Expt.
: Dynamical viscosity of a liquid and Stokes’ law
Aim: To determine the coefficient of viscosity of a liquid using a falling ball viscometer (employing Stokes’ law)
Experimental apparatus: The main experimental apparatus (Fig. 1) consists of a glass tube containing the
experimental liquid. P and Qare two adjustable reference marks along the tube length. The entire glass system is
supported bya wooden stand. Besides this you will need a few steel balls of different diameter, screw gauge, digital
balance, vernier calliper, stopwatch, and meter scale for this experiment.
Principle of the experiment: A body moving in a fluid is acted
on by a frictional force in the opposite direction of its velocity.
The magnitude of this force depends on the geometry of the
2R body, its velocity, and the internal friction of the fluid. A
measure for the internal friction is given by the dynamic
viscosity . For a spherical ball of radius moving at
P velocity in an infinitely extended fluid of dynamic
viscosity , G. G. Stokes derived the viscous force to be:
.If the spherical ball (density ) is
dropped from rest at the upper surface of a vertical liquid
(density ) column (as in Fig. 1), gravitational force
( acceleration due to gravity) and buoyancy
force act on it besides viscous force
. Directions of forces are schematically shown in Fig. 2.
Q Initially, is zero because ball started at rest. So, the ball
accelerates downwards because there is a net downward force.
Then starts to increase. Eventually a force balance
(A) (B) is reached and the ball attains a steady terminal
velocity . Using the force balance condition one can easily
derive
Figure 1: Experimental setup: (A)
Photograph, (B) Schematic.
Actually, Eq. (1) [derived under the assumption of infinitely extended liquid] should be corrected forthe finite size of the
liquid column. For the movement of the spherical ball along the axis of a liquid cylinder of radius and length , the
viscous force is ( )( ) . For the experimental situation in our lab, and
. Thus, finite length correction ( ) may be ignored. Incorporating the correction due to finite
radius of the liquid column, Eq. (2) becomes:
( )
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Procedure:
A. Measure radius and density of steel balls
1. Take steel balls of 3 different sizes, 5-7 balls of each 3 sizes. Measure diameters of all the balls and calculate the
average radius for balls of same sizes. Present data in tabulated form.
2. Use measured radius data to calculate total volume of the all the balls. Measure the total mass of all the balls
together using a digital balance. Calculate density of the balls using appropriate formula. Present data in
tabulated form. *** All balls are of same material; measuring mass of all balls together will reduce error. ***
B. Measure terminal velocity
1. Set the pointer P at about cm below the top surface of the liquid column. (The distance of the pointer P
should be chosen such that by the time a ball reach at P, it should attain terminal velocity. So, you should check
if the balls are attaining terminal velocity before reaching at P.) Set the pointer Q about cm below the
pointer P (Fig. 1). Measure the actual distance between P and Q using a meter scale and record data in tabular
form.
2. Be prepared with a stop watch to measure the time a ball takes to cross the distance between P and Q.
3. Take 1 ball of the smallest size and drop it just above the top surface, near the axis of the liquid column. It is
expected to attain terminal velocity before reaching to the pointer P.
4. Start the stop watch just when the ball crosses pointer P and stop the stop watch just when the ball crosses
pointer Q. This gives the time required to cross the distance with a uniform (terminal) velocity .
5. Repeat steps 3 and 4 for all the balls and record data in tabular form. Calculate average terminal velocity for
balls of same sizes.
6. Measure the inner diameter of the liquid containing glass cylinder by a vernier calliper and calculate its radius.
7. Ask your instructor for the value of the density of the liquid.
8. Use Eq. (3) to calculate coefficient of dynamic viscosity for different size of balls. Calculate average
9. Coefficient of dynamic viscosity depends sensitively on the temperature. So, record the room temperature
and mention it in the result.
Error analysis and discussion: Do it yourself. Consult the notes on error analysis available at the course webpage in
WeLearn, if necessary. Base the error analysis on Equation 2.
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