Falling-Ball Viscometer Calculator

How to use

1. Confirm that a rigid sphere reaches terminal speed in a Newtonian liquid and that walls and ends are sufficiently remote.
2. Select Distance and time or Terminal velocity.
3. Enter sphere diameter in mm and sphere/fluid densities in kg/m³; sphere density must be greater.
4. Enter positive fall distance in mm and time in s, or positive terminal velocity in mm/s, plus local gravity in m/s².
5. Optionally enter independent relative standard uncertainties in percent.
6. Select Calculate to update results; select Reset to restore the example.
7. Reject results with Re ≥ 0.1 or when terminal, Newtonian, no-slip, or unbounded-flow assumptions are not credible.

Equations used

v_t = l/t
μ = g d² (ρ_s − ρ_f) / (18 v_t)
ν = μ/ρ_f
Re = ρ_f v_t d / μ
u_μ/μ = √[(2u_d/d)² + (u_Δρ/Δρ)² + (u_g/g)² + (u_v/v_t)²]

Symbols and units.d is sphere diameter (m); ρ_s and ρ_f are sphere and fluid density (kg/m³); Δρ = ρ_s − ρ_f; g is positive downward gravity (m/s²); l is timed distance (m); t is time (s); v_t is positive downward terminal speed (m/s); μ is dynamic viscosity (Pa·s); ν is kinematic viscosity (m²/s, displayed as mm²/s); Re is dimensionless; and the u terms are independent relative standard uncertainties.

Assumptions and limits. The sphere is rigid and smooth; the fluid is homogeneous, Newtonian, and no-slip; terminal speed and constant properties apply; ρ_s > ρ_f; wall/end and rotation effects are negligible; and Re < 0.1. Do not use for inertial settling, accelerating or rotating spheres, non-Newtonian/multiphase fluids, slip, close boundaries, or standards-critical measurement.

References. Bird, Stewart & Lightfoot, Transport Phenomena, 2nd ed., Ch. 2, p. 61; Engineers Edge equation background; ASTM D1343 method context (no conformance claim).

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