Rotating Equipment

Pump Viscosity Correction: ANSI/HI 9.6.7 Engineering Fundamentals

Centrifugal pump curves are drawn on cold water. On a viscous liquid the head, flow, and efficiency fall and the power rises. The ANSI/HI 9.6.7 parameter-B method converts the water curve to the real, viscous performance.

Screening parameter

B ≤ 1 → no correction

Below B = 1.0 the viscous effect is negligible; water performance applies.

Valid range

1–4000 cSt

Newtonian liquids, specific speed ns ≤ 60, head per stage.

PD crossover

> ~300 cP

Very viscous service usually points to a positive-displacement pump.

Use this guide when you need to:

  • Convert a water pump curve to a viscous liquid.
  • Find corrected head, flow, efficiency, and power.
  • Decide when viscosity warrants a PD pump.

1. Why Viscosity Matters

Every centrifugal pump performance curve a manufacturer publishes is measured on cold water, with a kinematic viscosity of roughly 1 cSt. The moment you pump something thicker — a lube oil, a heavy crude, a glycol-rich solution, an amine, a residuum — the pump no longer follows that curve. It produces less head, shifts its best-efficiency flow down, runs at lower efficiency, and draws more brake power. Size the driver from the water curve and you can badly under-power the pump.

ANSI/HI 9.6.7 (Effects of Liquid Viscosity on Rotodynamic Pump Performance) gives an empirical correlation that converts the water (subscript w) BEP performance into the viscous (subscript vis) performance using a small set of correction factors. This guide explains why the correction is needed, what the method does, where it is valid, and works the standard's own example.

Key Terms

Term Symbol Units Definition
Kinematic viscosityνcStLiquid viscosity (centistokes). Water ≈ 1 cSt.
BEP flow (water)QBEPwgpm, m³/hFlow at best-efficiency point on the water curve.
BEP head per stage (water)HBEPwft, mHead per stage at BEP on the water curve.
Parameter BBDimensionless screening parameter driving all factors.
Flow correctionCQQvis = CQ·Qw
Head correctionCHHvis = CH·Hw
Efficiency correctionCηηvis = Cη·ηw
The headline rule: compute one number, parameter B. If B ≤ 1.0, the viscous effect is negligible and you use the water curve directly. If 1 < B < 40, apply the correction factors. If B ≥ 40, the correction is too uncertain to trust — a detailed loss analysis is warranted.

2. What Viscosity Does to the Curve

Inside a centrifugal pump, energy is added to the liquid by the spinning impeller, but some of the shaft power is always lost to friction. A more viscous liquid increases two of those loss mechanisms sharply:

  • Disk friction — the drag of the liquid against the rotating impeller shrouds. This scales strongly with viscosity and is dissipated directly as heat, never reaching the discharge as head.
  • Hydraulic (skin) friction — losses in the impeller and casing flow passages. Higher viscosity thickens the boundary layers and raises the pressure drop through the pump's own internal passages.

The net effect on the performance curve:

QuantityDirection on a viscous liquidWhy
Head (H)↓ DownMore internal friction converts head into heat.
Flow at BEP (Q)↓ DownThe whole curve shrinks and BEP shifts to lower flow.
Efficiency (η)↓ DownA larger share of input power becomes friction loss.
Brake power (P)↑ UpLower efficiency means more shaft power for the same duty.
Why power rises even though head falls: power is P = Q·H·SG / (k·η). Head and flow drop, but efficiency drops faster and the dense, viscous liquid often has a higher specific gravity — so the absorbed power climbs. This is exactly the trap that catches an undersized motor.

3. The Parameter-B Method (ANSI/HI 9.6.7)

The method starts from the pump's water performance at its best-efficiency point and the liquid viscosity. Everything keys off the single dimensionless parameter B.

Step 1 — Parameter B (Eq 3 USC / Eq 2 SI)

US customary (ν in cSt, QBEPw in gpm, HBEPw in ft/stage, N in rpm): B = 26.6 · ν^0.50 · HBEPw^0.0625 / ( QBEPw^0.375 · N^0.25 ) SI (QBEPw in m³/h, HBEPw in m/stage): B = 16.5 · ν^0.50 · HBEPw^0.0625 / ( QBEPw^0.375 · N^0.25 )

Step 2 — Apply the rules

  • B ≤ 1.0: no correction. CQ = CH = Cη = 1.
  • 1 < B < 40: compute the factors below.
  • B ≥ 40: highly uncertain; the correlation is not reliable. Perform a detailed loss analysis per HI 9.6.7 §9.6.7.5.2 rather than reporting a number.

Step 3 — Correction factors (Eq 4–7)

Flow (Eq 4): CQ = 2.71^( −0.165 · (log₁₀ B)^3.15 ) → Qvis = CQ · Qw Head at BEP (Eq 5): CBEP-H = CQ → HBEPvis = CBEP-H · HBEPw Head at a point (Eq 6): CH = 1 − [ (1 − CBEP-H) · ( Qw / QBEPw )^0.75 ] → Hvis = CH · Hw Efficiency (Eq 7): Cη = B^( −0.0547 · B^0.69 ) → ηvis = Cη · ηw

Note that CH depends on where you are on the curve. At BEP (Qw/QBEPw = 1) it equals CQ; at lower flows the head penalty is smaller, so CH approaches 1.

