Fixed recirculation with an orifice plate sized for Q70
When a pump runs far to the left of its curve (oversized) and cannot be replaced, a fixed recirculation line with an orifice plate bleeds part of the flow back to the tank, pushing the operating point toward Q70.
When to use
Use this method when the installed pump is clearly oversized for the duty — it runs far to the left of its curve, with low flow, high discharge pressure and a risk of internal recirculation, overheating and vibration — and swapping it for a smaller machine is not practical (cost, lead time, spare-parts standardization). Instead of throttling the discharge (which only shifts the problem and wastes energy), you install a fixed bypass downstream of the discharge that returns to the top of the source tank. A calibrated orifice plate imposes the required head loss on that bypass so that the sum Q_discharge + Q_recirc reaches Q70 = 70% of the pump's maximum flow rate, the range in which most centrifugal pumps run at good efficiency and well clear of the safe minimum continuous flow zone.
The problem: a pump that is too big
An oversized pump runs far to the left of its characteristic curve — low flow, high discharge pressure. That region is hostile: internal recirculation develops in the impeller, the liquid heats up through dissipation, vibration and noise rise, and bearing and seal life drops. The manufacturer usually publishes a safe minimum continuous flow, below which prolonged operation is not recommended (ANSI/HI 9.6.3).
When replacing the pump with a smaller one is not practical — because of cost, lead time or spare-parts standardization — the classic remedy is to open a recirculation path: a bypass downstream of the discharge that returns part of the flow to the source tank. This raises the total flow the pump must deliver and pushes the operating point to the right, into the healthy range. The design target here is Q70 = 70% of the pump’s maximum flow rate.
Why a fixed orifice plate
The bypass cannot be an open pipe: it would bleed off too much flow. We need a calibrated restriction that dissipates exactly the excess pressure so the recirculated flow balances out. The orifice plate is the ideal element: cheap, robust, with no moving parts, fixed (no operation required) and with physics well standardized by ISO 5167-2. Unlike a control valve, the plate does not drift out of adjustment and needs no maintenance — once sized, it keeps the operating point stable.
Mind the physical sign: throttling the discharge pushes the pump left (worse). Recirculation does the opposite — it creates parallel flow and pushes right. They are opposite interventions.
How the method works, step by step
The sizing is inverse: we know the flow the plate must pass and we look for the geometry (β and the bore) that produces the right loss. The calculation is done at the mean tank level (the design case):
- Operating point without recirculation. Solve the intersection of the pump curve with the system curve (discharge + suction) to find the flow the destination actually draws,
Q_discharge. - Target recirculation flow. From the closure condition,
Q_recirc = Q70 − Q_discharge. If this value is not positive, the pump is not oversized enough and the method does not apply. - Target permanent loss (Δω). Run the hydraulic balance of the bypass: the pump head at Q70 minus the discharge losses, the static lift Δz and the losses of the recirculation line itself defines how much permanent loss the plate must impose — this is the target Δω.
- Iteration on β (bisection). For each β candidate, compute the discharge coefficient C_d from Reader-Harris/Gallagher, the Δp measured between tappings and, from it, the permanent loss Δω (§5.4.2). The bisection sweeps β until the computed Δω equals the target Δω. The resulting β gives the bore diameter
d = β·D.
Fundamentals: C_d, Δp and the permanent loss
The metering equation relates flow and differential: Q = C_d · E · A₂ · √(2·g·Δp_meas), with E = 1/√(1 − β⁴) correcting the velocity of approach. The discharge coefficient is not constant — it depends on β, the Reynolds number Re_D and the tapping type (flange or D–D/2), and is given by the Reader-Harris/Gallagher correlation of ISO 5167-2.
The subtle point, and the one most often gotten wrong in practice, is confusing the Δp_meas (pressure difference between the tappings) with the permanent loss Δω. Downstream of the plate the jet re-expands and recovers part of the pressure; what remains, irreversible, is Δω — and only that portion actually resists the flow in the recirculation line. The standard gives the ratio between them (§5.4.2), always Δω < Δp_meas. Sizing by Δp_meas overestimates the bleed and produces an undersized bore.
Practical design considerations
- Keep β in the useful range (0.20–0.75). Very small bores clog, amplify manufacturing error and demand longer straight runs upstream; a high β falls outside the validity of C_d.
- Check the Reynolds number. In viscous liquids or at low flow, Re_D can drop below the standard’s minimum — C_d loses its certification. The tool warns when this happens.
- Control the velocity in the recirculation line (1.5–3.0 m/s). High velocity downstream of the plate causes noise and erosion (jet cavitation); too low favors sedimentation.
