2. Newton’s Law of Viscosity
This law states that viscous force F
developed by liquid layer is
Directly proportional to the surface area “A”
Directly proportional to the velocity gradient
F ∝ A
F ∝
𝑑𝑣
𝑑𝑦
F ∝ A
𝑑𝑣
𝑑𝑦
∴ μ = co-eff of viscosity
F = μ A
𝑑𝑣
𝑑𝑦
v2
F
3. Newton’s Law of Viscosity
Unit of co-eff of viscosity is
𝑁
m2 1
𝑠
or
𝑁−𝑠
m2 or Pascal-second (S-I unit) and
𝑑𝑦𝑛𝑒−𝑠
cm2 (CGS system)
Note:
𝑑𝑦𝑛𝑒−𝑠
cm2 = 1 Poise (most common unit)
Note:
𝑑𝑦𝑛𝑒−𝑠
cm2 =
1
10
𝑁−𝑠
m2 = 0.1
𝑁−𝑠
m2
Simply, 10 poise = 1 Pascal-second
F = μ A
𝑑𝑣
𝑑𝑥
μ =
F
A 𝑑𝑣
𝑑𝑥
4. Newton’s Law of Viscosity
Co-efficient of viscosity:
It is defined as viscous force developed between two layers of unit
surface area for unit velocity gradient.
Definition of Poise: (1 Poise =
𝑑𝑦𝑛𝑒−𝑠
cm2 )
The co-efficient of viscosity is said to be 1 poise if 1 dyne viscous
force is developed between two layers of 1 cm2 area for unit
velocity gradient.
F = μ A
𝑑𝑣
𝑑𝑥
μ =
F
A 𝑑𝑣
𝑑𝑥
μ =
F
A 𝑑𝑣
𝑑𝑥
μ =
F
1x1
μ = F
5. Newton’s Law of Viscosity
dθ
dy
u + du
Excess Distance Covered
V =
dx
dt
dx= Vdt
So excess distance = dudt
Tan(dθ) =
dudt
dy
(1)
As “dθ” is very small
so tan (dθ) = dθ
Equation (1) becomes
dθ =
dudt
dy
dθ
dt
=
du
dy
∴
du
dy
= 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑔𝑟𝑎𝑑𝑖𝑛𝑡 or rate of
shear strain
Shear Stress ∝ Angular Deformation
or Rate of shear
strain
τ ∝
dθ
dt
𝐴𝑠
dθ
dt
=
du
dy
so, τ ∝
du
dy
τ = μ
du
dy
μ = dynamic viscosity of fluid
v2
τ
6. Now, Let us discuss again
Viscosity, its effect on
temperature
and its types…..
7. Viscosity (Different Definitions)
It is defined as the property of a fluid which offers resistance to
the movement of one layer of fluid over another adjacent layer
of the fluid.
The property of a liquid on account of which liquid tries to
oppose the relative motion between its different layers.
The viscosity of a fluid is a measure of its “resistance to
deformation.”
Informally, viscosity is the quantity that describes a fluid’s
resistance to flow.
8. Types of Viscosity
Two types of viscosity
1. Dynamic Viscosity (Absolute Viscosity)
2. Kinematic Viscosity
Dynamic Viscosity
Dynamic (absolute) viscosity is defined as “the shear force per unit area
required to move one horizontal plane of fluid with respect to an other
plane - at a unit velocity - when maintaining a unit distance apart in the
fluid”
OR
It is defined as the viscous force developed between two layers of unit
surface area for unit velocity gradient.
It is denoted by “μ”
9. Kinematic Viscosity
The ratio of the viscosity of a fluid to its density.
• Kinematic viscosity can be obtained by dividing the absolute viscosity of a fluid
to the fluid density like
ν = μ / ρ
• Kinematic viscosity is a measure of the resistive flow of a fluid under the
influence of gravity.
• It is frequently measured using a device called a capillary viscometer —
basically a graduated can with a narrow tube at the bottom.
• When two fluids of equal volume are placed in identical capillary viscometers
and allowed to flow under the influence of gravity, the more viscous fluid takes
longer than the less viscous fluid to flow through the tube.
10. Unit of Kinematic Viscosity
Unit of kinematic viscosity is
m2
s
Common unit:
cm2
s
, also called stoke (st)
ν =
μ
ρ
ν =
𝑁−𝑠
m2
1
𝑘𝑔
𝑚3
ν =
𝑁−𝑠
m2
m3
𝑘𝑔
∴𝑁 = kg
m
s2
ν = kg
m
s2
𝑠
m2
m3
𝑘𝑔
ν =
m2
s
11. Difference between Dynamic and
Kinematic Viscosity
In simple words, dynamic viscosity tells us about the force needed to
make the fluid flow with a certain velocity.
Dynamic viscosity is a measure of a fluid’s resistance to flow when
an external force is applied.
The other way is to measure the resistive flow of a fluid under the
weight of gravity. The result is kinematic viscosity.
Put another way, kinematic viscosity is the measure of a fluid’s
inherent resistance to flow when no external force, except gravity, is
acting on it.
12. Factors Affecting Viscosity
Viscosity is first and foremost a function of material.
The viscosity of water at 20 °C is 1.0020 millipascal seconds.
Most ordinary liquids have viscosities on the order of 1 to 1,000
mPa s, while gases have viscosities on the order of 1 to 10 μPa s.
Pastes, gels, emulsions, and other complex liquids are harder to
summarize.
Some fats like butter or margarine are so viscous that they seem
more like soft solids than like flowing liquids.
13. Factors Affecting Viscosity
From everyday experience, it should be common knowledge that
viscosity varies with temperature.
Honey and syrups can be made to flow more readily when heated.
Engine oil and hydraulic fluids thicken appreciably on cold days and
significantly affect the performance of cars and other machinery during
the winter months.
In general, the viscosity of a simple liquid decreases with increasing
temperature.
As temperature increases, the average speed of the molecules in a
liquid increases and the amount of time they spend "in contact" with
their nearest neighbors decreases.
Thus, as temperature increases, the average intermolecular forces
decrease.
14. Factors Affecting Viscosity
Viscosity is normally independent of pressure, but liquids under
extreme pressure often experience an increase in viscosity.
Since liquids are normally incompressible, an increase in pressure
doesn't really bring the molecules significantly closer together.
15. Factors Affecting Viscosity
• While liquids get runnier as they get hotter, gases get thicker.
The viscosity of gases increases as temperature increases and is
approximately proportional to the square root of temperature.
• This is due to the increase in the frequency of intermolecular
collisions at higher temperatures.
16. Factors Affecting Viscosity (Summary)
• The viscosity of typical fluids depends upon temperature.
• As the temperature increases, the viscosities of all liquids decrease, whereas
the viscosities of all gases increase.
Reason
Liquid:
Temperature decreases
cohesive force b/w molecules
Gases:
Temperature increases
intermolecular interaction
17. Ideal and Real Fluid
Ideal Fluid:
A fluid in which there is no friction, it is inviscid (its viscosity is zero).
OR
A fluid which has no viscosity is known as ideal fluid.
Such a fluid does not exist in reality.
Real Fluid:
A fluid which has viscosity is known as real fluid.
