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 viscosity | ν | cSt | Liquid viscosity (centistokes). Water ≈ 1 cSt. |
| BEP flow (water) | QBEPw | gpm, m³/h | Flow at best-efficiency point on the water curve. |
| BEP head per stage (water) | HBEPw | ft, m | Head per stage at BEP on the water curve. |
| Parameter B | B | — | Dimensionless screening parameter driving all factors. |
| Flow correction | CQ | — | Qvis = CQ·Qw |
| Head correction | CH | — | Hvis = CH·Hw |
| Efficiency correction | Cη | — | ηvis = Cη·ηw |
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:
| Quantity | Direction on a viscous liquid | Why |
|---|---|---|
| Head (H) | ↓ Down | More internal friction converts head into heat. |
| Flow at BEP (Q) | ↓ Down | The whole curve shrinks and BEP shifts to lower flow. |
| Efficiency (η) | ↓ Down | A larger share of input power becomes friction loss. |
| Brake power (P) | ↑ Up | Lower efficiency means more shaft power for the same duty. |
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)
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)
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)
4. Applicability & Limits
The HI 9.6.7 correlation is empirical and was fitted to test data over a bounded range. Stay inside it:
| Limit | Range | Note |
|---|---|---|
| Pump type | Radial-discharge rotodynamic | Single or multistage. |
| Specific speed | ns ≤ 60 (Ns ≤ 3000) | High-ns mixed/axial flow is outside scope. |
| Liquid | Newtonian only | Slurries and shear-thinning fluids do not follow this method. |
| Viscosity | 1 < ν < 4000 cSt | Experimental data extends to ~3000 cSt. |
| Parameter B | B < 40 | At or above 40, do a loss analysis instead. |
| Head basis | Per stage | For 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.
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, QBEPw | 110 m³/h |
| BEP head per stage, HBEPw | 77 m |
| Speed, N | 2950 rpm |
| Water efficiency, ηw | 68 % |
| Viscosity, ν | 120 cSt |
| Specific gravity, s | 0.90 |
At the best-efficiency point (Q/QBEP = 1.0)
At part load (Q/QBEP = 0.60), water head Hw = 87.3 m
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
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