- Remember the plate is fixed. Sized at the mean level, it recirculates a little more or less as the tank fills/empties. Verify that at the extremes the pump still stays within a safe range.
- Provide straight runs upstream and downstream of the plate per ISO 5167-2, otherwise the real C_d will diverge from the tabulated value.
Link to the standards
The plate geometry, the C_d (Reader-Harris/Gallagher) correlation and the permanent loss follow ISO 5167-1/2. The friction losses in the discharge, suction and recirculation use Darcy-Weisbach with the friction factor from Colebrook-White (Serghides). The choice of Q70 as the target aligns with ANSI/HI 9.6.3 (preferred region and minimum continuous flow), and good practice for installing process pumps refers to API 610 / ASME B73.1. The result is a cheap, auditable and stable intervention that recovers the operating point without replacing the machine.
Formulas and fundamentals
Q_discharge + Q_recirc = Q70 = 0.70 · Q_max The pump is forced to deliver the total flow Q70 (70% of the pump's real maximum flow rate, in m³/h). The discharge supplies what the destination demands at the mean tank level (Q_discharge); the recirculation (Q_recirc) absorbs the excess. All flow rates in m³/h.
C_d = 0.5961 + 0.0261·β² − 0.216·β⁸ + 0.000521·(10⁶·β/Re_D)^0.7 + (0.0188 + 0.0063·A)·β^3.5·(10⁶/Re_D)^0.3 + tapping terms C_d (dimensionless) is the discharge coefficient of the concentric sharp-edged orifice plate. β = d/D is the diameter ratio (bore/pipe), Re_D the Reynolds number referenced to the pipe diameter D, and A = (19000·β/Re_D)^0.8. For D < 71.12 mm the small-diameter term applies. The pressure tappings (flange or D–D/2) enter through the M'₂ terms.
Q = C_d · E · A₂ · √(2·g·Δp_meas) , E = 1/√(1 − β⁴) Relates the flow rate Q (m³/s) through the bore to the measured differential pressure Δp_meas (in m H₂O). A₂ = π·d²/4 is the bore area (m²), E the velocity-of-approach factor and g = 9.81 m/s². Inverted, it gives the Δp_meas each β produces for a given recirculation flow rate.
Δω/Δp_meas = (√(1 − β⁴·(1 − C_d²)) − C_d·β²) / (√(1 − β⁴·(1 − C_d²)) + C_d·β²) Δω is the permanent (unrecovered) head loss imposed by the plate — it, and not the Δp_meas between tappings, is what actually "brakes" the recirculation line. The ratio Δω/Δp_meas grows as β decreases (smaller bore = more permanent loss).
H_pump(Q70) − h_discharge − Δz − Δω − h_recirc = 0 At the mean tank level, the head delivered by the pump at Q70 minus the discharge losses, the static lift Δz and the friction/local losses of the recirculation line itself must equal the permanent loss Δω the plate has to impose. This target Δω feeds the iteration that solves for β.
Standards & methods
- ISO 5167-1 (general principles of differential-pressure flow measurement)
- ISO 5167-2 (orifice plates — geometry, Reader-Harris/Gallagher C_d and permanent loss §5.4.2)
- Darcy-Weisbach equation with the friction factor from Serghides / Colebrook-White
- ANSI/HI 9.6.3 (preferred operating region and minimum continuous flow of rotodynamic pumps)
- API 610 / ASME B73.1 (good practice for process centrifugal pumps)
Typical reference values
| Quantity | Typical range | Note |
|---|---|---|
| Diameter ratio β = d/D | 0.20 to 0.75 | ISO 5167-2 is valid for 0.10 ≤ β ≤ 0.75; very small bores amplify error and clog. |
| Pump target flow rate (Q70) | 70% of maximum flow | Good-efficiency and thermally safe range for most centrifugal pumps. |
| Discharge coefficient C_d | 0.60 to 0.63 | Concentric sharp-edged plate in fully developed turbulent flow. |
| Minimum Reynolds (Re_D) for validity | ≥ 5000 (β ≥ 0.56) or ≥ 170·β²·D | Below this, C_d falls outside the standard's certified range. |
| Velocity in the recirculation line | 1.5 to 3.0 m/s | Above this, noise and downstream erosion of the plate; below it, sedimentation. |
| Permanent loss Δω/Δp_meas | 0.5 to 0.9 (low β) | The smaller β, the larger the fraction of pressure permanently dissipated. |
Worked example
Oversized pump with fixed recirculation to Q70
Inputs
- Pump maximum flow rate (Q_max)
- 120 m³/h
- Target flow Q70
- 84 m³/h
- Flow required at destination (mean level)
- 60 m³/h
- Recirculation line diameter (D)
- 80 mm
- Pressure tapping
- Flange —
- Target permanent loss (Δω)
- 21.4 m H₂O
Results
- Recirculated flow (Q_recirc)
- 24 m³/h
- Diameter ratio β
- 0.452 —
- Bore diameter (d)
- 36.2 mm
- Discharge coefficient C_d
- 0.608 —
- Δp measured between tappings
- 30.9 m H₂O
Left to itself, the pump would deliver just over 60 m³/h against the system — far to the left of the curve. The closure condition requires Q_recirc = 84 − 60 = 24 m³/h through the bypass. The iteration searches for the β that imposes exactly Δω = 21.4 m H₂O of permanent loss for that flow: it converges on β = 0.452 (a 36.2 mm bore). Note that the Δp_meas between tappings (30.9 m H₂O) is larger than Δω (21.4 m H₂O) — part of the pressure is recovered downstream; it is Δω that governs the balance. With the plate installed, the pump now delivers a total of Q70 = 84 m³/h and operates in a healthy region of the curve.
