To determine the coefficient of viscosity of a given viscous liquid by measuring terminal velocity of a given spherical body.

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To determine the coefficient of viscosity of a given viscous liquid by measuring terminal velocity of a given spherical body.

Viscosity of a liquid – Stoke’s method:

Objective

To determine the coefficient of viscosity of a given viscous liquid by measuring terminal velocity of a given spherical body.

Theory

How do you define viscosity?

Viscosity is the property of a fluid by virtue of which an internal resistance comes into play when the liquid is in motion, and opposes the relative motion between its different layers. Thus, it is the resistance of a fluid to flow.

When liquid flows over flat surface, a backward viscous force acts tangentially to every layer. This force depends upon the area of the layer, velocity of the layer, and the distance of the layer from the surface.

Where η is the coefficient of viscosity of the liquid.

Stoke’s Law

Stoke’s law was established by an English scientist Sir George G Stokes (1819-1903).

When a spherical body moves down through an infinite column of highly viscous liquid, it drags the layer of the liquid in contact with it. As a result, the body experiences a retarding force.

Then according to Stokes law, the viscous drag force,

,

where,  r – Radius of the spherical body

v – Velocity of the spherical body

It gives the relationship between retarding force and velocity. When viscous force plus buoyant force becomes equal to force due to gravity, the net force becomes zero. The sphere then descends with a constant terminal velocity (v t).

Now,

where,  ρ – Density of the liquid

σ – Density of the spherical body

Learning Outcomes

• Students understand the behavior and properties of fluids
• Students get the knowledge about viscosity of liquids.
• Students understand the quantity, coefficient of viscosity and the various factors affecting its value.
• Students get the concept of terminal velocity.

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LABAPPARA 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,
• Calculate the terminal velocity of the ball, v using the relation,
• Now, the coefficient of viscosity of the liquid can be calculated by using the formula,
• 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.
Procedure
• 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,   = ............. Nsm-2

Square of radius versus Terminal velocity Graph :

Slope of the graph,   Coefficient of viscosity,   = ............... Nsm-2  Result The coefficient of viscosity of the given liquid, η By calculation, = .................Nsm-2 From graph,     = .................Nsm-2