Types of Viscometers and Their Working Principles

This article discusses different types of viscometers and their working principles including falling sphere viscometer, capillary tube viscometer, rotational viscometer, and orifice viscometer. It also explains how to calculate dynamic and kinematic viscosity of fluids at different temperatures and pressures.

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Mechanical Fluids
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Mechanical Fluids
Task 1
1.1. Falling sphere viscometer
This is a type of viscometer that measures dynamic viscosity of a fluid using a falling sphere
of known radius and density. The device measures the time taken for the falling sphere to move
from one point to another through a fluid (Brookfield Engineering, (n.d.)). This time is used to
calculate viscosity of the fluid. The working principle of falling sphere viscometer is based on
Stokes’ law, which states that an object falling or moving through a viscous fluid experiences
some resistance that opposes its motion (Yuan & Lin, 2008). The viscosity of the fluid is
calculated using equation 1 below
η= d2 g( ρs−ρ 1)
18 V ……………………………………………… (1)
Where η = viscosity of the fluid, d = diameter of the sphere, g = gravitational acceleration, ρs =
density of sphere, and ρ1 = density of fluid.
1.2. Capillary tube viscometer
This is a type of viscometer that measures kinematic viscosity of a fluid by determining the
time that a volume of fluid takes to pass through a particular length of capillary tube by gravity
and comparing it with the time that is needed by a Newtonian fluid of known viscosity to pass
through the same length of capillary tube. The device is usually used in the lab (Gupta, 2014).
The viscosity is determined using equation 2 below
η= π r4 tΔP
8 LV ………………………………………………………………. (2)

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Where η = viscosity of the fluid, r = inside radius of the capillary tube, ΔP = pressure head in
dyne/cm2, L = capillary length, and V = fluid volume.
Capillary tube viscometer is very accurate in measuring viscosity of Newtonian fluids that have
low viscosity.
1.3. Rotational viscometer
This is a type of viscometer that measures dynamic viscosity of a fluid by determining the
fluid’s resistance to torque (Bright Hub Engineering, (n.d.)). The device measures the torque that
is needed for an object to turn in a fluid and relates it to viscosity of that fluid. The torque is
measured on the shaft rotating a spindle in a cup. Rotational viscometers are used to measure
viscosity of a wide range of liquid and semi-solid samples. There are two main types of
rotational viscometers: spring-type and servo motor rotational viscometers (Anton Paar, (n.d.)).
The torque values are read on the dial of the viscometers. The apparent viscosity of a fluid using
a spring-type rotational viscometer is calculated using equation 3 below
η= Akl
1000 ……………………………………………………………… (3)
Where η = apparent viscosity, A = coefficient based on viscometer’s torque model, k =
coefficient based on combination of rotational speed and spindle, and l = dial value.
1.4. Orifice viscometer
This is a type of viscometer comprising of a cup and a hole. It measures viscosity of a fluid
by determining the time taken for the cup to empty. The cup is simply dipped into the fluid then
the fluid starts flowing through the hole until the cup empties (Bonner, 2017). The longer the
time it takes for the fluid to flow through the hole/orifice until the cup empties the higher the

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viscosity, and vice versa. The viscometer works by gravity and measures kinematic viscosity.
Orifice viscometers are simple, low cost and reliable. They are widely used in gas and oil
industries. Viscosity of a fluid using orifice viscometer is calculated using equation 4 below
v= η
ρ =kΔt− K
Δt ……………………………………………… (4)
Where v = kinematic viscosity, η = dynamic viscosity, k = 0.073, 0.0216 and 0.00226, K =
0.0631, 0.60 and 1.95, and Δt = change in time.
Task 2
2.1. Dynamic viscosity at 5°C
The dynamic viscosity at 5°C is calculated as follows:
μ=μ 15 e
E
Ro ( 1
T 5 − 1
T 15 )
But E
Ro =1952 K
5°C = 278.15 K
μ=1.21 x 10−3 e1952 ( 1
278.15− 1
288.15 ) = 1.21 x 10-3 x 1.276344 = 1.5444 mPa s
2.2. Kinematic viscosity at 32°C
Kinematic viscosity, ν, is calculated using the formula ν= μ
ρ (where μ = dynamic
viscosity and ρ = density of the fluid). The first step is to determine the dynamic viscosity at
32°C. The dynamic viscosity is calculated as follows:

