Physics
Falling-sphere viscometer
A ball dropped in a liquid stops accelerating: weight, buoyancy and Stokes drag balance. Time it between the marks and the viscosity follows.
What happens
Two columns side by side, so the comparison needs no memory. A sphere released at the surface reaches terminal speed within a fraction of a second in a thick liquid; time it between the two marks and the viscosity follows from v∞ = 2r²(ρs−ρf)g/(9η). Stokes' law only holds while the flow creeps - Re below about one. A steel ball in water exceeds that by five orders of magnitude, and the panel says so instead of quietly reporting a wrong answer.
Equations used in the module
Equations b = 6πηr Wall correction (Ladenburg, tube 2 cm): b = 6πηr(1+2.4r/R) m v′ = (ρ_b−ρ_f)Vg − bv v_t = (ρ_b−ρ_f)Vg/b; τ = m/b v(t) = v_t+(v₀−v_t) exp(−t/τ) Re = 2rρ_f|v|/η η(T) = η₂₀ exp(−B(T−20))
