This guide practises inferring liquid viscosity from a falling sphere using an explicit force model. The outline is a starting point for a locally approved method and risk assessment, not a complete validated procedure. Check the current Pearson specification and practical guide for course-specific requirements.
Aim and scientific principle
Infer dynamic viscosity from the terminal speed of a rigid sphere falling through a Newtonian liquid. The uncorrected Stokes model requires very low Reynolds number and negligible wall and end effects; steady speed alone does not establish those conditions.
Begin by translating the title into a testable question. Identify what is deliberately changed, what is measured directly, what is calculated and what must remain controlled. Predict a relationship only after naming the mechanism. A prediction without a reason is weak; a reason without measurable variables cannot guide a practical design.
Apparatus and setup
Use transparent tube, viscous liquid, small spheres, micrometer, timing marks, timer or video, thermometer and density data. Consider measuring range, resolution, uncertainty, calibration and suitability for the sample, not the instrument name alone. Draw a labelled scientific setup that shows the working geometry and exactly where readings are taken. Include a control or blank when it distinguishes the target effect from drift, contamination or background response.
Before collecting results, check zero readings, calibration, leaks, alignment or sterility as relevant. Record the instrument resolution beside the first raw-data table. If a digital device displays more digits than its underlying accuracy supports, do not treat every digit as equally certain.
Method
Choose either a radius investigation at fixed liquid temperature or a temperature investigation using the same sphere. Measure sphere diameter in several orientations, obtain sphere and liquid densities appropriate to the conditions, and record liquid temperature and tube dimensions.
Release the fully immersed sphere centrally from rest without a push or attached bubbles. Keep it clear of the walls, liquid surface and bottom, and allow initial acceleration to finish before the timing region.
Compare speeds over successive measured intervals. Use a region in which they agree within the measurement uncertainty; repeat the release and inspect the original readings. For temperature changes, allow the liquid to equilibrate and use density values appropriate to each temperature.
Calculate speed from measured distance and time. Apply the weight-upthrust-drag balance only when the Stokes and terminal-speed assumptions are supported. Check the Reynolds number and sphere-to-tube size ratio; use a validated correction or change the apparatus if finite-boundary or inertial effects are material.
Check this topic from memory
Attempt the matching topic bank before reopening the notes. Use each missed idea to decide what to review next.
Plan the analysis before starting. This reveals whether an additional measurement is needed for a derived quantity and prevents a completed experiment from lacking a mass, length, concentration, background or calibration value. A method should be detailed enough for another trained student to reproduce, while avoiding decorative steps that do not affect validity.
Variables and controls
Independent variable: sphere radius at fixed temperature, or liquid temperature with the same sphere; specify one design.
Dependent variable: travel time over the timing region and calculated terminal speed; infer viscosity only under the stated model. Record the timing-region distance as a measured input.
Important controls: liquid composition, tube geometry, timing region and release procedure; hold temperature fixed for a radius investigation and sphere size/material fixed for a temperature investigation.
For each control, state how it is maintained or monitored. Simply writing "keep temperature constant" is incomplete if the method has no bath, probe, equilibration time or other means of doing so. Choose a range wide enough to reveal the relationship but within safe and scientifically valid limits. Choose the number, range and spacing of values for the expected response and analysis. Concentrating values near an uncertain threshold or optimum can be more useful than uniform spacing; no fixed count establishes an adequate design.
What is distinctive about this practical
For a rigid, no-slip sphere in creeping flow, Stokes drag has magnitude FD=6πηrv. At terminal speed the force balance is 34πr3(ρs−ρl)g=6πηrvt, giving η=9vt2r2(ρs−ρl)g. Here the sphere density exceeds the liquid density, r is the radius, and the densities and dynamic viscosity refer to the stated temperature.
Use Re=2ρlrvt/η to check the very-low-Reynolds-number assumption, Re≪1. Also check that tube walls, the surface and the bottom do not materially change the drag. A central release and a steady speed do not, by themselves, validate an unbounded-fluid Stokes calculation. Radius, density, temperature and geometry are model inputs, not incidental details.
Recording and processing results
Calculate interval speeds and assess terminal motion before inferring viscosity. In a fixed-temperature radius investigation with unchanged sphere material and liquid, the model predicts vt∝r2; plot terminal speed against radius squared only within the supported Stokes regime. For a temperature investigation, calculate viscosity with the relevant density inputs at each temperature. Discuss wall, end and non-terminal effects. Put units in column headings, record raw readings consistently with instrument resolution and the method and distinguish repeats from calculated means. Do not delete an anomaly merely because it is inconvenient. Recheck the condition, look for a procedural explanation and state any exclusion rule.
