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This knowledge base article describes the value of a system resistance curve in understanding of how the various elements in a fluid piping system operate together.
System resistance curves can be used to graphically determine flows and pressures in process systems where there is typically one supply pressure or tank, a centrifugal pump, a control valve, and one destination tank or pressure. Using this graphical approach one can visually determine:
- The flow rate through a pipeline or series of pipelines
- The flow rate through a pumped system
- Determine how multiple pumps operate in a system
- Determine the differential pressure across a control valve to restrict flow to a specified value
- See how changes to the pump curve can be employed
In this article we’ll describe how to create a system resistance curve, and how to best gain information from it. In future articles we’ll discuss means of controlling the flow rate, along with limitations of a system resistance curve, and explore ways to see how to visualize more complex piping systems.
Developing the System Resistance Curve
The first step in developing a resistance curve is to develop resistance curves for each loss element found in a piping system. These elements include pipelines and components such as filters and heat exchangers. These elements are typically represented by a second order equation based on the flow rate. Equation 1 shows the basic equation
Equation 1 Determining the Pipeline Losses
The Darcy equation (Equation 2) is used to easily calculate the pipe head loss in a single pipeline for a specific flow rate.
Equation 2hL head loss in ft of fluid
f Darcy friction factor
L pipe length
D pipe diameter
v fluid velocity
g gravitational constant
By performing multiple head loss calculations for a range of expected flow rates, a curve can be developed showing the pipeline head loss for any flow rate within a defined range. See Figure 1.
Figure 1. The pipeline resistance curve is generated by calculating the head loss in a pipeline for a variety of flow rates and graphing the results.
A single pipeline head loss graph can be used to easily determine the head loss for a given flow rate. For example with a flow rate of 240 gpm through the pipeline there is a 12 ft head loss. Using this graphical approach one can easily determine the head loss for a given flow rate without having to resort to calculations.
There is no such thing as a free lunch, because the multiple head loss calculations for the various flow rates still must be performed in order to develop the curve.
Determining the flow rate from a given head loss using the Darcy equation is a much more difficult calculation. That is because both the head loss and the Darcy friction factor are a function of the velocity of the fluid through the pipeline. Since one cannot isolate the fluid velocity term in the Darcy equation, the equation must be solved using an iterative approach. In other words a guess must be made at a flow rate in order to calculate the head loss. If the head loss for the guessed flow rate does not match the desired value, the guessed flow rate must be adjusted and the calculations performed again. This process is repeated until the head loss for the improved guessed flow rate equals the desired head loss value. This approach requires multiple calculations of the Darcy equation.
Instead of performing iterative calculations the pipeline resistance curve can be used to graphically determine the flow rate. For example to determine the flow rate through the pipeline graphed in figure 1 that results in a 15 ft head loss, you can enter the curve on the head axis at 15 ft and proceed horizontally across graph until you intersect the resistance curve. In this case the flow rate of 260 gpm provides results for a 15 ft head loss in the pipeline.
Components such as filters, heat exchangers, and orifices, have a similar second order equation to that of a pipeline.
Multiple Pipelines & Components
Since a system is made of multiple pipelines, the next step is to see how to generate a system curve with multiple pipelines in a series. When the multiple pipelines (and components) are placed end to end, the flow rate through each pipeline is identical, so one can determine the head loss from multiple pipelines in series by adding the head loss for each pipeline. By graphing the pipeline resistance curves for each pipeline, the head losses for each pipeline can be added for a range of flow rates. The resulting curve shows the total head loss for all pipelines in series. Figure 2 show a composite curve of three pipelines in series.
Figure 2 – The head loss for a given flow rate or head loss can be determined from the pipeline resistance curve. The graph shows clearly the total head loss across the pipelines with a 280 gpm flow rate.
The System Resistance Curve
The performance of the pump, its head and flow rate, is shown on the manufacturers supplied pump curve. By superimposing the manufacturer's pump curve on a pipeline resistance curve, a pump system resistance curve is identified. The value of the pump system resistance curve is it shows graphically how the pump and system interact. For example the flow rate through the system occurs at the intersection of the pump curve and the pipeline resistance curves.
Figure 3 shows a typical system resistance curve, from which it can be easily determined that the intersection of the pump and system curve occurs at 403 gpm with a head of 70 ft. If there is a need to adjust the flow rate to a value other than the 403 gpm, then either the shape of the pump curve or system curve must be adjusted to achieve a different intersection point.
Figure 3- By inserting the pump curve (in red) and pipeline resistance curves (in blue) on the same graph, the flow rate through the system can be easily determined at the intersection of the two curves.
The adjustments in the flow rate (intersection point) through the system can be accomplished by:
- Installing a control valve which increases the resistance in the pipeline
- Varying the pump speed which varies the shape of the pump curve
- Varying the pumps impeller diameter which changes the shape of the pump curve.
- Varying the number of pumps in operation which changes the shape of the pump curve by the creation of a composite pump curve.
