Studies On Falling Ball Viscometry

Abstract

A new method of accurate calculation of the coefficient of viscosity of a test liquid from experimentally measured terminal velocity of a ball falling in the test liquid contained in a narrow tube is described. The calculation requires the value of a multiplicative correction factor to the apparent coefficient of viscosity calculated by substitution of terminal velocity of the falling ball in Stokes formula. This correction factor, the so-called viscosity ratio, a measure of deviation from Stokes limit, arises from non-vanishing values of the Reynolds number and the ball/tube radius ratio. The method, valid over a very wide range of Reynolds number, is based on the recognition of a relationship between two measures of wall effect, the more widely investigated velocity ratio, defined as the ratio of terminal velocity in a confined medium to that in a boundless medium and viscosity ratio. The calculation uses two recently published correlation formulae based on extensive experimental results on terminal velocity of a falling ball. The first formula relates velocity ratio to Reynolds number and ball-tube radius ratio. The second formula gives an expression of the ratio of the drag force actually sensed by the ball falling in an infinite medium to that in the Stokes limit as a function of Reynolds number alone. It is shown that appropriate use of this correction factor extends the utility of the technique of falling ball viscometry beyond the very low Reynolds number 'creepy flow' regime, to which its application is presently restricted. Issues related to accuracy are examined by use of our own measurements of the terminal velocity of a falling ball in a narrow tube and that of published literature reports, on liquids of known viscosity coefficient.