A Literature Review done on different Viscometers and their working principles

1. `
CH 2100 Fluid Dynamics
Assignment
Viscosity Measurement and Instruments Used
NAME : BENARAGAMA B.V.C.M.
INDEX NO : 170070D
DATE OF SUB : 29/03/2019
Department of Chemical and Process Engineering
University of Moratuwa

2. • INTRODUCTION
Viscosity is simply the resistance of a fluid to
flow. Measuring liquid viscosity is important in
both industrial and academic applications, in
order to determine the flow type, energy
consumption, in optimal designing etc.
Instruments used to measure Viscosity are known
as Viscometers. Viscometers are generally of six
types depending on the principle they use.
1. Capillary viscometers
2. Orifice viscometers
3. High temperature high shear rate viscometers
4. Rotational viscometers
5. Falling object viscometers
6. Vibrational viscometers
7. Ultrasonic viscometers
There are some viscometers where above
principles are used combined. In this report, we
discuss three viscometers namely,
1. Redwood Viscometer
2. Ubbelohde Viscometer
3. Hoppler Viscometer
• REDWOOD VISCOMETER
Redwood Viscometer belongs to the very first
type of Orifice viscometers, which is very
commonly used in England even now. It was first
designed by an engineer named, Redwood, and
got the approval of Society of Chemical Industry
in 1886. It can generally be used on Newtonian
liquids, in the case where the kinematic viscosity
of liquids is needed to be found. The principle is
a little similar to Capillary Viscometers, where the
viscosity is found using the time taken to collect a
fixed volume of the liquid.(Viswanath, 2007)
(Islam, n.d.)
THEORY
The thread with the ball is lifted and the volume
of liquid (say, V) collected is recorded for a time,
t. Knowing the length of the capillary tube, L, and
its radius, r, using Poiseuille equation, the head
difference, ΔH across the tube, due to friction
(lamina flow) can be found.
∆𝑷 =
𝟖𝝁𝑳𝑽
𝝅𝒓 𝟒 𝒕
Using 𝜟𝑷 = 𝜟𝑿𝝆𝒈,
𝜟𝑿 =
𝟖𝑳𝑽𝜼
𝝆𝒈𝝅𝒓 𝟒 𝒕
The head loss due to turbulence flow, ΔY, at
entrance and exit is a linear function of kinetic
energy of the liquid. Hence it can be written
below, with m, as a constant, and using continuity
equation,
𝚫𝒀 =
𝒎𝒗 𝟐
𝒈
=
𝒎
𝒈
(
𝑽
𝛑𝐫 𝟐 𝒕
)
𝟐
The Total Head difference can be taken using the
sum of two head differences.
(𝜟𝑿 + 𝚫𝒀) =
𝟖𝑳𝑽𝜼
𝝆𝒈𝝅𝒓 𝟒 𝒕
+
𝒎
𝒈
(
𝑽
𝛑𝐫 𝟐 𝒕
)
𝟐
Subjecting
𝜼
𝝆
= 𝝁 in the equation above we get,
𝝁 =
𝜼
𝝆
=
𝝅𝒈𝒓 𝟒(𝜟𝑿 + 𝚫𝒀)
𝟖𝑳𝑽
𝒕 −
𝒎𝑽
𝟖𝝅𝑳
(
𝟏
𝒕
)
The equation can be rearranged with,
𝑨 =
𝝅𝒈𝒓 𝟒(𝜟𝑿+𝜟𝒀)
𝟖𝑳𝑽
, 𝑩 =
𝒎𝑽
𝟖𝝅𝑳
𝝁 =
𝜼
𝝆
= 𝑨𝒕 − (
𝑩
𝒕
)
Given the properties of the system, L, r, the values
of A and B can be calculated. But they may
change according to the value of t, which will be
specified by the manufacturer.(Cannon, Manning,
& Bell, 1960)
APPLICATIONS
Redwood Viscometer is mainly used in
petroleum industry in order to measure kinematic
viscosity of petroleum components and crude oil.
The main advantage is unlike in Capillary
Viscometers, Redwood viscometer counts the
head losses due to turbulent flow. Hence the
values obtained will be better in accuracy. It is
also used in Industries, Research Organizations

