This experiment measures the viscosity of glycerine by dropping steel spheres through it. Stokes’ law says the terminal velocity goes as the square of the radius, so plotting log velocity against log radius should give a straight line of slope exactly 2.

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BEFORE YOU START
Viscosity — Shear Rate, Shear Stress and Newton’s Law

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What makes this one different

In projectile range and friction on an incline, the culprit was an instrument: a tape with an offset, a hand late on the stopwatch. Here nothing is broken. The light gates work, the radii are exactly as marked, the times are almost noise-free. Your answer still comes out wrong.

The reason is that Stokes solved the problem for an unbounded fluid, and you are applying it inside a tube a few centimetres across. The fluid the sphere pushes aside has nowhere to go but back past the sphere itself, which slows it down. A larger sphere fills more of the tube, so it is slowed more — the error grows with size and drags the slope away from 2. Drop a single sphere and you will never know; what gives it away is the trend in the error, not the error itself.

The general lesson: “my instrument was precise” does not guarantee “my answer is right”. Every formula has a domain of validity, and part of designing an experiment is asking whether you are inside it.

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