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μ=μ 15 e
E
Ro ( 1
T 5 − 1
T 15 )
But E
Ro =1952 K
32°C = 305.15 K
μ=1.21 x 10−3 e1952 ( 1
305.15− 1
288.15 ) = 1.21 x 10-3 x 0.6861 = 0.8302 x 10-3 Pa s
The density of water, ρ, at 32°C is estimated from the table provided as 0.9950 g/cm3 = 995
kg/m3.
Hence ν= μ
ρ =0.8302 x 10−3 Pa s
995 kg/m3 =8.344 x 10−7 m2 / s
2.3. Fluidity at 60°C
Fluidity, Ø, is calculated as follows: Ø= 1
μ (where μ = dynamic viscosity). Therefore the
first step is to determine viscosity of water at 60°C. This is estimated as follows:
μ=μ 15 e
E
Ro ( 1
T 5 − 1
T 15 )
But E
Ro =1952 K
32°C = 333.15 K
μ=1.21 x 10−3 e1952 ( 1
333.15− 1
288.15 ) = 1.21 x 10-3 x 0.401103 = 0.4853 x 10-3 Pa s
Thus Ø= 1
μ = 1
0.4853 x 10−3 Pa s =2,060.58 m2 /Ns

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2.4. Dynamic viscosity
It is assumed that the water is flowing through the pipe where the pressure is 500 KPa and the
atmospheric pressure = 101,325 Pa.
μ= π x ΔP x R4
8 x L x Q
Where R = radius of pipe, L = length of pipe and Q = flow rate
Q = VA, where V = velocity and A = cross-sectional area
V has been given as 0.25 m/s
Area of pipe, A = πr2; where r = 0.05m
A = π x 0.052 = 0.007854m2
Hence Q = 0.25 m/s x 0.007854 m2 = 0.0019635 m3/s
L = 10 m
R = 0.05 m
ΔP = 500,000 Pa – 101,325 Pa = 398,675 Pa
Therefore μ= π x ΔP x R4
8 x L x Q = π x 398,675 x 0.054
8 x 10 x 0.0019635 =49.834 Pa s
2.5. Viscosity at 5°C
The dynamic viscosity at 5°C is calculated as follows:
μ=μ 15 e
E
Ro ( 1
T 5 − 1
T 15 )

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But E
Ro =1952 K
5°C = 278.15 K
μ=1.21 x 10−3 e1952 ( 1
278.15− 1
288.15 ) = 1.21 x 10-3 x 1.276344 = 1.5444 x 10-3 Pa s
Kinetic viscosity, ν of sea/salt water (70%)
Density of salt water = 1,027 kg/m3
ν= μ
ρ x 70 %= 1.5444 x 10−3 Pa s
1027 x 0.7=1.053 x 10−6 m2 /s
Kinetic viscosity of fresh water (30%)
Density of salt water = 1,000 kg/m3
ν= μ
ρ x 30 %= 1.5444 x 10−3 Pa s
1000 x 0.3=4.6332 x 10−7 m2 /s
Total viscosity = (1.053 x 10-6 m2/s) + (4.6332 x 10-7 m2/s) = 1.51632 x 10-6 m2/s

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References
Anton Paar, (n.d.). Rotational Viscosity. [Online]
Available at: https://wiki.anton-paar.com/en/rotational-viscometry/
[Accessed 22 November 2018].
Bonner, M., 2017. 6 Different Types of Viscometers & How They Work. [Online]
Available at: https://blog.viscosity.com/blog/6-different-types-of-viscometers-how-they-work
[Accessed 22 November 2018].
Bright Hub Engineering, (n.d.). Types of Viscosity Measurement Devices: Viscometers and Rheometers.
[Online]
Available at: https://www.brighthubengineering.com/fluid-mechanics-hydraulics/83996-viscosity-
measurement-equipment/
[Accessed 22 November 2018].
Brookfield Engineering, (n.d.). Falling Ball Viscometer. [Online]
Available at: https://www.brookfieldengineering.com/products/viscometers/laboratory-viscometers/
falling-ball-viscometer
[Accessed 22 November 2018].
Gupta, S., 2014. Rotational and Other Types of Viscometers. In: Viscometry for Liquids. Cham: Springer,
pp. 81-105.
Yuan, P. & Lin, B., 2008. Measurement of Viscosity in a Vertical Falling Ball Viscometer. [Online]
Available at: https://www.americanlaboratory.com/913-Technical-Articles/778-Measurement-of-
Viscosity-in-a-Vertical-Falling-Ball-Viscometer/
[Accessed 22 November 2018].