3. for Standardization in order to test and compare
viscosities of Newtonian liquids. The main
disadvantage of the equipment is not being able to
be used for Non-Newtonian liquids. (“Redwood
Viscometer,Redwood Apparatus Manufacturers,
Red Wood Viscometer Exporters,” n.d.)
• UBBELOHDE VISCOMETER
It is a Capillary type of a viscometer, very
closely related to Ostwald Viscometer. The liquid
is introduced into the reservoir, sucked via the
capillary tube, is allowed to travel back to the bulb
The time taken for the considered liquid to pass
through two calibrated marks is then measured.
There is a venting tube from the end of the
capillary is open to the atmosphere. (Young,
1981)
THEORY
The behavior of the liquid is assumed to be
Newtonian, incompressible, and flow is
considered lamina. Viscosity is assumed to be
pressure independent.
Applying Hagen-Poiseuille Law for the
capillary section we get,
∆𝑷 =
𝟖𝝁𝑳𝑽
𝝅𝒓 𝟒 𝒕
Here the symbols refer to the same symbols used
for capillary section in Redwood Viscometer. The
equation is rearranged to head loss, the same we
followed before.
𝜟𝑿 =
𝟖𝑳𝑽𝜼
𝝆𝒈𝝅𝒓 𝟒 𝒕
In this case we neglect the turbulent losses,
considering the streamed line shape of the tubes.
For this case 𝜟𝑿 = 𝒉m . When used for different
liquids, the only dependent factors will be, 𝜼, 𝒕,
and 𝝆 . Now with all constants taken as K,
following equation can be obtained.
𝝁 =
𝜼
𝝆
= 𝑲𝒕
Where, K is called Viscometer constant, a
constant that depends on the viscometer system. It
either will be provided by the manufacturer, or
can be calculated using a viscosity known liquid
like water.
𝑲 =
𝚫𝑿𝒈𝝅𝒓 𝟒
𝟖𝑳𝑽
Though we expect a linear relationship between
𝝁 and t, the turbulent losses affect the behavior .
(Visco handbook THEORY AND APPLICATION OF
VISCOMETRY WITH GLASS CAPILLARY VISCOMETERS, n.d.)
In order to correct the time error due to turbulent
losses, a time correction factor comes tabulated
along with the equipment, for different types of
standard capillary tubes. (Refer APPENDIX
:TABLE 01, TABLE 02) (Department, 2010b)
APPLICATIONS
The Ubbelohde Viscometer is often used
industrially to measure the viscosity of highly
viscous polymers. The main advantage of this
equipment is, its value doesn’t change with
temperature, which K enables easy calculations
and quick results. Small sample is sufficient for
the testing and the accuracy is very high in this
equipment, which is one of the reasons to be used
in standardization applications.
The main disadvantage in this equipment is, the
inability of determining the viscosity of highly
coloured and non-transparent liquids, because of
the difficulty in observing the menisci in such
instances. (CHAPTER-4 MICROCONTROLLER BASED
UBBELOHDE VISCOMETER FOR MEASUREMENT OF
VISCOSITY OF LIQUIDS, n.d.)

