Hydraulic

Sizing a pumping system with a recirculation line and two control valves

The recirculation line returns the pump's excess flow to the source tank, keeping the pump at a safe operating point while the dosing demand varies. Here you size, in a coupled way, the dosing valve and the recirculation valve per IEC 60534-2-1.

When to use

Use this whenever a centrifugal pump must deliver a variable process flow (dosing) but cannot operate below a safe minimum flow, or when you want to lock the pump's operating point (typically around 70% of the curve's maximum flow, where efficiency and stability are good) regardless of demand. It is the classic arrangement for chemical dosing skids, modulated tank-to-tank transfer, systems with positive-displacement pumps (where recirculation is the only relief path) and batch processes, in which the dosing can close completely and the entire flow must return to the source.

What recirculation pumping is

In many processes the pump must serve a variable demand — a chemical dosing that sometimes calls for 25 m³/h, sometimes 5 m³/h — yet the pump itself cannot follow that variation freely. Running a centrifugal pump well below its minimum flow causes internal recirculation, heating of the liquid, noise and vibration; near shutoff the curve becomes unstable. The classic solution is to decouple the pump flow from the process flow: the pump works at a fixed, safe flow, and a recirculation line returns the excess to the source tank.

The arrangement therefore has two control valves working together from a single branch node on the discharge: the dosing valve, which regulates what goes to the process, and the recirculation valve, which absorbs the rest. Sizing this system means, in practice, solving a flow balance and sizing both valves per IEC 60534-2-1.

Rationale: why fix the pump at ~70% of the maximum flow

The real maximum flow of a pump is not the highest point you read on the datasheet, but the point where the curve crosses H = 0. By fitting three points of the H×Q curve through Lagrange interpolation, you obtain the polynomial H_pump(Q) = a·Q² + b·Q + c; the positive root of a·Q² + b·Q + c = 0 is Q_cat. The adopted target point is:

Q70 = 0.70 · Q_cat

This value places the pump in a region of good efficiency, stability and NPSH margin, usually above the MCSF stated by the manufacturer. It is the total flow that the suction and the pump casing always see, regardless of how much the process doses.

How the method works, step by step

Curve fit and Q70. Three H×Q points → Lagrange polynomial → Q_cat (root with H = 0) → Q70 = 0.70·Q_cat.
Pressure at the branch. At Q70, compute the suction loss and obtain P_deriv = H_pump(Q70) − h_suc(Q70). It is the energy available at the node where the two branches split.
Flow balance. For each dosing scenario, Q_rec = Q70 − Q_dos. The recirculation flow is whatever is left over from the pump’s fixed flow.
Drop across the recirculation valve. ΔH_valve = P_deriv − Δz_recirc − h_recirc(Q_rec). Because the return enters through the top of the source tank, the elevation Δz_recirc varies between a full and an empty tank and changes the ΔP.
Flow coefficient (IEC 60534-2-1). Convert ΔH to ΔP (bar) and compute Kv = Q·√(ρ/ρ0 / ΔP), then Cv = 1.1561·Kv. First, check for choking: ΔP_choked = FL²·(P1 − FF·Pv), with FF = 0.96 − 0.28·√(Pv/Pc). If ΔP ≥ ΔP_choked, cavitation occurs.
Extreme scenarios and rangeability. In continuous duty, the extremes are minimum dosing (maximum recirculation) and maximum dosing (minimum recirculation). In batch duty the dosing can close, so the extreme is Q_dos = 0 (all of Q70 recirculates). The required rangeability is the ratio between the two Kv values; it must fit within the valve’s installed rangeability R.

The dosing valve follows exactly the same IEC equation, but with the process branch’s ΔP and its own flows Q_max/Q_min. Both selections come from the same node — that is why the calculation is coupled.

Practical design considerations

Cavitation is the dominant risk. The recirculation valve dissipates almost all the pump energy; it is there that the drop is largest. Always compare ΔP with ΔP_choked. When there is no margin, prefer multi-stage anti-cavitation trim or split the drop with a downstream orifice plate.
Authority and working range. Keep the operating opening between 20% and 80% of stroke. Above 90% the valve becomes a bottleneck and loses control; below 10% control turns unstable and the trim erodes.
Valve type. For recirculation with a wide variation, equal-percentage globe valves (FL ~0.90, R ~50:1) give the best combination of authority and rangeability. Butterfly valves (FL ~0.6) are cheap but cavitate early.
Tank level. Because the return enters through the top, Δz_recirc changes with the level. Check the sizing at both extremes (full and empty) — frequently the empty tank is the critical scenario.
Line velocity. Keep 1–3 m/s in the recirculation branch to avoid noise/erosion without oversizing the piping.