Choose a fitted line, curve or ruled joins according to the data, scientific relationship and question; do not connect or smooth points mechanically. A gradient should use a large triangle and values read from the fitted line. When a relationship is linearised, explain the transformation and connect gradient or intercept to the requested physical quantity. When observations are categorical, define the category rule before seeing the result.
Safety, ethics and responsible practice
Secure the tall tube, clean spills promptly and handle dense or viscous liquids according to local guidance. A useful safety statement names the hazard, identifies who or what could be harmed and gives a control that reduces likelihood or severity. "Take care" does not specify an action that reduces the identified risk.
Worked application: from raw evidence to a defensible conclusion
As a model comparison rather than a measured result, consider doubling the sphere radius while keeping liquid temperature, sphere material and liquid composition unchanged. The Stokes terminal-speed model predicts a fourfold speed increase. However, because Reynolds number is proportional to radius times speed for unchanged liquid properties, it increases eightfold. A radius range that was valid for the smaller sphere may therefore leave the Stokes regime; a straight-looking graph alone cannot resolve that issue.
In actual measurements, compare successive interval speeds, inspect repeats and quantify the material length, time, diameter and density uncertainties. Retain raw observations and justify exclusions. Do not simultaneously describe temperature as deliberately changed and held constant. If the supported speed is smaller than the unbounded terminal-speed prediction because of additional wall drag, substituting it into the uncorrected viscosity expression biases the inferred viscosity high.
This chain is stronger than a memorised recipe because every step answers the practical question. If the graph contradicts the prediction, report the evidence honestly and investigate method, range, controls and model assumptions before claiming a new scientific law.
Evaluation: limitation, effect and improvement
Limitation: the sphere may not reach terminal speed or may experience wall effects.
Likely effect: for a sphere released from rest in initially still liquid, timing during acceleration underestimates its terminal speed. Additional wall drag also reduces speed relative to the unbounded model. In either case, substituting the smaller speed into the uncorrected Stokes expression biases inferred viscosity high; a pushed release needs a separate analysis.
Targeted improvement: verify a terminal region using successive intervals, use appropriate central release and a wider/deeper vessel where feasible, and control or equilibrate temperature. Calibrated video may improve timing, but does not remove wall effects or establish low Reynolds number. Use only a validated correction for the actual geometry and flow regime.
Separate random variation, systematic bias and model limitation. Repeats help reveal random variation but do not remove a zero error. Calibration establishes the relation between reference values and indications; appropriate adjustment or correction can address an identified offset. It does not make biased sampling representative. Finer resolution and greater repeatability are distinct properties, and finer resolution may improve an estimate only when the reading is a material source of uncertainty.
Common misconceptions and corrections
Repeats automatically make a result accurate. Repeats estimate random variation; they do not correct a biased method or calibration error.
A control variable is just a list item. Explain the apparatus or procedure that keeps it stable.
The line must pass through every point. Use the overall pattern and a best-fit relationship, then investigate justified anomalies.
Percentage error and percentage uncertainty are interchangeable. Error compares a measured value with a suitable reference. Uncertainty characterises dispersion of values attributed to the measurand; it may be expressed as a standard uncertainty or an interval with stated coverage, and includes more than resolution alone. State the reference, denominator and uncertainty convention used.
A successful endpoint proves the theory. The observation supports a conclusion only within the method, range and assumptions tested.
More sophisticated apparatus is always better. The improvement must address the dominant limitation and be practical in the stated context.
Assessment guidance
Pearson states that IAL practical skills are assessed mainly in Unit 3 and Unit 6, with related theory also assessable in the other unit papers. Planning answers need an operational independent variable, a measured dependent variable, a justified range, controls, repeats, safety and a stated analysis. Data answers need units, consistent precision, sensible significant figures and transparent calculations. Graph answers need labelled axes, a scale using the grid well and line treatment appropriate to the data and question. Evaluation answers should use a limitation-effect-improvement chain specific to the apparatus. Do not claim that a memorised core-practical recipe is the only acceptable method when the question supplies a different valid context.
Retrieval practice
Extend or adapt this practical to answer a related question. Where the design uses a continuous variable, justify its planned values. List apparatus with range and resolution where relevant, control methods, a raw record layout, the expected analysis and one hazard-control pair. Then identify one random uncertainty, one systematic bias and one model limitation. Explain which can be reduced by repeats, which needs calibration followed by appropriate correction or adjustment, or a redesign, and how your conclusion would change if the anomaly were confirmed.
