System Head Curve, or by right-clicking on a pump in the model and choosing System Head Curve.

Note: in SewerGEMS, System Head Curves can only be generated when using the GVF-Convex (SewerCAD) solver. See: Generating a System Head Curve in SewerGEMS

In the upper left, you would select the pump for the system head curve, as well as a maximum flow and number of intervals. The maximum flow will be automatically filled in based on the pump definition that you have assigned to the pump, but you can change this to another value if you want.

The number of intervals is how the flow range will be split. The system head curve is generated by finding the difference in head for different flows. If you have a maximum flow of 3000 gpm and an interval of 10, the program will start with a zero flow case and find the head across the pump. It will then set the flow at 300 gpm and find the head across the pump. Then it will find the head across the pump for a flow of 600 gpm, and so on. The end result will be similar to the screenshot below.

The blue line is the system head curve; the red line represents the pump definition. If you click on the Data tab, you will see the numerical results.

The columns in the screenshot above called “0.000 hours Flow” and “0.000 hours Head” are the data from which the system head curve is generated. When the flow is 0.00 gpm, the difference in head between the suction side and the discharge system of the pump is 16.4 feet. When the flow is 1500 gpm, the difference in head is 147.4 feet. (Note: The model this system head curve is based on in Example1.wtg, which can be found at C:\Program Files (x86)\Bentley\WaterGEMS\Samples\Example1.wtg.) As mentioned above, the system head curve is based on the elevation of the sources on either side of the pump, as well as the physical characteristics of the system, demands, and the status of other pumps in the model. Because of this, the system demands and the headlosses in the pipes are important for determining the head on either side of the pump.

Since the system head curve can depend on the conditions at a given time, demand patterns and a change in level in a tank will be important to the system head curve. Because of that, it is often a good idea to look at other time steps as well. The screenshot below shows the system head curves for the system at 0 hours and at 20 hours.

Between the start of the simulation and hour 20, the tank on the discharge side has been filling and thus has a higher elevation than at the start of the model run. Because of this, the head on the discharge side is higher, resulting in a higher system head curve.

The point where the system head curve and the pump definition intersect is the operating point of the pump. As conditions in the system change, the pump operation is expected to change as well.

The green line in the screenshot above is the pump definition. The blue line is the system head curve at hour 0 and the red line is the system head curve at hour 20. As you can see, the pump will need to generate more head at hour 20 since the elevation in the tank is higher at that time. Based on the pump definition, this means the flow will be slightly less than what you would see at hour 0, when the elevation in the tank is smaller.

## Setting the Vertical Axis

Starting the the CONNECT Edition releases of WaterGEMS, WaterCAD, and SewerCAD, you now have the ability to adjust the vertical axis on the system head curve. This can be useful when the head range is large and make the system head curve more legible or include the most important information. To do use this feature, select the checkbox for "Specify vertical axis limits" and enter minimum and maximum head values. This will adjust the vertical axis to include only a select range of head values.

The screenshot below shows a system head curve without limiting the vertical axis:

If you wanted to limit the vertical axis to a maximum value of 600 feet of head, select the "Specify vertical axis limits" check box and enter a minimum head 0 feet and a maximum head of 600 feet.

## Displaying a Legend

Starting with WaterGEMS and WaterCAD CONNECT Edition Update 1, you can now more easily display a legend to better understand the curves in the system head curve. Click the small black triangle next to the Chart Options button to choose the option to show the legend. This will allow you to quickly identify the curves in the System Head Curve graph. In older versions, you would need to go into Chart Options to generate the legend.

## System Head Curves for Variable Speed Pumps

Starting with WaterGEMS and WaterCAD CONNECT Edition Update 1, you can now view pump characteristic curves for different pump speeds in the system head curve tool. This provides a more accurate and complete illustration of the operating point as a VSP changes speed during the simulation. If your model includes a variable speed pump, you will see a check box that says “Show Variable Speed Pump Curves?”

Video

If you leave this unchecked, pump curves will show the pump characteristic curve at full speed. By checking this box, you will be able to view the system head curves at times that you select, as well as the pump curve at the relative speed factor calculated at that time step.

