Theoretical Correction of Viscosity Coefficient Measurement by Falling Ball Method

Abstract

The measurement of viscosity coefficient of liquids is vital in plentiful fields. There are numerous ways to measure the viscosity coefficient such as capillary and rotary rheometry in which falling ball method is mostly widely used. The uncertainty of the terminal velocity and the limit of the viscosity coefficient scale are the principled disadvantages of the method. In our work, the relationship between the displacement and time is obtained by integral calculation. What's more, we considered the radius of the ball, the radius of the graduated cylinder, and the height of the graduated cylinder by theoretical correction of the stokes expression. The new correction expression broadens the measured viscosity coefficient scale and also improves the precision dramatically. Experimental verification is also well processed which fits well with our theory. The deviation between the viscosity coefficient of castor oil measured by the new correction method and the standard value is only 0.045. The relationship between displacement and time is consistent with the theoretical prediction, and the room mean square error of the two is 0.065. Based on them, this method can be widely used in scientific researches and teaching practices.