Parallel Pumping Simulator

Two pumps working into one system: choose each pump's H₀ / Qb parabola (with an optional rising, unstable characteristic), and read pump 1, pump 2 and the parallel combined curve against the system curve. Toggle pump 2 and watch the duty point jump; when unstable curves meet a flat system the tool raises the hunting red light. A pumpXSolver engineering tool.

Duty point — intersection with the system curve

Pump 1 curve — H₀ / Qb parabola

Pump 2 curve — same family

System — static + friction

How pumps add in parallel — flows add at equal head

$$H_{combined}(Q) = H_{pump}\!\left(\tfrac{Q}{2}\right)\ \text{(identical pumps)}\qquad\Longleftrightarrow\qquad Q_{combined}(H) = Q_1(H) + Q_2(H)$$

Parallel pumps share a common discharge header, so they run at the same head and their flows add. For two identical pumps the combined curve is simply the single-pump curve stretched twice to the right — every point (Q, H) becomes (2Q, H). The duty point is where this combined curve crosses the system curve \(H_{sys} = H_s + k\,Q^2\), and the anchor identity this page draws for you: at the single-pump duty head H₁, the combined curve passes exactly 2×Q₁ (the hollow marker on the chart). Note the flow per pump in parallel operation is smaller than the single-pump duty flow whenever the system curve is not flat — the operating point slides up the system curve as the combined flow grows.

The pump curve model

$$\frac{H}{H_0} = 1 - \left(\frac{Q}{Q_b}\right)^{\!2}\qquad\text{(stable)}\qquad\qquad \frac{H}{H_0} = 1 - \left(\frac{Q}{Q_b}\right)^{\!2} + K_H\!\left(\frac{Q}{Q_b}\right)^{\!2}\!e^{-3Q/Q_b},\; K_H=4\quad\text{(rising / unstable)}$$

The stable form is the textbook parabola through (0, H₀) and (Qb, 0). The unstable option adds a low-flow hump: head climbs from shut-off to a local peak of ≈ 1.06·H₀ near 0.28·Qb before falling — the drooping (rising) characteristic of high-efficiency low-nq or axial machines, drawn here as a schematic. Any duty point on that rising segment is unstable: a momentary drop in system demand raises pump head, which pushes flow down further — the feedback loop runs the wrong way.

Hunting — the red-light criteria

ConditionVerdictWhat happens
Delivered curve and system curve cross more than once🔴 HuntingFlow and head oscillate between the intersections; the low-flow crossing sits on the rising branch where restoring forces are absent. Typical with humped curves against nearly flat systems — press the preset button to reproduce it.
Duty point lies on the rising branch (dH/dQ > 0)🔴 Unstable dutyAny transient moves the point away instead of back; in parallel operation one pump may capture the whole flow while the other runs at shut-off.
Any running pump below 30 % of Qb🟡 Minimum flowSuction recirculation, vibration and temperature rise; provide a recycle line or trim the impeller.
Single crossing on the falling branch🟢 StableThe system curve restrains the duty point — normal parallel operation.

Symbol table

SymbolMeaningUnits
H₀shut-off head (zero flow)m / ft
Qbflow at zero head (parabola reference)m³/h / gpm
Hsstatic head of the systemm / ft
kresistance coefficient, defined by the friction head at the reference flowm/(m³/h)²
Q*, H*duty point — total flow and head at the intersection

Worked anchor (self-check)

Two identical stable pumps, H₀ = 50 m, Qb = 200 m³/h, system Hs = 20 m with 25 m friction at 300 m³/h. Pump 1 alone meets the system at Q₁ ≈ 140 m³/h, H₁ ≈ 25.5 m. With both pumps running the combined curve passes (2 × 140, 25.5) — the on-chart hollow marker — and the new duty point settles near Q* ≈ 225 m³/h at H* ≈ 34 m: well below the naive 2 × 140 = 280, exactly because the system curve climbs with Q. Flip to the hunting preset (both pumps unstable, Hs = 51.5 m, friction 1 m) and the intersection count jumps to two — the red light.

Engineering criteria applied