Step 4 — Viscous power (Eq 9 USC / Eq 8 SI)

US customary (Qvis gpm, Hvis ft, P hp, s = SG): Pvis = Qvis · Hvis · s / ( 3960 · ηvis ) SI (Qvis m³/h, Hvis m, P kW): Pvis = Qvis · Hvis · s / ( 367 · ηvis )
Use head per stage. For a multistage pump, HBEPw in the B equation is the head per stage, not the total. Using total head inflates B and over-corrects.

4. Applicability & Limits

The HI 9.6.7 correlation is empirical and was fitted to test data over a bounded range. Stay inside it:

LimitRangeNote
Pump typeRadial-discharge rotodynamicSingle or multistage.
Specific speedns ≤ 60 (Ns ≤ 3000)High-ns mixed/axial flow is outside scope.
LiquidNewtonian onlySlurries and shear-thinning fluids do not follow this method.
Viscosity1 < ν < 4000 cStExperimental data extends to ~3000 cSt.
Parameter BB < 40At or above 40, do a loss analysis instead.
Head basisPer stageFor multistage pumps.

The > 300 cP crossover to positive displacement

As viscosity climbs, the centrifugal pump's efficiency penalty grows until the pump is simply the wrong machine. A common practical rule (general industry practice, not part of the HI 9.6.7 equation set) is that above roughly 250–300 cP a positive-displacement pump — rotary gear, screw, or lobe — becomes the better choice: its delivered flow is nearly independent of viscosity and its efficiency actually improves with thicker liquids (less internal slip). Treat the viscosity correction as the tool for moderately viscous service and the PD pump as the answer for heavy, sticky service.

When the result is suspect: a high B (approaching or exceeding 40), a specific speed above 60, a non-Newtonian liquid, or viscosity beyond the validated range all mean the correction is an extrapolation. Use it for screening and confirm the final selection with the pump vendor's own viscous-test data.

5. Worked Example (matches the calculator)

This reproduces the ANSI/HI 9.6.7 worked example. A single-stage pump with the following water performance at BEP is asked to handle a 120 cSt, 0.90 SG oil:

Input (water, at BEP)Value
BEP flow, QBEPw110 m³/h
BEP head per stage, HBEPw77 m
Speed, N2950 rpm
Water efficiency, ηw68 %
Viscosity, ν120 cSt
Specific gravity, s0.90

At the best-efficiency point (Q/QBEP = 1.0)

B = 16.5 · 120^0.50 · 77^0.0625 / ( 110^0.375 · 2950^0.25 ) = 5.52 CQ = 2.71^( −0.165 · (log₁₀ 5.52)^3.15 ) = 0.938 HBEPvis = 0.938 · 77 m = 72.2 m Cη = 5.52^( −0.0547 · 5.52^0.69 ) = 0.738 ηvis = 0.738 · 0.68 = 0.502 (50.2 %) Qvis = 0.938 · 110 = 103.2 m³/h Pvis = 103.2 · 72.2 · 0.90 / ( 367 · 0.502 ) = 36.4 kW

At part load (Q/QBEP = 0.60), water head Hw = 87.3 m

CH = 1 − [ (1 − 0.938) · 0.60^0.75 ] = 0.958 Hvis = 0.958 · 87.3 m = 83.6 m
Read the result: on this oil the pump makes about 6 % less head at BEP, its efficiency drops from 68 % to ~50 %, and it absorbs ~36 kW. A driver sized off the water curve at 68 % efficiency would be well undersized.

Common Mistakes to Avoid

  • ❌ Using total head instead of head per stage in the B equation for a multistage pump
  • ❌ Mixing units — the USC (26.6) and SI (16.5) coefficients are not interchangeable
  • ❌ Sizing the motor from the water efficiency instead of the corrected viscous efficiency
  • ❌ Trusting the result when B ≥ 40 or viscosity is outside 1–4000 cSt
  • ❌ Applying the method to non-Newtonian slurries
  • ❌ Forgetting that CH varies along the curve (only equals CQ at BEP)
  • ❌ Ignoring the > 300 cP crossover where a PD pump is the right machine

Key Standards & References

  • ANSI/HI 9.6.7-2010 – Effects of Liquid Viscosity on Rotodynamic Pump Performance (Eq 2–9)
  • ANSI/HI 9.6.1 – Rotodynamic Pumps Guideline for NPSH Margin
  • API 610 (12th Ed) – Centrifugal Pumps for Petroleum, Petrochemical and Natural Gas Industries
  • API 676 – Rotary Positive-Displacement Pumps (the PD alternative for heavy viscous service)
  • Cameron Hydraulic Data – Industry reference handbook

Frequently Asked Questions

When do you need to correct a centrifugal pump for viscosity?

Pump curves are published on cold water (about 1 cSt). When the liquid is appreciably more viscous, head, flow, and efficiency drop while absorbed power rises. ANSI/HI 9.6.7 screens this with parameter B: B at or below 1.0 means no correction; once B exceeds 1.0 you apply the correction factors.

What is the parameter B in ANSI/HI 9.6.7?

B is a dimensionless parameter combining viscosity, BEP head per stage, BEP flow, and pump speed. The correction factors CQ, CH, and Cη are all functions of B. B ≤ 1.0 means no correction; 1 < B < 40 uses the equations; B ≥ 40 is highly uncertain.

Why does viscosity cut a pump's head and efficiency?

A viscous liquid raises disk friction on the impeller shrouds and skin-friction losses in the impeller and casing passages. Those losses turn shaft power into heat instead of head, so developed head, best-efficiency flow, and efficiency all fall, which raises the brake power for the same duty.