Flow gain = Q_op / (N · Q_alone) × 100%. It shows how efficiently parallel capacity multiplies versus running N independent single-pump duties.

When should I use series pumps?

When H_static + friction exceeds what one pump can develop (boosters, multi-stage trains). Series needs N·H_so > H_static for an intersection.

If per-pump or single-alone flow exceeds about 1.25 × Q_rated, the duty is far right of BEP — check motor amps, NPSHa, and vibration before relying on one-pump contingency.

Multiple Pump Parallel & Series Operation — Chilled water 3× parallel · 1500 GPM | FieldEngineersKit

Engineering Reference & ASME Code Basis

1. Core Formula & Variable Definitions

ANSI/HI 14.3 — Rotodynamic Pumps for Design and Application · Hydraulic Institute Engineering Data Book (system / pump curve practice) · Crane TP-410 — resistance / friction head screening basis

H_pump = H_so − a Q² · H_sys = H_static + k Q²

Parallel: Q_op = √[(H_so−H_st)/(k+a/N²)] · Series: Q_op = √[(N·H_so−H_st)/(k+N·a)]

ANSI/HI 14.3 · quadratic pump & system screening · Crane TP-410 resistance style

Code HI 14.3Parallel Q addsSeries H addsWarn Runout 1.25×

Fit a from (H_so, H_rated, Q_rated) and k from friction head at the same Q_rated. Parallel multiplies capacity at common head; series multiplies head at common flow. Flow gain = Q_op/(N·Q_alone); head gain = H_op/(N·H_alone). Warns on diminishing parallel return and runout (>1.25× Q_rated).

H_so (Shut-off head) — Single-pump zero-flow head used in the quadratic fit.
a (Pump curve coefficient) — a = (H_so − H_rated) / Q_rated².
k (System resistance coefficient) — k = ΔH_friction(Q_rated) / Q_rated².
N (Pump count) — Number of identical operating pumps (1–4).
Q_op (Operating flow) — Intersection of combined pump curve and system curve.
Q_alone (Single-pump operating flow) — Intersection with N = 1 on the same system curve.

2. Allowances, Tolerances & Standards

Quadratic curves are a TA first pass. OEM multi-point curves and measured system resistance govern final selection.

Runout warnQ > 1.25 × Q_rated

Per-pump or single-alone duty far right of BEP — check motor and NPSH.

Parallel diminishing return< +15% vs one pump

Steep system friction — extra parallel pumps buy little capacity.

Identical pumpsAssumed

Unequal parallel curves can deadhead the weaker pump.

Series static limitN·H_so > H_static

Otherwise no intersection — need more stages or lower static.

Quick Reference Lookup Table

Illustrative multi-pump cases (this app)
Case	Mode	Focus
2× · 100 m³/h · H_so 60 m	Parallel	Default duty
Cooling 2× · 250 m³/h	Parallel	Friction-heavy loop
BFW 2× · 80 m³/h · H_st 150 m	Series	High static
HVAC 3× · 1500 GPM	Parallel	Imperial chilled water
Booster 2× · 800 GPM	Series	Pipeline boost

3. Material & Code Limitations

Identical rotodynamic pumps on a shared system curve. Not for PD pumps or strongly dissimilar parallel sets.

Material Group	Temperature Range	Allowable Stress / Limit	Engineering Notes
Cooling / HVAC parallel	N/A — hydraulic screen	Motor at runout	Watch diminishing return on high-friction loops.
Boiler-feed / pipeline series	N/A	N·H_so vs H_static	Series needed when static exceeds one-pump shut-off.
One-pump trip on multi-train	N/A	Runout 1.25× Q_rated	Q_alone on the multi-pump system can overload the survivor.

Code Applicability & Safety Boundaries

Field screening only — not an HI performance acceptance test.
Quadratic fit ignores multi-hump / flat OEM curves.
Assumes matched pumps; unequal parallel not solved.
Export / PDF is a TA worksheet — not a stamped pump datasheet.

4. Step-by-Step Worked Example

Field VerificationShow

Worked example — 2× parallel · 100 m³/h

Two identical pumps: H_so = 60 m, Q_rated = 100 m³/h, H_rated = 45 m. System: H_static = 15 m, ΔH_f = 20 m at Q_rated.

Mode / N:Parallel · 2Pump:H_so 60 m · H_rated 45 m · Q_rated 100 m³/hSystem:H_st 15 m · ΔH_f 20 m @ Q_rated

Coefficients

a = (H_{so} - H_{r}) / Q_{r}^{2}, k = Δ H_{f} / Q_{r}^{2}

a = 15/10000 = 0.0015 · k = 20/10000 = 0.0020

Result:a = 0.0015 · k = 0.0020

Single-pump alone

Q_{a l o n e} = (H_{so} - H_{s t}) / (k + a)

√(45/0.0035) ≈ 113.4 m³/h

Result:Q_alone ≈ 113 m³/h

Two pumps parallel

Q_{o p} = (H_{so} - H_{s t}) / (k + a / N^{2})

√(45/0.002375) ≈ 137.7 m³/h · H_op ≈ 53 m

Result:Q_op ≈ 138 m³/h

Open /par-2p-100m3h-hso-60m-hr-45m-hs-15m-hf-20m for the live default.

Conclusion: Two pumps raise capacity from ~113 to ~138 m³/h (~+21%), not 2× — friction dominates. Confirm motor/NPSH at ~69 m³/h per pump.

5. Frequently Asked Questions & Technical References

Show

System head rises with Q². The combined pump curve intersects the system at less than 2× the single-pump operating flow — often only +15–40% on friction-heavy loops.