The screenshot above shows system head curves at hours 0, 10, and 24 (which are curving up) and the pump definition (which are curving down) at the calculated relative speed factor at hours 0, 10, and 24. The color coding used for both the pump curve and the system head curve is the same for each time step being displayed. The color coding is set up this way to clarify which system head curve relates to which pump definition. For instance, for the curves at hour 0 (denoted in blue), the pump is operating at a relative speed factor of 0.824, as shown in the legend. The operating point is where the pump curve and the system head curve at hour 0 intersect, which is a flow of 1500 gpm and a head of 155 feet. It is important to note that where the system head curve for hour 0 intersects the pump curve at hours 10 and 24 are essentially meaningless, since the pump doesn’t operate at the same relative speed factor at these times.

The gray pump curve that is displayed is the pump curve at full speed, or a relative speed factor of 1.0. If one of the pumps happened to operate at full speed at some point during the calculation, the gray curve would be replaced by the actual pump curve. Where the system head curve intersects with the pump curve at full speed would give the user an idea of the operating point if such a condition were used at that time step. You can add a legend to the system head curve by clicking the Options button and selecting Show Legend. See the section “Show Legend option added to System Head Curve dialog” below for details.

# Troubleshooting

### System Head Curves in Closed Systems

Normally a system head curve is determined based on a system where there is a source of flow on either side of the pump. However, there may be cases where you want to find a system head curve for a closed system or a system with no downstream source.

If you tried to compute a system head curve with no downstream source, you may end up with a curve that looks similar to the one below:

The system head curve option is invalid for this condition. The scale exaggeration throws off the graph--really what we are seeing plotted is a near-vertical line for the system head curve. This is displayed as a large change in head for a small change in flow. Only the single point at which the pump is operating (the point where the system head curve and the pump curve intersect) is valid since the flow from the pump can only be the demanded flow on the discharge side.

However, it is possible to find a valid system head curve in a closed system if you use pressure dependent demands. With pressure dependent demands, the demands can change based on the pressure at a node. This provides WaterGEMS and WaterCAD with the information necessary to create an accurate system head curve. Note: when using PDD with system head curves and no downstream storage, it is important that the PDD function be configured to have no threshold limit. This way, with increasing pressure the PDD demand can be increased above the base demand of the corresponding scenario to calculate the system head curve for flows larger than the total demand of all demand nodes in the closed network.

Note: If the tank on the upstream or downstream end of the pump is empty, you will see results like this as well. If a tank is empty, the results will not be valid.

### Impact of other pumps and multiple downstream tanks

The system head curve will be dependent on the status of other pumps in the system. If you look at the graph, the y-intercept is only equal to 'static head' in the simple case where there is one pump in the system. However, if you have more than one pump the results are slightly different.

Take an example where you have two pumps in parallel, PMP-1 and PMP-2. When looking at the system head curve for PMP-1, the value where Q=0 is the minimum head that a pump must provide before it can deliver any water into the pipeline. This is dependent on what the second pump in your system is doing. When PMP-1 and PMP-2 are both off (and assuming there are no demands in the system), the hydraulic grade (HG) elevation at the common downstream node is the level of water in the downstream reservoir. The minimum head that pump PMP-1 must provide before it can deliver any water is the difference between the HG on the discharge side of the pump and the suction side of the pump. That is what we know as “static head.”

Now, if PMP-2 is turned on and PMP-1 is still off, the HG elevation at the common downstream node, would be something higher than when both pumps are off, since PMP-2 is now adding head. The minimum head that PMP-1 must provide before it can deliver any water is the difference between the HG on the discharge side and the HG on the suction side. This explains the head value on the system head curve when flow is zero. You could say that pump PMP-1 must overcome the static head plus the dynamic head of PMP-2 before it can deliver any water.

If you are designing PMP-1, you must pick a pump that works well when PMP-2 is either on or off, so you need to look as system head curves for both cases.

Note that if you have the latest version of WaterCAD or WaterGEMS, you can use the Combination Pump Curve tool, which always shows the system head curve with all others pumps turned off.

