A spherical body of radius r and density σ falls freely through a viscous liquid of density ρ and viscosity η, and attains a terminal velocity v₀. The estimated maximum error in the quantity η is (ignore the errors associated with σ, ρ and g, the gravitational acceleration)

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(1) (2Δ r)/r+(Δ v₀)/(v₀). Given: a sphere falling at its terminal speed v₀, so weight, buoyancy and Stokes drag balance. 4/3π r³(σ-ρ)g=6πη rv₀, which gives η=(2r²(σ-ρ)g)/(9v₀). Only r and v₀ are measured here, and in that expression η∝(r²)/(v₀). For a product of powers the fractional errors add, each weighted by the magnitude of its exponent. (Δη)/η=2(Δ r)/r+(Δ v₀)/(v₀).

A spherical body of radius r and density σ falls freely through a viscous liquid of density ρ and viscosity η, and attains a terminal velocity v₀. The estimated maximum error in the quantity η is (ignore the errors associated with σ, ρ and g, the gravitational acceleration)

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