4. • HOPPLER VISCOMETER
Also known as “Falling Ball Viscometer”, and
it’s a type of a falling object Viscometers. It was
invented as the very first Viscometer in the world,
by the German Engineer named, Hoppler. A ball
is made to fall down in a tube, containing a liquid,
and the principle of achieving terminal velocity by
an moving object in a viscous liquid, is used for
determination of the viscosity.
THEORY
The force F, acting on a sphere of radius r,
moving in a fluid medium having viscosity 𝜼, at a
velocity 𝝂, can be derived using Stoke’s equation
to be,
𝑭 = 𝟔𝝅𝜼𝒓𝝂
The Upthrust U, acting on the sphere will be,
𝑼 = 𝑽𝝆𝒈 =
𝟒
𝟑
𝝅𝒓 𝟑
𝝆𝒈
The weight W, of the object with mass m,
density d, is,
𝑾 = 𝒎𝒈 =
𝟒
𝟑
𝝅𝒓 𝟑
𝒅𝒈
At the terminal velocity, the Weight of the
object downwards, will be balanced by Upthrust
and Viscous force acting, upwards. So that,
𝑾 = 𝑭 + 𝑼
Further,
𝟒
𝟑
𝝅𝒓 𝟑
𝒅𝒈 =
𝟒
𝟑
𝝅𝒓 𝟑
𝝆𝒈 + 𝟔𝝅𝜼𝒓𝝂
𝜼 =
𝟐𝒓 𝟐 𝒈(𝒅−𝝆)
𝟗𝒗
Knowing the distance between two calibration
points at a distance L, from each other, distant
enough from the corner of the tube to achieve
terminal velocity, measuring the time t, taken for
it to travel through calibrated points, the viscosity
can be determined.
𝜼 =
𝟐𝒓 𝟐
𝒈(𝒅 − 𝝆)𝒕
𝟗𝑳
For a given viscometer, the viscometer constant
K, can be defined as,
𝜼 = 𝑲(𝒅 − 𝝆)𝒕
(Department, 2010a)
APPLICATIONS
The general purpose is to determine the
viscosity of nano fluids. Nano fluid are the types
of fluid where the particles are of Nano size. They
are most often transparent. In colloidal liquids,
collision of particles with the sphere will produce
extra forces. And most of the microfluids are
opaque or translucent obscuring the ability to see
the ball through the liquid. To find the viscosity
of opaque liquids, sensors are used in this kind of
viscometers.
The experiment can be repeated turning the tube
upside down as many times as needed is one of
the main advantages of this method. It’s a cheap
method, but the amount of liquid needed will be
high. The homogenous bath of water around the
tubes supports a constant temperature. The
calibration is generally done using distilled water.
It is commonly used in measuring the viscosity of
following industrial liquids and solids such as,
Beverages, Coatings, Cosmetics, Detergents,
Food, Paint, Petroleum Products,
Pharmaceuticals, Polymers, Soap etc.
(“Falling Ball Viscometer,” n.d.)

5. • APPENDIX
(Department, 2010b)
• REFERENCES
Cannon, M. R., Manning, R. E., & Bell, J. D. (1960). Viscosity
Measurement. Kinetic Energy Correction and New
Viscometer. Analytical Chemistry, 32(3), 355–358.
https://doi.org/10.1021/ac60159a015
CHAPTER-4 MICROCONTROLLER BASED UBBELOHDE
VISCOMETER FOR MEASUREMENT OF VISCOSITY OF
LIQUIDS. (n.d.). Retrieved from
http://shodhganga.inflibnet.ac.in/bitstream/10603/9661/10/10
_chapter 4.pdf
Department, E. (2010a). SOP for Falling Ball viscometer
(Höppler). Retrieved from
https://www.kth.se/polopoly_fs/1.291037.1550154338!/Menu
/general/column-content/attachment/KTH-SOP-Höppler-
Visc-NanoHex- Final.pdf
Department, E. (2010b). SOP for UBBELOHDE viscometer.
Retrieved from
https://www.kth.se/polopoly_fs/1.291026.1550155426!/Menu
/general/column-content/attachment/KTH-SOP-
UBBELOHDE-Visc-NanoHex_Final.pdf
Falling Ball Viscometer. (n.d.). Retrieved March 29, 2019,
from
https://www.brookfieldengineering.com/products/viscometers/l
aboratory-viscometers/falling-ball-viscometer
Islam, M. S. (n.d.). Measurement and Industrial
Instrumentation ME 3225 Credit: 3.00 Measurement of
Viscosity and Pressure. Retrieved from
http://www.kuet.ac.bd/webportal/ppmv2/uploads/154140843
28.Measurment of viscosity & Pressure.pdf
Redwood Viscometer,Redwood Apparatus Manufacturers,Red
Wood Viscometer Exporters. (n.d.). Retrieved March 29,
2019, from http://www.sciencelabproducts.com/redwood-
viscometer.htm
Visco handbook THEORY AND APPLICATION OF
VISCOMETRY WITH GLASS CAPILLARY VISCOMETERS.
(n.d.). Retrieved from http://www.si-
analytics.com/fileadmin/upload/Informationen/Kapillarviskos
imetrie/INT/Visco-Handbook_2015_2.7-MB_PDF-
English.pdf
Viswanath, D. S. (2007). Viscosity of liquids : theory,
estimation, experiment, and data. Springer. Retrieved from
https://b-ok.cc/book/654828/ee136d
Young, R. J. (Robert J. (1981). Introduction to polymers.
Chapman and Hall. Retrieved from
https://en.wikipedia.org/wiki/Ubbelohde_viscometer