Common mistakes
- Sizing the plate from the Δp_meas between tappings instead of the permanent loss Δω — this overestimates the bled flow.
- Applying the plate to a pump that is not sufficiently oversized: forced to Q70 it cannot overcome Δz to the destination, and the plate has no solution.
- Forgetting the static lift Δz and the losses of the recirculation line itself in the balance, distorting the target Δω.
- Choosing β outside the ISO 5167-2 range (β < 0.20 clogs; β > 0.75 invalidates C_d).
- Sizing at a single level and ignoring that the plate is fixed: at the high/low tank levels the recirculated flow changes.
- Operating with Re_D below the standard's minimum (viscous liquid, low flow), invalidating the discharge coefficient.
Frequently asked questions
Why aim at exactly 70% of the maximum flow (Q70)?
Q70 is a practical benchmark: most centrifugal pumps reach good efficiency there and stay above the safe minimum continuous flow recommended by ANSI/HI, well clear of the internal recirculation, overheating and vibration that occur on the left of the curve. If the manufacturer states a different minimum continuous flow, set the target to that value.
What is the difference between throttling the discharge and using recirculation with a plate?
Throttling the discharge with a valve only adds head loss downstream of the pump, pushing the operating point even further left — it worsens the low-flow problem. Recirculation does the opposite: it creates a parallel path that increases the total flow rate pumped, shifting the point to the right (Q70).
Why size by the permanent loss Δω and not by the Δp between tappings?
The Δp_meas between the tappings includes pressure that is recovered downstream of the plate as the jet re-expands. What actually "brakes" the recirculation line is the permanent loss Δω (ISO 5167-2 §5.4.2), always smaller than Δp_meas. Using Δp_meas overestimates the bled flow and leads to the wrong bore.
Does the plate work at every tank level?
The plate is fixed, sized at the mean level (the design case). Because β and the bore are constant, the recirculated flow varies slightly as the tank fills or empties, because the static lift and the available pressure change. The tool shows this behavior at the high/low levels for information.
What if the pump is not oversized enough?
If, forced to Q70, the discharge head cannot overcome the static lift to the destination, there is no positive target Δω and the plate cannot be sized. This indicates the pump is not as oversized as assumed — the method applies to clearly oversized machines.
What range of β is acceptable?
ISO 5167-2 is valid for 0.10 ≤ β ≤ 0.75, but in practice keep it between 0.20 and 0.75: very small bores (low β) clog easily and amplify manufacturing errors; β above 0.75 falls outside the certified range of the discharge coefficient.
Glossary
- Q70
- Target flow rate equal to 70% of the pump's real maximum flow; the healthy operating point the sizing aims to reach.
- Orifice plate
- Disc with a concentric sharp-edged bore that imposes a calibrated head loss and thereby measures or controls flow (ISO 5167-2).
- Diameter ratio (β)
- Ratio of the bore diameter (d) to the pipe internal diameter (D); the geometric parameter that governs C_d and the plate's loss.
- Discharge coefficient (C_d)
- Factor correcting the ideal flow for the real contraction and friction of the jet; for a sharp-edged plate it stays around 0.60-0.63.
- Permanent loss (Δω)
- The portion of the differential pressure that is NOT recovered downstream of the plate; it is the loss that actually resists recirculation.
- Recirculation flow
- The portion of the pump's total flow diverted back to the source tank through the bypass, equal to Q70 minus the flow required at the destination.