Viscosity of Liquids

Introduction

When a sphere of density r_s and radius R is dropped into a fluid of density r (recall that a fluid can be either a liquid or a gas) it accelerates to a constant terminal velocity, v_t, at which point the downward force due to the influence of gravity on the sphere, 4/3 pR³r_s g, is equal to the sum of the bouyancy force, 4/3pR³rg and the drag force 6phRv_t, where h is the viscosity of the fluid.

provided that the Reynolds number is <0.1. This is known as Stokes’ Law. The Reynolds number, which is dimensionless, is given by

Experiment

In this laboratory you are provided with a transparent liquid whose viscosity you are to determine using Stokes’ Law. First, using the density bottles, you must determine the density of the liquid. The liquid is then placed in a burrette and the terminal velocity of small steel ball bearings is measured by measuring the time required for the ball to drop a given distance - don’t forget to measure the diamter of the ball first. From the measurements you have made you should be able to determine the viscosity of the liquids. Using the Reynolds number, ascertain whether or not your results were obtained under streamline flow. The terminal velocity of the balls is to be measured in tubes of different internal diameter.

The experiment is to be carried out using 20 balls of each of the two diameters. The liquid supplied is glycerine.

Statistics

(i) measure the diameter of each ball and determine a mean and standard deviation (error).
(ii) measure the time of each ball to fall the set distance. Determine the mean and error.
(iii) determine the velocity and error in velocity

Measure the liquid density using the density bottles provided. The density of the steel ball bearings is 7.81gcm^-3 .

Using the information given above determine the viscosity and error in viscosity of each of the four liquids.

Report

A report containing the experimental procedure, a table of results and the respective viscosities is required. Please indicate potential sources or error other than those mentioned in this laboratory hand out. Hint. What are the effects of tube size, and tube diameter to ball diameter.