## Maximizing the Value of the System Resistance Curve for Branching Systems

Generating a system resistance curve for piping systems with multiple destinations can often be challenging. In this article we will explore these difficulties as well as how this type of system can be better understood using a Pump System Energy Balance.

By calculating the static head, along with the fluid losses in the pipelines for various flow rates we are able to develop a pipeline resistance curve. By superimposing the pump curve on the pipeline resistance curve we can develop a system resistance curve. The maximum flow rate through the system occurs where the pump curve intersects the pipeline resistance curve.

To achieve a different flow rate through the system we must either change the shape of the system curve (by adding a control valve), or the pump curve (by trimming the impeller or adjusting the pump speed). This method works for a system consisting of a single source of fluid, single pump and single destination. It quickly becomes much more difficult to show this graphically when multiple destination tanks are added.

In this example, we will look at a system with one source of fluid, one pump and two destination tanks. The system in Figure 1 shows a single pump feeding a common header supplying fluid to two destinations. In order to develop a pipeline resistance curve, there are two destinations for the fluid to go. By attempting to calculate the system resistance by fixing the flow rate through the pump to a set value, we cannot perform a direct calculation because with two unconstrained flow rates in the paths we have a hydraulic network. Figure 1. Here is a system with multiple destinations at different tank elevations, levels and pressures.

The following steps are the only way to develop a system curve:

1.     Develop a pipeline loss curve as a function of the flow rate for each pipe in the system.
2.     Develop the pipeline resistance curves for path 1, taking into account the static head component from the junction to tank 1.
3.     Develop the pipeline resistance curve for path 2, once again taking into account the static head component from the junction to tank 2.
4.     Combine the two parallel paths by taking a head value and summing the flow rates from the resistance curve to arrive at a combined flow rate for the parallel paths.
5.     Develop the pipeline resistance curve for pipe 1 and pipe 2 in series, taking into account the static head from the supply tank to the elevation of the junction.
6.     Combine the curves from steps 4 and 5 to develop a system curve.
7.     Superimpose the system curve on the pump curve to develop a system resistance curve. Figure 2 – The resulting system resistance curve consisting of the combined static head and combined dynamic head. The intersection of pump and system curve is balanced flow rate.

Unlike the resistance curve for a system with only one destination pipe we are not able to determine flow rate through each path because the flow can go down either path. The system resistance curve with multiple paths will show the total flow through the pump but not through each branch. This is because of the two paths available for the fluid to flow. If any changes are made to the system (valve position, tank level or pressure), then we will need to create a new system curve. Also the difference between the pump and resistance curves does not represent the differential pressure across the control valves, which is common in the single circuit curve.

Now for the good news, in most process piping systems the flow rate through each branch is constrained to a set value and regulated by a control valve. For example, to limit the flow rate through each branch to 300 gpm, the valves would have to be throttled to the set amount. If the flow rate through branch 1 was set to 400 gpm and branch 2 to 200 gpm the value positions would have to change. There is no easy way to determine the required differential pressure across the controls with multiple destinations using a system resistance curve, because any change to one of the paths will change the flow rate through both paths.