Link to the standards

Valve sizing follows IEC 60534-2-1 (and its equivalent ISA 75.01.01), which provides the Kv/Cv equations for liquids, the critical-pressure-ratio factor FF and the choked-flow criterion via FL. Defining the pump’s minimum flow and allowable region relies on the ANSI/HI 9.6.3 guidelines (operating region) and ANSI/HI 9.6.1 (NPSH margin). Head losses use the friction factor from the Colebrook-White (Serghides) method. Following these references ensures the pump operates in a safe zone and that both valves have adequate authority, rangeability and cavitation protection across the entire operating range.

Formulas and fundamentals

Pump target flow (Q70) Q70 = 0.70 · Q_cat , with Q_cat = positive root of a·Q² + b·Q + c = 0

Q_cat (m³/h) is the REAL maximum flow of the pump curve — the point where H = 0, obtained from the physical root of the Lagrange polynomial fitted to 3 points (a, b, c). Q70 (m³/h) is the total flow the pump sustains in operation; this is the flow the suction always sees.

Flow balance at the discharge node Q70 = Q_dos + Q_rec

Downstream of the branch node, the total flow Q70 (m³/h) splits between the dosing Q_dos (m³/h, goes to the destination tank) and the recirculation Q_rec = Q70 − Q_dos (m³/h, returns to the top of the source tank). The less you dose, the more you recirculate.

Available pressure at the branch P_deriv = H_pump(Q70) − h_suc(Q70)

P_deriv (m H2O) is the head available at the discharge node: the pump's total head at the full flow minus the suction head loss at Q70. It is the energy left over to overcome the recirculation branch and be dissipated across the valve.

Differential pressure across the recirculation valve ΔH_valve = P_deriv − Δz_recirc − h_recirc(Q_rec)

ΔH_valve (m H2O) is the drop the valve must absorb: the branch pressure minus the geometric return elevation Δz_recirc (m H2O, top of the source tank) and the distributed + local head loss of the recirculation line at flow Q_rec. In bar: ΔP = ΔH_valve·ρ·9.8/100.

Flow coefficient (IEC 60534-2-1, non-choked liquid)

Kv = Q · √(ρ/ρ0 / ΔP)  ;  Cv = 1.1561 · Kv  ;  FF = 0.96 − 0.28·√(Pv/Pc)  ;  ΔP_choked = FL²·(P1 − FF·Pv)

Kv (m³/h per bar) is the coefficient required to pass Q (m³/h) at a drop ΔP (bar); ρ/ρ0 is the relative density to water (≈1 for water). Cv is the US value. Flow chokes (cavitates) when ΔP ≥ ΔP_choked, computed with FF (the liquid critical-pressure ratio factor), FL (the valve pressure-recovery factor), P1 upstream and Pv/Pc the vapor and critical pressures (bar abs).

Standards & methods

IEC 60534-2-1 — Industrial-process control valves: flow capacity, sizing equations for incompressible fluids
ISA 75.01.01 — Flow Equations for Sizing Control Valves (ANSI equivalent)
ANSI/HI 9.6.3 — Rotodynamic Pumps: Guideline for Allowable Operating Region (minimum flow / MCSF)
ANSI/HI 9.6.1 — NPSH Margin
Colebrook-White (Serghides) for the friction factor

Typical reference values

Quantity	Typical range	Note
Target operating point (Q70)	70% of the curve's maximum flow	Trade-off between efficiency, stability and NPSH margin; align with the manufacturer's MCSF.
Minimum continuous stable flow (MCSF)	25–40% of BEP	Recirculation must guarantee Q_rec ≥ MCSF even at maximum dosing.
Valve working travel	20–80% of stroke	Outside this band there is low authority (>90%) or unstable control (<10%).
Typical rangeability (R)	20:1 to 50:1	Equal-percentage globe ~50:1; butterfly ~20:1; segmented ball ~100:1.
FL factor (equal-% globe)	0.85–0.95	Butterfly ~0.55–0.70; the lower it is, the more prone to cavitation.
Velocity in the recirculation line	1–3 m/s	Above 3 m/s there is noise and erosion; too low oversizes the piping.

Worked example

Treated-water recirculation, continuous operation

Inputs

Curve maximum flow (Q_cat): 100 m³/h
Maximum dosing: 25 m³/h
Minimum dosing: 5 m³/h
Relative density: 1.00 —
Return Δz (full→empty): 0 → 4 m
Equal-% globe valve, FL: 0.90 —

Results

Pump target flow (Q70): 70 m³/h
Q_rec (max dosing scenario): 45 m³/h
ΔH across recirc. valve (max): ~32 m H2O
Required Cv (critical scenario): ~29 —
Required rangeability: ~2.4 : 1 —

With Q70 = 70 m³/h fixed, the recirculation varies from 45 m³/h (dosing 25) to 65 m³/h (dosing 5). The valve needs Cv ~29 at the highest return flow and closes gradually as the dosing drops. The ratio between the two extreme Kv values gives a required rangeability of only ~2.4:1 — well within any globe valve (50:1), which indicates ample control margin. Since ΔP ≈ 3.1 bar against a ΔP_choked typically >5 bar (water, high P1), there is no cavitation; the selection is governed by authority, not by choking.

