Pump & Fan Affinity Laws and VSD Savings Lab
See the affinity laws at work: flow follows speed, pressure follows speed squared and power follows speed cubed. Put a pump or fan on its system curve, run it through a real day of part load and compare throttling, bypass and variable speed control for energy, cost and payback.
How to use: enter the design duty, the share of the head that stays fixed (static lift or the differential pressure setpoint) and pick a daily load profile. Tap i for help.
1. Inputs
2. Curves and part load
Machine curves at reduced speed with the system curve, power for each control method, and a day of operation.
3. Checks
4. Annual energy by control method
5. Hour by hour on the design day
6. How it works
Affinity laws
For the same machine at a new speed: flow changes in proportion to speed, pressure with speed squared and power with speed cubed. At 80% speed a pump delivers 80% flow at 64% head for about 51% of the power. That cube is why VSDs save so much on part load.
System curve and the fixed part
The system needs pressure to push the flow through pipes or ducts, rising with flow squared, plus a fixed part that does not fall with flow: static lift in an open system, or the differential pressure setpoint across the index circuit in a closed chilled water system. The bigger the fixed part, the less the VSD can slow down and the smaller the saving.
Control methods
Throttling closes a valve or damper and rides back up the fixed speed curve: flow drops but power only falls a little. Bypass keeps the pump at full flow and sends the surplus round a bypass, so power stays flat. A VSD slows the machine to match the system curve. ASHRAE 90.1 and the Dubai Building Code expect variable flow with VSDs on larger pumps and fans.
Model uses a typical curve shape and efficiency that holds along each affinity parabola. Use the maker's curves and a measured load profile for a real business case.