Formula used
For an ideal cone-plate rheometer with small cone angle, the shear rate is uniform and the torque relates directly to shear stress.
- Keep α small to maintain a nearly uniform shear rate.
- Use a clean, bubble-free sample and stable temperature.
- If the fluid is non-Newtonian, report μ at the computed γ̇.
How to use this calculator
- Enter the measured torque and select its unit.
- Provide cone radius and cone angle for your geometry.
- Enter rotation as rpm, rad/s, or revolutions per second.
- Optionally add density to compute kinematic viscosity.
- Click Calculate to view results above the form.
- Use Download CSV or Download PDF for reporting.
Example data table
| Torque (mN·m) | Radius (mm) | Angle (deg) | Speed (rpm) | Viscosity (Pa·s) | Viscosity (cP) |
|---|---|---|---|---|---|
| 1.25 | 20 | 2.0 | 60 | 0.00361 | 3.61 |
| 8.00 | 25 | 1.0 | 30 | 0.00815 | 8.15 |
| 0.40 | 15 | 4.0 | 120 | 0.00200 | 2.00 |
Example values are illustrative; your instrument may require geometry factors.
Technical Notes for Cone-and-Plate Viscosity
1) Why cone-and-plate geometry is popular
Cone-and-plate fixtures deliver an almost uniform shear rate across the radius, simplifying viscosity reporting. With small cone angles (commonly 0.5–4°), the film thickness is controlled, and torque maps cleanly to shear stress for many liquids and melts.
2) Geometry inputs that drive accuracy
The critical terms are cone radius R, cone angle θ, and truncation gap h if the tip is blunted. Small angle or radius errors propagate into shear rate and viscosity, so verify units carefully (mm vs m, mN·m vs N·m).
3) What the torque-to-viscosity step assumes
For Newtonian flow under ideal conditions, torque scales linearly with viscosity at fixed angular speed. The calculator applies the standard cone-and-plate torque relation (with SI conversions) and then outputs viscosity and supporting values in your selected units.
4) Shear rate and shear stress interpretation
Nominal shear rate is approximately γ̇ ≈ ω/θ; doubling angular speed doubles γ̇. Shear stress follows from torque and radius and is useful for sanity checks. Reporting ω, γ̇, and τ makes results easier to compare across instruments.
5) Temperature control and repeatability
Viscosity is strongly temperature dependent. Many fluids shift by several percent per °C near room temperature, so a stable plate (often ±0.1 °C or better) improves repeatability. Log setpoint, equilibration time, and evaporation controls when relevant. Document ambient humidity for volatile solvents too.
6) Practical ranges you may encounter
Typical cone radii are 10–25 mm, and speeds often span ~0.1 to 100 rad/s within torque and inertia limits. Torques can range from µN·m to tens of mN·m. With good control, measurements can cover roughly 1 to 105 mPa·s. Smaller angles raise shear rate at the same speed.
7) Non-Newtonian samples and apparent viscosity
For shear-thinning or shear-thickening materials, viscosity depends on shear rate. A single torque reading yields an apparent viscosity at that γ̇. For characterization, sweep speed, export the dataset, and fit a model (power-law, Carreau) if needed.
8) Good measurement practice and reporting
Report geometry (R, θ, gap), temperature, angular speed, and the calculated shear rate. Watch for wall slip: unexpectedly low viscosity at high shear or poor repeatability can be a clue. If drift appears, check alignment, loading, and edge effects before interpreting changes.
FAQs
1) Do I enter the cone angle in degrees or radians?
Use the unit you select in the form. The calculator converts the angle to radians internally so shear rate and viscosity remain consistent.
2) What if my cone is truncated with a gap?
Enter the truncation gap if your cone has a flat tip. Ignoring a real gap can bias the viscosity, especially for low-angle cones.
3) Can I use this for non-Newtonian fluids?
Yes. Treat the output as apparent viscosity at the computed shear rate. Measure multiple speeds to build a viscosity-versus-shear-rate curve.
4) Why does temperature change the result?
Many liquids change viscosity by several percent per °C. Stable temperature control and adequate equilibration reduce scatter and improve comparability.
5) My torque is extremely low—what should I do?
If torque is near instrument resolution, noise dominates. Increase speed, use a larger radius, or choose a more sensitive torque range when available.
6) Which export should I choose?
CSV is best for analysis and plotting, while PDF is convenient for sharing a fixed report. Include geometry and temperature with any export.
7) How can I check for wall slip?
Repeat at different shear rates and compare smooth versus roughened surfaces if permitted. Low viscosity at high shear or poor repeatability may indicate slip.