Experimental Investigation of Wall and Inertial Effects on a Disk Sedimenting at Low Reynolds Number.
Date of Award
Doctor of Philosophy (PhD)
R. G. Hussey
Measurements have been made of the drag on a thin disk of diameter d moving broadside through a liquid of viscosity $\mu$ and density $\rho$. The liquid is bounded on the outside by a cylindrical tube, diameter D, which is coaxial with the disk. The geometrical parameter $\xi$ = d/D ranges from 0.0189 to 0.112. The Reynolds number Re = $\rho$Ud/$\mu$ ranges from 0.0167 to 6.89. When the measured values are extrapolated to Re = 0, the results agree with the calculations of Shail and Norton. When extrapolated to $\xi$ = 0, the results agree with the matched-asymptotic series solution of Breach for Re $<$ 1. Comparison of the experimental data to a new theoretical result, that is based upon the Oseen approximation and that includes both inertial effects and boundary effects, shows agreement over the range $4\xi<\rm Re<0.62$ as long as $\xi<0.05.$ An empirical scheme is developed to represent our measurements for Re $<$ 5 and $\xi<0.13.$ Comparison is made between our results for the drag on a disk and the results of Sutterby for the drag on a sphere.
Pulley, Joe Wade, "Experimental Investigation of Wall and Inertial Effects on a Disk Sedimenting at Low Reynolds Number." (1996). LSU Historical Dissertations and Theses. 6275.