Affinity Laws for Pumping Systems

  1. APLS is a simplified method of predicting single stage pump and system interactions for the most general system curve relationship: H=Hstatic + KQ^n, where n can be any exponent. (Normally, n=2, but any value can be used.) The one key requirement of this analysis is that the pump performance curve be linearized so that it is in the form: H=Ho+mQ, where Ho is the point where a line tangent to pump curve, at the location of interest (Q1, H1), intersects the vertical axis, i.e. the ordinate. The slope “m” represents the instantaneous slope at the point of interest. The friction only and general system curves are also linerarized at the point of interest. With these simplifications, ALPS can arrive at solutions for Qsystem and Hsystem, the expected operating point at the new conditions.
  2. You can read more details about ALPS in the August, 2007 issue of Pumps & Systems Magazine.
  1. ALPS can only be applied to a single stg pump on a system curve with the general form Hs+KQ^n.
  2. ALPS cannot handle the complication of a control valve in the pump's discharge line.
  3. ALPS is only valid for small, i.e. 0 to 10% 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.
  4. ALPS assumes you in a stable operating condition, i.e. no presence of cavitation, recirculation, etc.
  5. ALPS is intended for 1-stg pumps with specific speeds below 3000. Consult the pump manufacturer if trimming impellers for pumps with specific speeds over 3000.

Step 1: Affinity Laws for Pumping Systems
1.1 Vertical axis intersection of pump curve tangent line at point Q1,H1 (ft)
1.2 System static head (ft)
1.3 Original head (ft)
1.4 Original flow (gpm)
1.5 Starting speed (rpm)
1.6 Ending speed (rpm)
1.7 Starting impeller diameter (inches)
1.8 Ending impeller diameter (inches)
1.9 System curve exponent (H=Hs+KQn)
1.10 Pump efficiency (as a decimal)
1.11 Specific gravity
Step 2: Solve
2.1 Proof steps
2.2 Solve for Affinity Laws for Pumping Systems