Determination of viscosity through terminal velocity: use of the drag force with a quadratic term in velocity

A correction to the term with quadratic dependency of the velocity in the Oseen´s drag force by a dimensionless factor is proposed in order to determine the viscosity of glycerin through the measurement of the terminal velocity of spheres falling inside the fluid. This factor incorporates the effect of the container´s wall over the movement of the spheres, analogously to the correction of the Stoke´s force by the Landenburg factor, and permits to make the Oseen´s force compatible with the experimental data for the drag coefficient up to Reynolds number near 30.

Admitting a proportionality relation between these factors, the viscosity coefficient turns into a linear coefficient in the relation between the parameter that corresponds to the viscosity that would be determined if only the Stokes’ force was considered and the product of the terminal velocity by the diameter of the spheres.

The experiment with steel spheres falling inside tubes of different diameters showed values for the viscosity coefficient of glycerin compatible with the expected, for the temperature range worked. This method might be applied to Reynolds number of order of ten of the sphere’s motion, relaxing the restriction of working with Reynolds numbers inferior to 0.5 for the determination of the viscosity through the Stokes’ method.