EDEXCEL
Core Practical 2 — Determine the Viscosity of a Liquid Using a Falling Ball
CP2 · AS Physics
Stokes' Law, terminal velocity and the determination of viscosity
When a ball falls through a viscous liquid three forces act on it: its weight W downward, the upthrust U upward (Archimedes' principle), and the viscous drag F upward (opposing motion). Initially the ball accelerates, but as speed increases, drag increases until the net force is zero — the ball then falls at constant terminal velocity.
At terminal velocity the forces balance:
where r = radius of ball, v = terminal velocity, η = dynamic viscosity, ρ = density
Rearranging for terminal velocity v gives the key equation:
Plotting v (y-axis) against r² (x-axis) gives a straight line through the origin.
Gradient m = 2(ρ_ball − ρ_fluid)g / 9η, therefore η = 2(ρ_ball − ρ_fluid)g / 9m
This linear relationship is the basis of the experiment — you measure terminal velocity for balls of different radii, then use the gradient of the v vs r² graph to find η.
Stokes' Law F = 6πηrv only applies when:
Glycerol is highly viscous which ensures laminar flow for small steel ball bearings, making it ideal for this experiment.
Note: viscosity of glycerol is highly temperature-dependent. Results vary significantly with temperature.
This is a controlled teaching model at 25 °C. The liquids use fixed reference values: glycerol 0.934 Pa·s, 1261 kg m⁻³; illustrative vegetable oil 0.084 Pa·s, 920 kg m⁻³. Real oil depends on composition; these are not universal certified values.
Motion includes weight, buoyancy and linear Stokes drag. Re ≤ 0.1 is a conservative modelling criterion. Wall, end, added-mass and fluid-history effects are neglected; the short release transient is illustrative. In real work use a wide container, controlled temperature and check constant speed.
The screw gauge resolves 0.01 mm. Students determine its fixed signed zero error and correct each reading. Orientation-dependent contact readings vary by up to ±0.01 mm; variation is held fixed while a reading is taken. Changing nominal sphere size starts a new set of diameter readings, but retains the instrument zero check. Timing has fixed marker offsets within ±0.003 s and independent crossing variation within ±0.002 s. The A–B spacing has a session offset within ±1 mm. Offsets persist across repeats. These are teaching assumptions, not instrument specifications.
Radius uncertainty is half the larger of the corrected-diameter half-range or 0.01 mm, allowing for both reading and zero-correction resolution. Timing uncertainty is the larger of time half-range or 0.001 s. %U(v) = %U(L) + %U(t); %U(r²) = 2%U(r). Repeats do not remove fixed offsets.
Follow these steps in the Simulation tab to collect your data
Tall measuring cylinder of glycerol · Steel ball bearings (3–5 different radii) · Micrometer screw gauge · Ruler · Stopwatch or light gates · Magnet (to retrieve balls) · Electronic balance
Choose a sphere size with the slider and start dropping immediately. Optionally use Screw gauge to practise zero correction and transfer a measured radius. Results label whether the radius came from the slider or micrometer.
Three markers define two successive 0.200 m intervals. Compare their times to test for constant speed. The first marker is 0.100 m below release.
Use Drop Ball in the toolbar immediately above the apparatus. The ball falls through the selected liquid. The timer records the time t for the ball to travel between the two bands. Realistic noise is added to simulate real timing uncertainty.
Take three drops in total at the same radius to obtain a mean time and assess random uncertainty.
Click Record Reading. First check the radius, mean time and speed, and identify the evidence for terminal velocity. Then record the set.
Change the ball radius and repeat steps 3–5. You need at least 5 different radii for a reliable graph.
Go to the Graph & Analysis tab. Plot v against r² and use the gradient to calculate η.
Radius source (screw gauge optional):
FALLING-BALL VISCOMETER · 25 °C
A–B and B–C are each 0.200 m. Track the sphere centre. Automatic virtual video timing; no manual reaction-time measurement. Cylinder and sphere are schematic and enlarged laterally.
A–B: — s · B–C: — s
MEASUREMENT WORKSHOP · LINKED TO YOUR SPHERE
Check zero → read both scales → correct three diameters → calculate radius.
Drag the ratchet up to close or down to open; click it for one division. Keyboard: focus the overview and use ↑/↓. Controls above do the same. Three gentle ratchet slips confirm contact in this teaching model; further slips do not squeeze the sphere.
The MSR/PSR is the last exposed sleeve graduation, including any half millimetre. The CSR is the circular division aligned with the horizontal datum.
Observed diameter = MSR + CSR × 0.01 mm.
Zero correction = −(signed zero error).
Corrected diameter = observed diameter − zero error.
Mean radius = mean corrected diameter ÷ 2.
For a negative zero error, the thimble zero lies above the datum when the empty faces touch. If division n aligns, the signed error is −(50 − n) × 0.01 mm. For positive error, zero lies below the datum and the signed error is +n × 0.01 mm.
The enlarged zero-check view hides negative sleeve numbers: use the thimble zero relative to the datum to determine the sign. It is not a negative diameter.
With no sphere, approach gently, then turn the ratchet until three slips. Read the circular division and zero-line position.
Orientation 1 of 3
This is an original teaching schematic of a metric outside micrometer with 0.5 mm screw pitch and 0.01 mm graduation. Parts, sleeve/thimble reading and the force-limiting ratchet are based on Mitutoyo’s measuring-instrument guide. The overview is not to scale; the enlarged reading panel preserves the scale arithmetic. It is not a replica or calibration certificate for a commercial instrument.
The intentional zero error stays fixed for the chosen instrument. Three orientation readings include small fixed contact variations. Zero correction removes the modelled zero offset; residual resolution and repeat spread still contribute uncertainty. The corrected readings are passed directly into the viscosity table, graph and CSV.
Auto-filled from simulation. You need at least 5 different radii for a reliable graph.
Plot of terminal velocity v (y-axis) against r² (x-axis). Read your gradient from the graph, then work out η yourself.
%U in v = %U in t + 0.5%, including the ±1 mm uncertainty in the 0.200 m interval.
Free-intercept fit. Horizontal bars: propagated radius uncertainty for micrometer measurements; slider radius is treated as a specified model value with no measurement uncertainty. Vertical bars: time half-range (minimum 0.001 s) plus 0.5% distance uncertainty. These are measurement estimates, not confidence intervals or uncertainty in η.
Write your answers below. Click "Show Model Answer" when ready to compare.