This document discusses fluid mechanics and viscosity. It begins by defining a fluid and explaining that fluids deform continuously under shear forces rather than resist deformation like solids. It then discusses viscosity, defining it as a fluid's resistance to flow. Viscosity exists due to molecular collisions and momentum transfer between layers of a fluid. Methods for measuring viscosity include viscometers that apply shear stresses between fluid layers. Viscosity affects fluid dynamics, causes drag, and is accounted for in the Navier-Stokes equations.

1. Department of Mechanical Engineering
Don Bosco College of Engineering and
Technology, ADBU
By Dipjyoti Deka
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2. INTRODUCTION
The two aspects of fluid mechanics:-
1. The nature of a fluid is much different to that of solid.
2. In fluids, we usually deal with continuous streams of fluid without a beginning or end.
We normally recognize three states of matter: solid, liquid and gas. However, liquid and gas
are both fluids; in contrast to solids they lack the ability to deformation. Because a fluid
cannot resist the deformation force, it moves up, it flows under the action of the force.
Its shape will change continuously as ling as force is applied.
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3. The deformation is caused by shearing forces which act tangentially to a surface. As we
can see the force F acting tangentially on a rectangular element ABCD. This is a
shearing force and produces the rhombus element A’B'
A
D
B
B’
C
A’
Shearing force F, acting on the fluid element.
Hence, we can say that A fluid is a substance which deforms continuously when subjected
to shearing forces.
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4. VISCOSITY
A property of fluid to resist the rate of deformation- a quantitive measure of a fluid’s
resistance to flow (water v/s syrup). It takes place when a fluid is acted upon by a shear
stress.
It is an important fluid property when analyzing liquid behavior and fluid motion near
solid boundaries. The shear resistance in a fluid is caused by intermolecular friction
exerted when layers of fluid attempt to slide by one another.
There are two related measures of fluid viscosity:
• Dynamic or Absolute
• Kinematic
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5. Why does viscosity exist in fluid flow
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Molecular collisions – the molecules of the fluid bump into each other,
slowing down their motion
Momentum transfer from higher momentum to lower - momentum is mass
times velocity, mu. During a collision, momentum will be transferred.
Measured by shear stress τ,, which is the tangential force divided by the
area

6. Fluid with low viscosity Fluid with high viscosity
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7. Newton’s law of Viscosity
Viscosity is the physical property that characterizes the flow resistance of simple fluids.
Newton’s law of viscosity defines the relationship between the shear stress and shear rate of
a fluid subjected to a mechanical stress. The ratio of shear stress to shear rate is constant,
for a given temperature and pressure, and is defined as the viscosity or coefficient of
viscosity. Newtonian’s fluids obey Newton’s law of viscosity.
Thus, Viscosity is independent of the shear rate. Similarly, Non-Newtonian fluids do not
follow Newton’s law and thus, their viscosity (ratio of shear stress to shear rate) is not
constant and is dependent on the shear rate.
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8. Dynamic viscosity:- It is the tangential force per unit area required to move one
horizontal plane with respect to an other plane- at an unit velocity- when maintaining an
unit distance apart in the fluid. The shearing stress between the layers of a non-turbulent
fluid moving in straight parallel lines can be defined for a Newtonian Fluid as:
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9. Fig shows two fluid layers at distance y and y+dy from the surface. They move with different
velocities u and u+du as shown in fig. The top layer causes a shear stress on lower while lower
layer causes shear stress on the top layer. The shear stress τ is proportional to the rate of change
of velocity with respect y.
Mathematically, 𝜏α
𝑑𝑢
𝑑𝑦
𝜏 = μ
𝑑𝑢
𝑑𝑦
Here constant of proportionality μ is known as the coefficient of dynamic viscosity
𝑑𝑢
𝑑𝑦
known as
the velocity gradient.
From the above equation μ=
𝜏
𝑑𝑢
𝑑𝑦
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10. Causes of Viscosity in Fluids
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Viscosity in Gasses
The molecules of gasses are only weakly kept in position by molecular cohesion (as they
are so far apart). As adjacent layers move by each other there is a continuous exchange of
molecules. Molecules of a slower layer move to faster layers causing a drag, while
molecules moving the other way exert an acceleration force. Mathematical considerations
of this momentum exchange can lead to Newton law of viscosity.
If temperature of a gas increases the momentum exchange between layers will
increase thus increasing viscosity.
Viscosity will also change with pressure - but under normal conditions this change
is negligible in gasses.

