Affinity Laws for Pumping Systems (ALPS) - Part Two


Written by:
Robert X. Perez

If your VFD and motor system can control to increments of 20-rpm or less, this means (in theory) you can reliably control flow in increments as small as 5.62-gpm. If this is tolerable for your process, this means that VFD control can be used in place of a control valve. (Note: I have been told by VFD experts that speed can readily be controlled in increments of ±0.5 percent or less. In this example, 0.5 percent of 3600-rpm is about 18-rpm.)

Caveats

You can see that ALPS is a powerful new tool for pump professionals, but it's not without its caveats. I want to clearly emphasize when and where ALPS should be used and when it shouldn't:

  • ALPS can only be applied to a single pump "riding" on a system curve with the general form Hs + KQn.  ALPS cannot handle the complication of a control valve in the pump's discharge line.
  • ALPS is only valid for small (0 percent to 10 percent) changes in speed or impeller diameters, similar to the affinity laws.
  • ALPS results are only estimates. If a more detailed analysis is required, you should graphically analyze the pump and systems curves.
  • The analysis assumes you in a stable operating condition, i.e. no presence of cavitation, recirculation, etc.

Closing Comments

To use ALPS, simply visit PumpCalcs.com and proceed to the expert calculator titled "ALPS." This offers users a new means of analyzing VFD applications and investigating impeller change implications. I hope ALPS finds its way into your pump analysis toolbox.  

References

  1. Karassik, Igor, et al, Pump Handbook, New York, McGraw-Hill Book Company, 1976, pp 2.135-2.142.
  2. Lobanoff, Val, Ross, Robert, Centrifugal Pump - Design and Application, Houston, Gulf Publishing, 1992, pp 12-14.

Appendix

Derivation of the ALPS Equations

Figure A. ALPS TriangleThe ALPS equation is based on the simple triangle that is formed by the linearized versions of the friction only system curve, friction + static head system curve and pump curve (see Figure A).

Point Q1, H1 of the triangle is the starting point. Point Qaffinity, Haffinity is the where the linearized H = KQ2 curve and linearized pump curve meet. Here, we assume the pump curve, in the simplified form H = Ho + mQ, is displaced upward according to the affinity laws while maintaining its same slope (m). Finally, point Qsystem, Hsystem is where the system curve and the displaced pump performance line meet.

Next, we assign 1) the slope of the H = KQ2 line at Q1, H1 the label A; 2) the slope of the system curve at Q1, H1 the label B; and 3) the slope of the linearized pump curve the label C.

 

Affinity EquationsWe can solve for Hsystem and Qsystem by starting with the relationships above.  

Thus, we can state that by knowing a few basic pumping system parameters, we can estimate the effect of small pump speed or impeller diameter changes on system performance. The PumpCalcs.com expert calculator entitled "APLS" does all of this math for you.

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See also:

Upstream Pumping Solutions

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