§ 7.3 Module 7 — Matching and Optimising
Parallel pumps add flow at equal head. The system decides how much of that sum survives.Module 7
By the end of this lesson
Two identical pumps in parallel share suction and discharge nodes, so each sees the same differential head. At each head, add their flows: the two-pump curve has Qset(H) = 2Qsingle(H). Pumps in series pass the same flow through one after another, so add head at each flow: Hset(Q) = 2Hsingle(Q). Adding both axes, or doubling one rated point, constructs neither curve.
For unlike pumps, parallel construction still adds flows at equal head, but the arithmetic must respect check valves and each unit's stable range. A stronger pump can force a weaker one toward shutoff or reverse flow if isolation fails. Series operation likewise requires compatible flow ranges and pressure ratings between stages. These are curve constructions first and piping decisions second.
single: H = H0 - k Q²
parallel (n): H = H0 - k (Qtotal/n)²
series (n): H = n(H0 - k Q²)For H = H₀ − kQ², the ideal identical-pump combinations are exact.
The doubled-flow statement belongs to one chosen head on the pump chart. The station does not remain at that head. As total flow rises, the system curve asks for more head; at the same time each pump's curve supplies less head at greater flow. The new operating point therefore lands well short of twice the one-pump flow.
With the teaching curves Hp = 42 − 900Q² and Hs = 18 + 2 500Q², one pump delivers 84.0 L/s. Two in parallel satisfy 42 − 900(Q/2)² = 18 + 2 500Q², giving 93.8 L/s: only 11.7% more flow, not 100%. The numbers are intentionally severe to expose the mechanism. The real gain comes from the actual curves.
A catalogue convention that became a persistent mistake
Manufacturers correctly plot parallel curves by summing flow at equal head. Trouble begins when that construction is copied without the system curve and retold as “two pumps give twice the flow.” Early multi-pump waterworks already staged units to follow demand; modern controls change the starting sequence, not the hydraulic rule. The missing rising curve is the entire error.
Interactive 3D instrument
Add a pump, then let the system answer
A 3D instrument you drive yourself, one variable at a time. It needs JavaScript and WebGL, so it is not shown in this static copy of the page.
Parallel operation adds flow at equal head — you add the curves horizontally. But adding flow raises system friction as the square of flow, so the combined operating point climbs to a higher head where each pump delivers less than it did alone. The steeper the system curve, the worse the return.
On a friction-dominated force main, two identical pumps commonly deliver 1.3–1.5 × the single-pump flow, and three deliver barely more than two. On a static-dominated system the gain is much closer to double, because the system curve is nearly flat. Same pumps, same station, completely different answer — and the difference is a property of the pipe, not the pumps.
Size for firm capacity from the actual N−1 combined curve intersection. If parallel gain is poor, the fix is a larger force main or a different pump, not more pumps — a third pump on a steep system can add almost nothing while adding a full set of valves, controls and failure modes.
Parallel units are valuable when demand varies, because one smaller pump can operate efficiently at low duty and additional units can be staged. They also provide redundancy, though firm capacity must be checked with the largest unit unavailable. They are least useful as a cure for a long, undersized main: that steep system curve consumes the added pump curve as head rather than flow.
Series pumps are a head solution: high lift, pressure-zone transfer or a staged booster arrangement. They do not increase zero-head flow the way parallel pumps do, and every downstream casing, seal and valve must withstand the accumulated pressure. In sewage service, solids passage and blockage risk may rule out an arrangement that looks attractive on clean-water curves.
| Need | First hydraulic response | Check before choosing |
|---|---|---|
| variable demand | parallel staging or speed control | each stage's BEP region and starts |
| more head at similar flow | series/staged boost | interstage pressure rating |
| more flow on a steep main | reduce system resistance | larger/parallel main lifecycle cost |
| firm capacity | multiple units | largest unit out, real system curve |
Check your understanding
Combine the curves
1 auto-graded question with an explanation for every wrong answer. Requires JavaScript. (m7-l3-q1)
Report both the total and the increment: “one pump 84 L/s; two pumps 94 L/s; second-pump increment 10 L/s.” The increment is what must justify the added pump energy, maintenance and controls. Then compare it with flattening the system curve through a larger main, opening an inadvertently throttled valve, or selecting a pump whose curve matches the duty. A nearly useless second pump is a symptom of resistance, not a mysterious pump defect.
Manufacturer guidance governs minimum continuous flow and permissible parallel operation. Do not assume identical nameplates imply identical delivered flow: unequal branch losses create unequal individual operating points even on a common header.
Lab 7.3
Compute the parallel-pump operating flow
Write parallelFlow(n, shutoffM, staticLiftM, pumpK, systemK) for identical quadratic pumps. The set curve is H = shutoffM − pumpK·(Q/n)² ; return total Q in m³/s. Graded in the browser against 2 assertions; the editor and harness require JavaScript.
Examination score
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A second pump is an addition to the pump curve, not an exemption from the system curve.