Rotational Viscometer Calculator
Calculate ideal friction torque or dynamic viscosity for coaxial-cylinder and cone-on-plate rotational viscometers.
Engineering screening tool—verify inputs and results independently. Use at your own risk.
Calculated response
Ideal Newtonian result for the selected geometry.
Equations used
Positive rotational speed N, viscosity η, shear rate γ̇, shear stress τ, and resisting-torque magnitude M are entered or reported as positive magnitudes. Convert all geometry to metres, N to rpm, M to N·m, and α to radians before evaluating.
Common relation
Coaxial cylinder
Cone on plate
Symbols: D is spindle diameter [m], D₂ is chamber diameter [m], δ is radial gap [m], L is effective wetted length [m], R is cone radius [m], α is cone angle [rad], N is speed [rpm], ω is angular speed [rad/s], η is dynamic viscosity [Pa·s], γ̇ is shear rate [s⁻¹], τ is shear stress [Pa], and M is torque magnitude [N·m]. D₂ must be greater than D; all dimensional magnitudes and N must be finite and strictly greater than zero.
How to use
- Select Coaxial cylinder or Cone on plate.
- Select Torque from viscosity when η is known, or Viscosity from torque when M is measured.
- Enter coaxial dimensions D, L, and D₂ in mm, with D₂ greater than D; or enter α in degrees and R in mm. α is converted from degrees to radians.
- Enter positive rotational speed N in rpm and the required positive η in Pa·s or M in mN·m.
- Select Calculate. Correct any red warning before interpreting the canonical result and supporting shear metrics.
- Report viscosity with geometry, speed, sample temperature, and instrument calibration. The coaxial shear rate is a narrow-gap estimate; cone shear rate is ideal and uniform.
- Select Reset example to restore the coaxial demonstration. Switching to cone mode uses its supplied geometry; set N=750 rpm for the worked cone example.
- Do not use the model for non-Newtonian material characterization, yield-stress fitting, turbulent/secondary flow, wall slip, temperature-sensitive self-heating, safety qualification, or an uncalibrated instrument.
Worked example
1. Choose Coaxial cylinder and Torque from viscosity. Enter D=20 mm, L=10 mm, D₂=22 mm, N=75 rpm, and η=0.1 Pa·s. 2. Calculate. Expected M=0.049348 mN·m, γ̇=78.5398 s⁻¹, and τ=7.85398 Pa. 3. The torque is the ideal resisting magnitude; an actual instrument may require end-effect and calibration corrections.
Theory and method
A rotational viscometer infers a Newtonian fluid’s dynamic viscosity from the proportionality between imposed angular speed and resisting torque. The coaxial-cylinder relation implemented here treats the annular velocity gradient as linear across δ. This is a narrow-gap approximation, not the exact finite-gap Couette solution. The cone-on-plate relation assumes a small ideal cone angle, negligible tip truncation, and uniform shear rate ω/α.
The model assumes steady, laminar, isothermal, incompressible, Newtonian flow; concentric/aligned rigid surfaces; no wall slip; and negligible edge, end, inertia, secondary-flow, free-surface, compliance, and meniscus effects. Effective cylinder length may need calibration for end effects. Instrument torque range and spindle-specific limits must be checked independently. For non-Newtonian samples, apparent viscosity changes with shear history and rate, so use a suitable rheometer method rather than interpreting this single-point result as a material constant.
References
- Barnes, H. A. (2000), A Handbook of Elementary Rheology, University of Wales Institute of Non-Newtonian Fluid Mechanics, rotational viscometry chapters.
- ASTM D2196-20, Standard Test Methods for Rheological Properties of Non-Newtonian Materials by Rotational Viscometer, doi:10.1520/D2196-20. This calculator does not replace the instrument, procedure, or reporting requirements of that standard.
Continue in TriboSolver
Use TriboSolver to refine rotating-clearance flow, thermal effects, non-Newtonian behavior, and geometry-specific shear fields when the ideal screening assumptions are insufficient.