If you have a case where there are multiple tanks downstream of the pump, this can be difficult to calculate by hand as well, since the hydraulic grade at the tanks may be different values. However the system head curve in WaterGEMS and WaterCAD will be looking at the cumulative impact of the tanks when looking at the head across the pump and the hydraulic grade on the discharge side.

As you can see from the screenshots above, system head curves are often parabolic, with the flow increasing with an increase in the head across the pump. However, there can be cases where the curve is not parabolic.

The most common reason for a system head curve that is not parabolic is water consumption between the pump and the downstream tank. When this consumption occurs, it lowers the system head at low flow. In fact, if the consumption between the pump and tank is greater than the pump output (such that flow goes from the tank toward the pump), then there is an inflection point in the pump curve.

If you want to check this out manually, put a single large demand between the pump and tank. WaterGEMS and WaterCAD will handle this automatically.

If the system head curve (not the pump curve) appears very flat, typically this indicates very little resistance (headloss) for the entire range of flow on the pump curve. Meaning, as the flow increases, the pipes are too smooth or large to induce any significant headloss. Check the diameter, roughness and length of pipes. Also check the pump curve to ensure that the flow units and range of flow is correct.

### Sudden change (or "kink") in system head curve

Usually a kink in the curve indicates that there has been some discrete change in the system. It may be a PRV or other dynamic valve changing position or a different pump is turning off when the flow through the pump reaches a certain point. Also see this forum post

### Manually generating a system head curve

With a simple system, it is possible to manually generate a system head curve. Detailed steps on doing this can be found in the Advanced Water Distribution Modeling and Management book available from Bentley’s website.

The easiest way to arrive at the system head curve is to remove the proposed pump from the model, leaving the suction and discharge nodes in place. For the curve to be computed properly, a tank or reservoir must be present on each side of the pump.

### System Head Curves with intermediate high point

The system head curve is based on the head values at sources on the upstream and downstream side of the pump. The pumps (and the system head curve) does not take into account intermediate highs points, which in model cases can result in negative pressures at the highs points. An air valve can be used to mitigate these negative pressures. When an air valve is present in the model, the system head curve may use the air valve as part of the calculation.

When you start up a pump, the downward sloping part of the pipe at the air valve will generally be empty or part-full. In such a case, you would calculate the system head curve from the suction reservoir to the air valve at the high point. Once the pipe is full, you would calculate the system head curve for the entire pipeline.

There are some exceptions to this. In some cases, the downward sloping pipe is so large and steep that it never runs full and the system head curve is always to the high point. In addition, if you don't have an air valve and the hydraulic grade at the high point drops below the vapor pressure of the fluid, the fluid will turn into vapor. This shows the importance of having an air valve at high points that are susceptible to negative pressure. Ideally, you would make the downward pipe so small that it easily flows full or so large that it always flows partly full. This will make the calculation of the system head curve easier over the course of the simulation.

### Option 1 - Exporting Data

If you're looking to export the data used to create the system head curve, do the following. After generating the system head curve, select the "Data" tab. Next, highlight the column headers and press CTRL+C to copy the data to the clipboard. You can then paste it into an external application, such as Excel

### Option 2 - Exporting Graph

To export the graph itself, either right-click on the choose "Chart Options" or click the Chart Options button above the graph.

Next, click the "Export" tab, choose the desired format, and click Save

There are a number of support solutions that already exist for some of the items described above. You can find those solutions below:

System Head Curves with no downstream storage

Pump Selection for a Closed System

System Head Curve changing depending on the statue of other pumps

Pump Stations and Combination Pump Curves

How to manually generate a system head curve

Estimating a pump curve for WaterGEMS and WaterCAD (pump design)

The following papers have information on system head curves as well:

Paper: Ormsbee, L. and Walski, T. "Developing System Head Curves for Water Distribution Systems," Journal AWWA, Vol. 81, No. 7, July 1989.

Paper: Walski, Hartell and Wu, 2010, "Developing system head curves for closed systems" JAWWA, 102:9:84, September.

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