Liquid column with two timing marks
Provide a 0.100 m timing distance below the initial settling region.
Physics / Stokes’ viscosity
FREE TO EXPLOREEXPERIMENT 05 · PHYSICS LABORATORY
Viscosity by Stokes’ falling-sphere method
Determine the dynamic viscosity of a liquid from the terminal speeds of small spheres and the gradient of a speed–radius-squared graph. Explore a virtual apparatus, collect readings and analyse a graph.
CHANGE · OBSERVE · MEASURE
Your virtual workbench.
TIME BETWEEN TWO GATES—
MEASUREMENT STATUS
Ready for a virtual observation.
Adjust the apparatus, then take a reading.
Timing is generated from the model; a short on-screen trial represents a longer physical interval. Animation is illustrative.
Simulation assumptions and limits
The calculation assumes an isolated rigid sphere in an unbounded, incompressible Newtonian fluid with constant density and viscosity and creeping flow. The illustrated column is a schematic timing gate; its walls exert no modeled correction. Initial acceleration, wall and end effects, bubbles, nonspherical beads and temperature drift are omitted. Timing starts after terminal motion is established. Virtual animation time is accelerated; reported elapsed time is physical model time. A fit error or perfect simulated line is not a complete experimental uncertainty estimate. The Newtonian liquid has a model viscosity of 1.20 Pa s at a fixed temperature. An effectively unbounded liquid is assumed. The simulated Reynolds number stays below 0.004 across the allowed radii. There are no wall/end corrections or temperature changes. Pre-terminal motion is not timed; the displayed fall is accelerated and not to scale.
Know your apparatus.
Spherical beads
Provide smooth spheres of known density and different measured radii.
Micrometer and ruler
Measure sphere diameter and vertical separation of the timing marks.
Timer and thermometer
Record transit time and monitor liquid temperature, which affects viscosity.
FOLLOW THE METHOD
A reason behind every step.
Determine the dynamic viscosity of a liquid from the terminal speeds of small spheres and the gradient of a speed–radius-squared graph. Suggested independent settings: 0.3, 0.45, 0.6, 0.75, 0.9 mm.
Record the controlled conditions
Record sphere density 2500 kg/m³, liquid density 1260 kg/m³ and g = 9.80665 m/s². In a physical lab also record temperature and confirm the liquid is suitable for a falling-sphere method.
Why this step matters
Density difference, gravity and temperature enter the interpretation of terminal speed.
Measure sphere sizes
Measure each sphere diameter in several orientations, halve it to obtain radius, and convert to metres before calculating r². Select virtual radii within 0.300–0.900 mm.
Why this step matters
The result depends on radius squared, making size measurement especially influential.
Define the timing gate
Set the vertical mark separation to 0.100 m below the release region. Release the sphere gently away from walls and verify steady motion before the upper mark.
Why this step matters
The terminal-speed equation does not apply to timing that includes initial acceleration.
Time and record each transit
Time the sphere centre between the marks and record radius, r², distance and physical elapsed time. Repeat for several radii; the animation accelerates viewing while retaining modeled physical time.
Why this step matters
Consistent crossing definitions and multiple sizes produce comparable observations.
Convert times to speeds
For each row calculate v = H/t. Fit v against r² and inspect the points and intercept. Calculate a trial viscosity and Reynolds number to check the creeping-flow condition.
Why this step matters
A model should be checked against its assumptions before interpreting a fitted parameter.
Determine viscosity and assess limits
Use the gradient in η = 2(ρs − ρl)g/(9s). State viscosity in Pa·s, report the low Reynolds numbers and discuss temperature, walls, radius and timing as uncertainty sources.
Why this step matters
A numerical answer is meaningful only together with the conditions under which it was inferred.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into a result.
Points are your observations. The fit uses SI x and y values before display scaling.
LINEAR FIT · y = mx + b
v = mr² + b; η = 2(ρₛ − ρₗ)g/(9m)
| # | Sphere radius r (mm) | Time between two gates (s) | Radius squared r² (10⁻⁶ m²) | Terminal speed v (mm s⁻¹) | Remove |
|---|
No readings yet. Take a virtual measurement and record it.
Calculate it yourself.
CHECK YOUR UNDERSTANDING