Wall Effect in Falling Ball Method for Viscosity

The wall effect for balls falling in a vertical cylindrical tube in a viscous fluid has been studied and expressed as an empirical function of the ratio of radii of the ball and tube. This function agrees well with observations at least to a ratio of 0.83 as compared with 0.09, the limit of agreement of Ladenburg's formula. The wall effect is probably independent of the absolute radii of the ball and tube and only slightly dependent upon the absolute viscosity. The bottom effect is negligible. For liquids of high viscosity the revised formula is $${\text{η=2gR}}^2{\mathrm{(\rho }}_1{\mathrm{-\rho }}_2{\text{)(1−R/r)}}^{\text{2.25}}\text{/9u.}$$