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# Modeling a Variable Speed Pump

When designing systems in which the system demand varies (for example, HVAC systems with varying loads throughout the day or year), variable speed pumps may be an effective cost savings option.  In these systems, the pump speed can be adjusted to meet the varying demands of the system.

Figure 1 below shows a pump curve superimposed on a system resistance curve for a simple system with one pump:

Figure 1

In this example, there are two different operating points:  The design point which the pump was originally sized for is at 600 gpm.  There is also a secondary operating point which is at 400 gpm.  When the system is required to operate at 400 gpm, there are two options:

1. Run the pump at a fixed speed and introduce more resistance into the system (for example, by using a control valve).  The dP shown in Figure 1 is the pressure drop required across the valve to limit the flow rate to 400 gpm.  The energy dissipated by the valve is wasted energy.
2. Use a variable frequency drive to adjust the pump curve down to meet the 400 gpm operating point (see Figure 2 below).  This option saves energy, but the savings in operating cost must be weighed against the cost of implementing a variable speed drive.

Figure 2

Once you have determined that a variable speed drive is feasible, and you have selected the pump from a manufacturer's electronic catalog, it can be modeled in PIPE-FLO by setting the pump to run at a variable speed setting.  When a calculation is performed, PIPE-FLO applies the Pump Affinity Rules to determine the speed necessary to meet the new operating point.  The speed is calculated using the following equation:

 $\bigg(\frac{H_1}{H_0}\bigg) = \bigg(\frac{N_1}{N_0}\bigg)^2$

where:  H = pump head in feet
N = impeller speed in rpm

In the above example, you would set the pump to run at a Variable speed flow rate of 400 gpm and then run the calculations.  When you point your mouse at the pump, the fly-by viewer at the bottom of the window will indicate the pump speed has been adjusted to 2920 rpm.  Also, the pump graph window will display the adjusted pump curve.