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Pumps in Series & Parallel Calculator

Combine two identical pump curves against a system curve to find the operating point — series adds head, parallel adds flow

🔗 Pumps in Series & Parallel
Enter one pump's curve (shutoff head + a rated point) and the system curve (static head + friction at the rated flow). The calculator combines two identical pumps and reports the operating point for the single, series, and parallel arrangements — where each pump curve intersects the system head curve.

Single Pump Curve

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Head developed at zero flow (top of the pump curve).
GPM
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Head at the rated flow. Must be less than the shutoff head (H₀ > Hr).

System Curve

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Elevation + pressure head the system must overcome at zero flow.
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System friction loss at the rated flow (Qr). Sets the curvature C = H_f / Qr².
Two identical pumps are assumed. The pump curve is fitted as H = H₀ − k·Q²; the system curve as H = Hstatic + C·Q².

What This Calculates

Single-Pump Point:
The flow and head where one pump's curve meets the system head curve.
Series (2 Pumps):
Heads add — the combined curve reaches a higher head, giving the high-lift / high-pressure operating point.
Parallel (2 Pumps):
Flows add — the combined curve delivers more flow, plus the flow gain vs a single pump (always < 2×).
Fitted Curves:
The pump coefficient k and system coefficient C used to model H = H₀ − k·Q² and H = Hstatic + C·Q².

📘 Series vs Parallel

Identical pumps combine in two complementary ways:

Series — heads add
  • At any flow, the combined head is the sum of each pump's head.
  • Two identical pumps double the shutoff head: 2·H₀.
  • Use for high-lift or high-pressure duty one pump can't reach.
Parallel — flows add
  • At any head, the combined flow is the sum of each pump's flow.
  • Each pump passes half the total flow (Q/2).
  • Use for high-flow duty; gain is < 2× because the system curve steepens.
Which to choose
  • Steep (friction-dominated) system → series helps more.
  • Flat (static-dominated) system → parallel approaches 2× flow.

How the Operating Point Is Found

The operating point is where the pump (or combined) curve crosses the system curve. Both are modeled as parabolas:

Pump:   H = H₀ − k·Q²   (k = (H₀−Hr)/Qr²)
System: H = Hstatic + C·Q²  (C = Hf/Qr²)

Single:   Q = √[(H₀−Hstatic)/(k+C)]
Series:   Q = √[(2H₀−Hstatic)/(2k+C)]
Parallel: Q = √[(H₀−Hstatic)/(k/4+C)]

Series doubles the curve's shutoff head and slope; parallel quarters the slope (each pump passes Q/2). The head at each point follows from the system curve, H = Hstatic + C·Q².

Standards Reference

  • ANSI/HI 1.3: Rotodynamic pump curve combination (series & parallel operation)
  • System head curve: H = Hstatic + C·Q² (rotodynamic pump application)
  • API 610: Centrifugal pumps for petroleum & gas service
  • Cameron Hydraulic Data / HI 1.6: Performance testing & curves

Frequently Asked Questions

Series vs parallel — what changes about the pump curve?

Pumps in series add head at the same flow: two identical pumps deliver twice the head of one at any given flow. Pumps in parallel add flow at the same head: two identical pumps deliver twice the flow of one at any given head. Series is for high-head (high-lift or high-pressure) duty; parallel is for high-flow duty where one pump cannot pass enough volume.

Why doesn't two pumps in parallel double the flow?

Parallel doubles the pump capacity at a fixed head, but the system does not run at a fixed head. As total flow rises, friction loss grows with the square of flow, so the system curve steepens and the new operating point lands at a higher head and well below twice the single-pump flow. The flatter the system curve (friction-light, static-dominated), the closer parallel comes to 2× flow.

How is the operating point found?

The operating point is the intersection of the pump (or combined) head curve with the system head curve. Each pump is modeled as a parabola H = H₀ − k·Q² fitted to the shutoff head and a rated point; the system is modeled as H = Hstatic + C·Q². Setting the two equal and solving for Q gives the operating flow, and the system curve gives the matching head. Series uses 2·H₀ − 2k·Q²; parallel uses H₀ − (k/4)·Q² because each pump passes half the total flow.