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Common mistakes

Sizing the recirculation valve only for the worst-case flow and forgetting the opposite scenario: the required rangeability comes from the RATIO between the two extremes (continuous: min × max dosing; batch: closed × max dosing).
Taking the highest flow among the 3 entered curve points as Q_cat. The real maximum flow is the root where H = 0; using an entered point underestimates Q70 and the entire recirculation.
Ignoring the return elevation Δz_recirc. Because the recirculation returns to the TOP of the source tank, the variable level changes the back pressure and, with it, the ΔP and the required Cv between a full and an empty tank.
Not checking cavitation: if ΔP ≥ FL²·(P1 − FF·Pv) the flow chokes. In recirculation the ΔP is usually high (all the pump energy is dissipated), making cavitation the dominant risk.
Confusing Cv and Kv (Cv ≈ 1.16·Kv) or applying the liquid equation to a fluid with dissolved gas / two-phase flow — IEC 60534-2-1 holds for single-phase, non-choked liquid.
Sizing the dosing valve and the recirculation valve in isolation. They share the same node (P_deriv) and Q70; changing one shifts the operating point and the ΔP of the other.

Frequently asked questions

Why does the pump run at 70% of the maximum flow instead of at the process flow?

Centrifugal pumps have an allowable operating region: below the minimum continuous stable flow (MCSF) there is internal recirculation, overheating and vibration; near shutoff the curve becomes unstable. Pinning the pump at ~70% of the maximum flow keeps it close to the best efficiency point (BEP) with a good NPSH margin, while recirculation absorbs the difference between this flow and the demanded dosing.

What is the difference between continuous and batch operation in the sizing?

It changes which scenarios define the recirculation valve's extremes. In continuous duty the dosing never stops: the extremes are minimum dosing (most recirculation) and maximum dosing (least recirculation). In batch duty the dosing can close completely — so the maximum-recirculation scenario is Q_dos = 0 (all of Q70 returns), which requires a larger Cv and widens the required rangeability.

Can the dosing valve and the recirculation valve be sized separately?

Not rigorously. Both share the branch node downstream of the discharge: the available pressure P_deriv and the total flow Q70 are common to both. Opening the dosing valve further reduces Q_rec and changes the ΔP across the recirculation valve, and vice versa. Coupled sizing ensures that, in any combination of openings, the balance Q70 = Q_dos + Q_rec holds.

How do I know whether the recirculation valve will cavitate?

Compute ΔP_choked = FL²·(P1 − FF·Pv), with FF = 0.96 − 0.28·√(Pv/Pc). If the working ΔP reaches or exceeds that value, the flow chokes and the valve cavitates. In recirculation this is common, because the valve must dissipate almost all the pump energy; in that case use anti-cavitation (multi-stage) trim or split the drop with a downstream orifice plate.

What rangeability do I need in the recirculation valve?

The required value is the ratio between the Kv of the maximum-return-flow scenario and that of the minimum. Compare it with the valve's installed rangeability (R, ~50:1 for an equal-% globe). If the required value exceeds the installed one, the opening will either drop below 10% (unstable control) or rise above 90% (no margin) at one of the extremes — a signal to change the trim or the valve type.

Do I need the full pump curve for this calculation?

Three reliable points of the H×Q curve are enough (preferably including one near shutoff and one near the maximum flow). They fit a 2nd-degree Lagrange polynomial, from which H_pump(Q) and the shutoff/maximum flow (the root with H = 0) are obtained. The better distributed the points, the more accurate the Q_cat and therefore the Q70.

Glossary

Dosing flow (Q_dos): Share of the pump flow actually delivered to the process / destination tank; it is the variable controlled by the dosing valve.
Recirculation flow (Q_rec): Share that returns to the source tank, equal to Q70 − Q_dos. It guarantees the pump never operates below the minimum flow.
Cv / Kv: Valve flow coefficients. Cv: flow in gpm of water at 1 psi drop; Kv: m³/h at 1 bar. Relation Cv ≈ 1.1561·Kv.
Choked flow pressure: Pressure drop above which raising ΔP no longer raises the flow; it marks the onset of cavitation. Given by FL²·(P1 − FF·Pv).
Rangeability (R): Ratio between the largest and smallest controllable Cv of a valve. It defines the flow range it regulates accurately.
MCSF (minimum continuous stable flow): Lowest flow at which the pump operates continuously without damage from internal recirculation, heat or vibration. Recirculation must always keep it satisfied.