VI. The equation of state

Abstract

An experimental study has been made of the free motion of a particle in a liquid rotating as a solid body, the liquid being water, glycerol, or three different mixtures of water and glycerol. Nylon, glass and steel particles of nominal diameters 2.4 mm, 3 mm and 3.2 mm were introduced, one at a time, into the rotating liquid, and their trajectories were recorded photographically, a stroboscope being used for lighting. By fitting polynomial relations to the displacement-time data, and differentiating them, the components of the velocity and the acceleration were obtained; from these the resultant drag and the components of the lift on the particle were calculated. The data for the drag and the lift components were correlated with the flow parameters into empirical expressions, and compared with the relevant theoretical solutions and experimental results of other workers. The range of the Reynolds number in the experiments described here was 0.035 $\leqslant$ ud/$\nu \leqslant$ 3365, the range of the Taylor number was 0.084 $\leqslant \omega$d$\nu \leqslant$ 312, and the range of the Rossby number was 0.24 $\leqslant$ u$\omega$d $\leqslant$ 20, where d is the diameter of the particle, u is its resultant velocity relative to the liquid, and $\omega$ and $\nu$ are the angular velocity and the kinematic viscosity of the liquid respectively. The ratio of the density of the particle to that of the liquid was between 1.15 and 8.14.