Combine two identical pump curves against a system curve to find the operating point — series adds head, parallel adds flow
Understand series vs parallel pump operation, the system head curve, and why parallel flow gain is less than 2×
Identical pumps combine in two complementary ways:
The operating point is where the pump (or combined) curve crosses the system curve. Both are modeled as parabolas:
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.
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.
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.
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.