This contains a basic idea about viscosity measurement devices and their principles. Working, principle, construction, and advantages of rotating viscometer are described here.

1. Viscosity Measurement
Rotation Viscometer

2. o VISCOSITY
 A fluid flow property.
 Internal property of a fluid that offers resistance to flow.
 It is a measure of how easily a fluid can flow.
 It can also be viewed as viscosity is a resistance to shear force
(𝑉𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦) 𝛼 Resistance
• Formula :
Viscosity =
Shear str𝑒𝑠𝑠
Shear 𝑅𝑎𝑡𝑒
Introduction

3. • There are two types of Viscosity:
• 1. Dynamic/Absolute Viscosity(𝝁)
Units:
1 Pa.s = 1 kg/(m.s) = 1 N.s/𝑚2
1 Poise = 100 cP = 0.1 Pa.s
• 2. Kinetic Viscosity(𝝑):
Units:
1 stoke = 1 𝑐𝑚2
/s = 0.0001 𝑚2
/s
• Relation between Dynamic and Kinetic viscosity :
𝜗(𝐾𝑖𝑛𝑒𝑡𝑖𝑐) =
𝜇 (𝐷𝑦𝑛𝑎𝑚𝑖𝑐)
𝜌

4. • Newtons law of Viscosity :
Newton’s law of Viscosity states that, the shear stress between adjacent fluid
layers is proportional to the velocity gradients between the two layers.
𝜏 ∝
ⅆ𝑢
ⅆ𝑦
𝝉 = 𝝁
ⅆ𝒖
ⅆ𝒚
Where, 𝝉 = Shear stress =
𝐹
𝐴
𝝁= Dynamic Viscosity
ⅆ𝒖
ⅆ𝒚
= Rate of Shear strain Shear strain

5. Methods of Viscosity Measurement
• Viscometers
• A Viscometer is an instrument used to measure the viscosity of a fluid.
• It is also known as Viscosimeter.
• Viscometers only measures under one flow condition.
Based on working principle, viscometers are divided into three categories:
1. Drag experienced by a falling ball through a fluid (Falling ball viscometer)
2. Drag experienced by one of the concentric cylinders carrying fluid between them
when the other cylinder is rotating (Rotating concentric cylinder viscometer)
3. Flow through a capillary tube (Capillary tube viscometer, Ostwald viscometer)

6. Rotating Viscometers
• These viscometers are suitable for both
Newtonian and non-Newtonian systems.
• Amongst the most widely used viscometer
• Very simple construction

7. Eg. MacMicheal
viscometer
Searle type
viscometer
(Upper cylinder
rotates)
Couette type
viscometer
(Lower cylinder
rotates)
Eg. Brookfield
viscometer
Rotation
Viscometer
Eg. Stormer
viscometer
Types :

8. Construction
• Lower cylinder (cup) revolving
• Upper cylinder (bob)
• Liquid under test
• Pulley
• Torsion wire
• Scale and pointer
 Lower cylinder revolving at
constant angular velocity.
 To get constant angular velocity,
motor is connected to pulley

9. Working
Principle:
• Newton’s law is the basis of the Rotating viscometer.
• Based on the principle that the fluid whose viscosity is being measured is sheared
between two surfaces.
• In these viscometer one of the surface is stationary and other is rotated by an external
drive and fluid fills the space in between.
• The measurements are conducted by Appling either a constant torque and measuring
the changes in the speed of rotation or applying a constant speed and measuring the
changes in the torque.

10. 1. Initially, Lower cylinder rotates at 𝜔0 and upper
cylinder rotates at 𝜔.
2. After some time, torsion wire get rotated by 𝜃 and
angular velocity of upper cylinder becomes zero.
3. At equilibrium condition, torque due to sheared
liquid and due to torsion wire will be equal.
4. No slip condition will be obtained at the
equilibrium.
5. Equating both torque, we get coefficient of
viscocity.

11. Derivation
Velocity gradient =
ⅆ𝑢
ⅆ𝑥
=
ⅆ(𝑤𝑥)
ⅆ𝑥
= w + x
ⅆ𝑤
ⅆ𝑥
Here angular velocity gradient = x
ⅆ𝑤
ⅆ𝑥
Considering any layer at distance x from centre line,
Force on second layer due first layer is given by,
𝐹 = −𝜂𝐴ⅆ𝑥
ⅆ𝑢
Where , 𝜂 – coefficient of viscosity
A – area of cylindrical layer
F = −𝜂(2𝛱𝑙)𝑥2 ⅆ𝑤
ⅆ𝑥
(negative due to sig
Now , torque is given by 𝜏 = 𝐹𝑥 = −𝜂(2𝛱𝑙)𝑥3 ⅆ𝑤
ⅆ𝑥
Therefore , ⅆ𝜔 =
𝜏
𝜂(2𝛱𝑙)𝑥2 ⅆ𝑥
Integratinng from x=R2 (bob), 𝜔=0 to x=R1 (cup) , 𝜔= 𝜔O

12. Finally, we get 𝜏 =
4𝛱𝜂𝑙𝑤𝑜
𝑅1
𝑅2
𝑅1
2−𝑅2
2
For torsion string, 𝜏 = c 𝜃 = (torsional rigidity) 𝑥 (angle rotated)
Equating both torque , we get value of coefficient of viscosity.
Final equation can be reduced to the form
η=K/w
Where , K - instrument constant

13. Advantages :
 Can measure viscosities of opaque, settling, or non-Newtonian fluids.
 Useful for characterizing shear- thinning and time dependent behavior.
 Speed of the rotating part easily adjusted.
 Often linked to computers for semiautomated measurement.
Disadvantages :
 Can be relatively expensive.
 Often large and not portable.