Viscosity of a liquid - Stoke's method

# Materials Required

• A long cylindrical glass jar
• Transparent viscous fluid
• Metre scale
• Spherical ball
• Screw gauge
• Vernier calipers
• Stop clock

# Real Lab Procedure

• Find the least count and zero correction of the given screw guage.
• Find the diameter (d) of the ball using the screw gauge. Now, the radius(r) of ball can be calculated as ; r = d/2
• Clean the glass jar and fill it with the viscous fluid.
• Place a meter scale vertically beside the jar.
• Measure the inner diameter of the jar using a vernier calipers. Hence the inner radius of the jar R can be found.
• Mark two reference points A and B on the jar using two threads. The marking A is made well below the free surface of liquid, so that by the time when the ball reaches A, it would have acquired terminal velocity v.
• Adjust the position the thread B so that the distance between A and B is 60cm.
• The ball of known diameter is dropped gently in the liquid. It falls down in the liquid with accelerated velocity for about one-third of the height. Then it falls with uniform terminal velocity.
• When the ball crosses the point A, start the stop watch and the time taken by the ball to reach the point B is noted.
• If the distance moved by the ball is d and the time taken to travel is t, then velocity,

${v}'=\frac{d}{t}$

• Calculate the terminal velocity of the ball, v using the relation,

$v={v}'(1+\frac{2.4r}{R})$

• Now, the coefficient of viscosity of the liquid can be calculated by using the formula,

$\eta =\frac{2}{9}\frac{r^{2}(\rho -\sigma )g}{v}$

• Now, repeat the experiment by changing the diameter of the ball. Calculate the value of r2/ v in each time.
• Plot a graph with r2 along X axis and terminal velocity along Y axis. We can calculate the coefficient of viscosity of the liquid by using the slope of the graph.

ie;         $\eta =\frac{2}{9}\left ( \rho -\sigma \right )g\frac{1}{slope}$

# Simulator Procedure (As performed through Online labs)

• Select the environment to perform the experiment from the 'Select the Environment' drop down list.
• Select the liquid for which the coefficient of viscosity is to be measured, from the 'Select Viscous Liquid' drop down list.
• Use the ‘Select jar diameter’ slider to change the diameter of the glass jar.
• Use the ‘Select ball diameter’ slider to change the diameter of the glass ball.
• Change the distance between A and B by dragging the corresponding arrows.
• Drag the glass ball towards the jar and drop it into the liquid in the jar.
• The stop watch runs automatically as the ball reaches the point A, and stops as it leaves the point B.
• The time shown in the stop watch is noted.
• Now, calculations are done as per the observation column and the coefficient of viscosity of the selected liquid can be found out.
• Enable the ‘Show result’ checkbox to view the coefficient of viscosity of the selected liquid.
• Click on the ‘Reset’ button to redo the experiment.

# Observations

## To find the inner diameter of the glass jar using vernier callipers:

Value of one main scale division            = ……mm

Number of divisions on the vernier          = …….

Least count (L.C.)                                = …….. mm

= ......... cm

 Sl.No. M.S.R. (cm) V.S.R. (div.) V.S.R. ×L.C. (cm) Total reading = M.S.R.+V.S.R.×L.C. (cm)

Mean diameter of the glass jar, D = .............. cm

## To find the diameter of the sphere using screw gauge:

Pitch of the screw gauge                               = .......... mm

Number of divisions on the circular scale        = ...........

Least count of the screw gauge (L.C.)            =............ mm

Zero correction of the screw gauge (z)            = …….... mm

 Glass spshere No. P.S.R. (mm) Observed H.S.R. (a) (div.) Corrected H.S.R. (a+z) (div) Corrected H.S.R.×L.C. (mm) Total reading = P.S.R.+(Corrected H.S.R.×L.C.) (d) (mm) Radius of the glass ball,   r=d/2 (×10-3 m)

## To find the terminal velocity of the sphere :

Density of the liquid, ρ                             = ………..kg/m3

Density of the sphere, σ                          = ……….kg/m3

Distance travelled by the sphere, s           = ………. 10-2 m

 Glass sphere No. Radius of glass sphere, r        (×10-3 m) Time taken to travel the distance s, t (s) Velocity, v' = s/t (m/s) Terminal velocity, v              = v' [1+(2.4r/R)]  (m/s) r2/ v (m s) 1 2 3 4 5

# Calculations

Radius of the sphere, r                        = d/2

=.......... mm

= .........×10-3 m

Inner radius of the glass jar, R              = D/2

=........... cm

=........... ×10-2 m

Coefficient of viscosity,

$\eta =\frac{2}{9}\frac{r^{2}\left ( \rho -\sigma \right )g}{v}$

= ............. Nsm-2

### Square of radius versus Terminal velocity Graph :

Slope of the graph,

$\frac{AB}{BC} = \frac{v}{r^{2}}$

Coefficient of viscosity,

$\eta =\frac{2}{9}\frac{\left ( \rho -\sigma \right )g}{slope}$

= ............... Nsm-2

# Result

The coefficient of viscosity of the given liquid, η

By calculation, = .................Nsm-2

From graph,     = .................Nsm-2

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