Home / Heat & fluids

Pump and system curves

Enter three points of the pump curve and the system curve to see the operating point, the effect of pumps in parallel or series, and how much a variable frequency drive saves versus a throttling valve.

Pre-sizing and estimating tool: results do not replace design, calculations or reports signed by a licensed professional, nor verification against the applicable codes and standards.

Pre-sizing
Pump curve (catalog, rated speed)
System
Flow control

Compares a throttling valve with reduced speed from a variable frequency drive (97% drive efficiency).

Economic analysis
Use the pump catalog points (paste from Excel)

Paste flow and head for several points of the manufacturer’s curve, in the page units, and efficiency in % if you have it. The curve is least-squares fitted and the three points and best efficiency point go to the fields above.

See what was read
—Operating point
—

Pump and system curves

Pump curve in the chosen arrangement, system curve, pump curve at reduced speed for the required flow, and the operating points.

Tap the chart to see the values.

Power versus flow

Electric power with throttling and with a drive, for flows from 40% to 100% of the operating point.

Tap the chart to see the values.

Project payback

Cash flow of the improvement: investment in year 0 and annual savings escalated at the rate entered, discounted at the MARR.

Tap the chart to see the values.

The report gathers this page's inputs, results, equations, assumptions and references, with fields for project, engineer and revision. In the print dialog, choose Save as PDF.

Method, assumptions and references

Equations used

Pump curve through 3 points: H(Q) = a + b·Q + c·Q²
System curve: Hsys(Q) = Hs + K·Q², with K = friction head at reference flow ÷ Qref²
Parallel (identical pumps): H(Q) = H1(Q ÷ 2); series: H(Q) = 2·H1(Q)
Affinity at relative speed s: Hs(Q) = s²·H(Q ÷ s); efficiency equal to the similar point η(Q ÷ s)
Pump efficiency: η(Q) = ηBEP · [1 − ((Q − QBEP) ÷ QBEP)²]
Electric power: P = ρ g Q H ÷ (ηpump · ηmotor · ηdrive)

Assumptions and limits

  • Water at about 68 °F (ρ = 998 kg/m³); parabolic efficiency curve around the best efficiency point.
  • Identical pumps in parallel and series; NPSH and minimum flow limits not checked.
  • Constant motor efficiency and 97% drive efficiency; at very low loads motor efficiency drops.

Standards and technical documents

  • ANSI/HI 9.6.3-2017: Rotodynamic Pumps — Guideline for Operating Regions (preferred and allowable)
  • ISO 9906:2012 / ANSI/HI 14.6-2016: Rotodynamic pumps — Hydraulic performance acceptance tests
  • Hydraulic Institute & Europump, Variable Speed Pumping: A Guide to Successful Applications
  • U.S. DOE, Improving Pumping System Performance: A Sourcebook for Industry; Pumping System Assessment Tool (PSAT)

U.S. regulations

  • DOE 10 CFR Part 431, Subpart Y: energy conservation standards for clean water pumps (PEI, including variable-load ratings)
  • DOE 10 CFR Part 431, Subpart B: electric motor efficiency standards
  • NFPA 70 (NEC), Article 430: motors and motor controllers, including adjustable-speed drives

Frequently asked questions

How do I find a pump operating point?

It is where the pump curve crosses the system curve. The calculator fits a parabola through the three catalog points and solves the intersection with H = Hs + K·Q².

Do two pumps in parallel double the flow?

No. They double flow at the same head, but the system needs more head at higher flow. The real gain depends on the system curve slope: in friction-dominated systems it is small.

When does a VFD pay off?

When flow stays below rated much of the time and the static share of head is low. With high static head, speed cannot drop much and savings shrink.