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Viscosity in Gasses

12. Viscosity in Liquids
There is some molecular interchange between adjacent layers in liquids - but as the
molecules are so much closer than in gasses the cohesive forces hold the molecules in place
much more rigidly. This cohesion plays an important roll in the viscosity of liquids.
Increasing the temperature of a fluid reduces the cohesive forces and increases the molecular
interchange. Reducing cohesive forces reduces shear stress, while increasing molecular
interchange increases shear stress. Because of this complex interrelation the effect of
temperature on viscosity has something of the
form:
where is the viscosity at temperature T°C, and is the viscosity at temperature 0°C. A
and B are constants for a particular fluid.
High pressure can also change the viscosity of a liquid. As pressure increases the relative
movement of molecules requires more energy hence viscosity increases.
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Viscosity in Liquids

14. Viscosity Measurements
• These viscometer give the value of the ‘dynamic viscosity’.
• It is based on the principle that the fluid whose viscosity is being measured is sheared
between two surfaces.
• In these viscometers one of the surfaces is stationary and the other is rotated by an external
drive and the fluid fills the space in between.
• The measurements are conducted by applying 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.
• There are two main types of these viscometers: rotating cylinder and cone-on-plate
viscometers.
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15. Viscosity Measurements continue…..
Rotating cylinder viscometer
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16. Cone-on-plate viscometer
Viscosity Measurements continue…..
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17. Fluid flow between two parallel plates
The bottom plate is fixed and the top plate is accelerated by applying
some force that acts from left to right.
The upper plate will be accelerated to some terminal velocity and the
fluid between the plates will be set into motion.
Terminal velocity is achieved when the applied force is balanced by a
resisting force (shown as an equal but opposite force applied by the
stationary bottom plate).
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18. As the upper plate begins to accelerate the velocity of the fluid molecules
in contact with the plate is equal to the velocity of the plate (a no slip
condition exists between the plate and the fluid).
Fluid molecules in contact with those against the plate will be
accelerated due to the viscous attraction between them... and so on
through the column of fluid.
The viscosity of the fluid ( , is the attraction between fluid molecules)
results in layers of fluid that are increasingly further from the moving
plate being set into motion.
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19. The velocity gradient (the rate of change in velocity between plates;
du/dy) will be constant and the velocity will increase linearly from zero
at the bottom plate to Uterm at the top plate.
Terminal velocity is achieved when the resisting force (the force shown
applied by the bottom plate) is equal but opposite to the force applied to
the top plate (forces are equal so that there is no change in velocity with
time).
The bottom plate and water molecules attached to it are stationary (zero
velocity; no slip between molecules of fluid and the plate) so that
eventually the velocity will vary from zero at the bottom to Uterm at the
top which is equal to the terminal velocity of the upper plate.
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22. Effect of viscosity on velocity profile
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Fluid flow is highly dependent on the viscosity of fluids. At the same time for a non-Newtonian
fluid, the viscosity is determined by the flow characteristics . Looking at Figure , we can
observe three very different velocity profiles depending on the fluid behavior. For all these
fluids, the shear rate at the walls (i.e. the slope of the velocity profile near the wall) is going to
determine viscosity. Successful characterization of viscosity is key in determining if a fluid is
Newtonian or non-Newtonian, and what range of shear rates needs to be considered for an
specific application.

23. Several fundamental effects are produced by viscosity:
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Drag: Skin friction drag caused by shear stresses at the surface contribute a majority of
the drag of most airplanes.
The pressure distribution: is changed by the presence of a boundary layer, even when no
significant separation is present.
Flow separation: Viscosity is responsible for flow separation which causes major
changes to the flow patterns and pressures.

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Viscosity and Navier–Stokes equations
The Navier–Stokes equations, describe the motion of viscous fluid substances. These
balance equations arise from applying Newton's second law to fluid motion, together with the
assumption that the stress in the fluid is the sum of a diffusing viscous term and a pressure
term—hence describing viscous flow.
Viscosity and Coutette’s flow
Couette flow is the laminar flow of a viscous fluid in the space between two parallel plates,
one of which is moving relative to the other. The flow is driven by virtue of viscous drag
force acting on the fluid and the applied pressure gradient parallel to the plates.

25. Viscosity Effects In Dynamic Light Scattering Measurements
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• Dynamic light scattering (DLS) is a method for monitoring crystallization processes, solutions.
• DLS measures how fast the particles diffuse through the liquid.
• Smaller particles diffuse faster than larger ones.
• Solvent viscosity effect the measurement.
• For precise determination of particle size, it is essential to know the exact viscosity value of
the solvent.

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